%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT097-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:00 PM UTC 2026
% Result : Unsatisfiable 2.96s 3.72s
% Output : CNFRefutation 10.40s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1344)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_trancl__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
cnf(cls_trancl__unfold__left_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
cnf(cls_trancl__converseI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X1,X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X1),X1,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
cnf(cls_trancl__converseD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X1),X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X1,X1),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
cnf(cls_converse__tranclE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
cnf(cls_tranclE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
cnf(cls_rtrancl__trancl__trancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
cnf(cls_trancl__rtrancl__trancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
cnf(cls_trancl__into__trancl2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
cnf(cls_Transitive__Closure_Otrancl__into__trancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
cnf(cls_trancl_Ocases_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a)),c_Transitive__Closure_Otrancl(X3,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Otrancl(X3,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
cnf(cls_tranclE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
cnf(cls_converse__tranclE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X3,X2,X4,X1),X1,X1)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
cnf(cls_tranclD_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
cnf(cls_tranclD2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X3,X2,X4,X1),X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
cnf(cls_tranclD2_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X3,X4,X1),X4,X1,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
cnf(cls_tranclD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X3,X2,X4,X1),X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
cnf(cls_trancl_Ocases_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Otrancl(X3,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
cnf(cls_rtrancl__into__trancl2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
cnf(cls_rtrancl__into__trancl1_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
cnf(cls_r__r__into__trancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
cnf(cls_rtrancl__eq__or__trancl_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
cnf(cls_trancl__into__rtrancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
cnf(cls_trancl__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ c_lessequals(X4,X3,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
cnf(cls_acyclic__def_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ c_Wellfounded_Oacyclic(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
cnf(cls_irrefl__trancl__rD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X1),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X1),X1,X1)),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
cnf(cls_rtranclD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
cnf(cls_rtrancl__eq__or__trancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
cnf(cls_trancl_Or__into__trancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
cnf(cls_trancl__unfold_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
cnf(cls_Range__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ORange(X4,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
cnf(cls_Range__def_0,axiom,
c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
cnf(cls_RangeE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ORange(X4,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
cnf(cls_r__into__trancl_H_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
cnf(cls_trancl__range_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
cnf(cls_wf__converse__trancl_0,axiom,
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
cnf(cls_RangeI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ORange(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X1)),c_Pair(X5,X2,X4,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
cnf(cls_Range__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ORange(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X1)),c_Pair(X5,X2,X4,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
cnf(cls_trancl__converse_0,axiom,
c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
cnf(cls_Range__insert_0,axiom,
c_Relation_ORange(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X2,c_Relation_ORange(X5,X3,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
cnf(cls_reflcl__trancl_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
cnf(cls_Nitpick_Ortrancl__def_0,axiom,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
cnf(cls_trancl__domain_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
cnf(cls_wf__trancl_0,axiom,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
cnf(cls_sym__trancl_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
cnf(cls_trancl__rtrancl__absorb_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
cnf(cls_trancl__unfold__right_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
cnf(cls_in__mkbot_4,axiom,
( X1 = X2
| X2 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
cnf(cls_in__mktop_4,axiom,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
cnf(cls_trancl__reflcl_0,axiom,
c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
cnf(cls_Range__Un__eq_0,axiom,
c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
cnf(cls_rtrancl__trancl__absorb_0,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
cnf(cls_wf__Un_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X3,X2,X2),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
cnf(cls_Range__converse_0,axiom,
c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2) = c_Relation_ODomain(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
cnf(cls_Range__rtrancl_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).
cnf(cls_Range__Id__on_0,axiom,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
cnf(cls_Range__Id_0,axiom,
c_Relation_ORange(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id_0) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_CHAINED_0_01,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_CHAINED_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
cnf(cls_PW_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P____)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PW_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_PW_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P____))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PW_0) ).
cnf(cls_CHAINED_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X1),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ c_lessequals(X1,v_n____,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_rel__compEpair_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,X6,X7,X2,X1),X4,X1,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X7,X2)),c_Pair(X3,X4,X7,X2)),c_Relation_Orel__comp(X5,X6,X7,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
cnf(cls_rel__compEpair_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,X6,X1,X7,X2),X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X7)),c_Pair(X3,X4,X1,X7)),c_Relation_Orel__comp(X5,X6,X1,X2,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
cnf(cls_cuts__eq_1,axiom,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5),X3,X4,X4)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
cnf(cls_setsum__restrict__set_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X5),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X3,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__restrict__set_0) ).
cnf(cls_setsum__delta_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_0) ).
cnf(cls_setsum__delta_1,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = c_HOL_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_1) ).
cnf(cls_vimage__if_0,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_0) ).
cnf(cls_vimage__if_2,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3)
| hBOOL(hAPP(hAPP(c_in(X1),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_2) ).
cnf(cls_vimage__if_1,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = X3
| hBOOL(hAPP(hAPP(c_in(X1),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_1) ).
cnf(cls_vimage__if_3,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_3) ).
cnf(cls_setsum__delta_H_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_H_0) ).
cnf(cls_setsum__delta_H_1,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = c_HOL_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_H_1) ).
cnf(cls_setsum__cases_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X5,X2,X1,X1)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X4),c_Lattices_Olower__semilattice__class_Oinf(X6,X3,tc_fun(X2,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__cases_0) ).
cnf(cls_setsum__commute_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X3,X1),X4,tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_bool),X1),X2),X2,tc_fun(X3,tc_bool),X1),X5)),X6) = hAPP(hAPP(c_Finite__Set_Osetsum(X3,X1),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X2,X1),c_COMBC(X4,X2,X3,X1),tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_bool),X1),X3),X3,tc_fun(X2,tc_bool),X1),X6)),X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__commute_0) ).
cnf(cls_setprod__delta_0,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_0) ).
cnf(cls_setprod__gen__delta_1,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),X5),X6,X2,X1) = c_Power_Opower__class_Opower(X5,c_Finite__Set_Ocard(X6,X2),X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X6))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__gen__delta_1) ).
cnf(cls_setprod__delta_1,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = c_HOL_Oone__class_Oone(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_1) ).
cnf(cls_cuts__eq_2,axiom,
( c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6)
| hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6)) != hAPP(X2,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
cnf(cls_setprod__delta_H_0,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_H_0) ).
cnf(cls_setprod__delta_H_1,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = c_HOL_Oone__class_Oone(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_H_1) ).
cnf(cls_wf__union__merge_1,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
cnf(cls_Image__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X4,X5,X1,X2),X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,X3,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
cnf(cls_ImageE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X4,X5,X1,X2),X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,X3,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
cnf(cls_setsum__left__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X2,X1,X1),X5)),X4)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
cnf(cls_setsum__divide__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(X1),X3,X1,tc_fun(X1,X1),X2),X2,X1,X1),X5)),X4)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__divide__distrib_0) ).
cnf(cls_wf__union__merge_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
cnf(cls_less__add__iff1_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
cnf(cls_congruent2_Ocongruent2_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(X3,X5,X6,X6)),X7))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X8,X8)),c_Pair(X2,X4,X8,X8)),X9))
| ~ c_Equiv__Relations_Ocongruent2(X9,X7,X1,X8,X6,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
cnf(cls_setsum__subtractf_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X4),X5))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).
cnf(cls_setsum__addf_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X4),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__addf_0) ).
cnf(cls_equiv__class__nondisjoint_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),tc_fun(X1,tc_bool))))
| ~ c_Equiv__Relations_Oequiv(X6,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
cnf(cls_rel__compI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Orel__comp(X5,X6,X1,X7,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X7,X2)),c_Pair(X8,X4,X7,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X7)),c_Pair(X3,X8,X1,X7)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
cnf(cls_rtrancl__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X4,X5,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X1,X4,X5,X3),X3,X3)),X5))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X2,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
cnf(cls_converse__rtrancl__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X1,X4,X5,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X4,X5,X3),X3,X3)),X5))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
cnf(cls_less__add__iff1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
cnf(cls_single__valued__confluent_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Relation_Osingle__valued(X4,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
cnf(cls_SigmaE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X5)),X4),c_Product__Type_OSigma(X2,X3,X1,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).
cnf(cls_Image__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Relation_OImage(X4,X2,X1,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
cnf(cls_ImageE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Relation_OImage(X4,X2,X1,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
cnf(cls_less__add__iff2_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
cnf(cls_converse__rtrancl__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X4,X5,X3),X4,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
cnf(cls_rtrancl__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X4,X5,X3),X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X2,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
cnf(cls_converse__rtranclE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1)))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
cnf(cls_rtranclE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X3,X4,X1),X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
cnf(cls_congruent2__implies__congruent_0,axiom,
( c_Equiv__Relations_Ocongruent(X1,hAPP(X2,X3),X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X6),X3),X7))
| ~ c_Equiv__Relations_Ocongruent2(X8,X1,X2,X6,X4,X5)
| ~ c_Equiv__Relations_Oequiv(X7,X8,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
cnf(cls_rtranclE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X3,X4,X1),X3,X1,X1)),X4))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
cnf(cls_converse__rtranclE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X2,X4,X1),X1,X1)),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
cnf(cls_rtrancl__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
cnf(cls_converse__rtrancl__into__rtrancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
cnf(cls_rtrancl_Ortrancl__into__rtrancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
cnf(cls_less__add__iff2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
cnf(cls_setprod__dividef_0,axiom,
( c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_Finite__Set_Osetprod(X2,X5,X3,X1)),c_Finite__Set_Osetprod(X4,X5,X3,X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__dividef_0) ).
cnf(cls_setprod__timesf_0,axiom,
( c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X2,X5,X3,X1)),c_Finite__Set_Osetprod(X4,X5,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__timesf_0) ).
cnf(cls_in__inv__image_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(hAPP(X2,X3),hAPP(X2,X4),X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(X3,X4,X6,X6)),c_Relation_Oinv__image(X5,X2,X1,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
cnf(cls_in__inv__image_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oinv__image(X4,X5,X6,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(hAPP(X5,X2),hAPP(X5,X3),X6,X6)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
cnf(cls_cuts__eq_0,axiom,
( hAPP(X1,X7) = hAPP(X6,X7)
| c_Recdef_Ocut(X1,X2,X3,X4,X5) != c_Recdef_Ocut(X6,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X7,X3,X4,X4)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
cnf(cls_single__valuedD_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X4)),c_Pair(X5,X2,X3,X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X4)),c_Pair(X5,X1,X3,X4)),X6))
| ~ c_Relation_Osingle__valued(X6,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
cnf(cls_O__assoc_0,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
cnf(cls_antisymD_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),X4))
| ~ c_Relation_Oantisym(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
cnf(cls_antisym__def_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),X4))
| ~ c_Relation_Oantisym(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
cnf(cls_wf__asym_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Wellfounded_Owf(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
cnf(cls_Domain__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X3,X4,X1,X2),X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X4,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
cnf(cls_DomainE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X3,X4,X1,X2),X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X4,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
cnf(cls_rtrancl__converseD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X1,X1),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
cnf(cls_rtrancl_Ocases_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a)),c_Transitive__Closure_Ortrancl(X3,t_a)))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Ortrancl(X3,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
cnf(cls_rtrancl_Ocases_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a)),X3))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Ortrancl(X3,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
cnf(cls_rtrancl__converseI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X1,X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
cnf(cls_rel__comp__distrib2_0,axiom,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
cnf(cls_rel__comp__distrib_0,axiom,
c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
cnf(cls_mlex__leq_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omlex__prod(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X5))
| ~ c_lessequals(hAPP(X4,X2),hAPP(X4,X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mlex__leq_0) ).
cnf(cls_converseD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
cnf(cls_converseI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
cnf(cls_converse__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
cnf(cls_tfl__cut__apply_0,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X6,X3,X4,X4)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
cnf(cls_cut__apply_0,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X6,X3,X4,X4)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
cnf(cls_in__mkbot_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
cnf(cls_in__mktop_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
cnf(cls_symD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Relation_Osym(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
cnf(cls_sym__def_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Relation_Osym(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).
cnf(cls_in__mktop_5,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
cnf(cls_in__mkbot_5,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
| X1 = X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
cnf(cls_in__mkbot_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
| X1 = X4
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
cnf(cls_in__mktop_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
| X2 = X4
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
cnf(cls_equiv__class__subset_0,axiom,
( c_lessequals(c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
cnf(cls_subset__equiv__class_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),tc_fun(X1,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
cnf(cls_Image__singleton__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
cnf(cls_acyclic__insert_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X4,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
cnf(cls_wf__insert_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X4,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
cnf(cls_rtrancl__induct_3,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X3,X2,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
cnf(cls_converse__rtrancl__induct_3,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X2,X3,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
cnf(cls_rel__comp__mono_0,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Relation_Orel__comp(X6,X7,X3,X4,X5),tc_fun(tc_prod(X3,X5),tc_bool))
| ~ c_lessequals(X2,X7,tc_fun(tc_prod(X4,X5),tc_bool))
| ~ c_lessequals(X1,X6,tc_fun(tc_prod(X3,X4),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
cnf(cls_Image__singleton__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
cnf(cls_SigmaD2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),c_Product__Type_OSigma(X6,X3,X5,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
cnf(cls_setsum__right__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Finite__Set_Osetsum(X3,X1),X4),X5)) = hAPP(hAPP(c_Finite__Set_Osetsum(X3,X1),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4,X1,X1,X3)),X5)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
cnf(cls_wfE__min_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X3,X4,X1),X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ c_Wellfounded_Owf(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
cnf(cls_wf__eq__minimal_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X3,X4,X1),X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ c_Wellfounded_Owf(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
cnf(cls_SigmaD1_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),c_Product__Type_OSigma(X3,X6,X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
cnf(cls_acc__induct__rule_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X5,X4),X4,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X5,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
cnf(cls_acc__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X5,X4),X4,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X5,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
cnf(cls_setsum__negf_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X3,X1,X1,X2)),X4) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
cnf(cls_of__nat__setsum_0,axiom,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,tc_nat),X3),X4)) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X1),X3,tc_nat,X1,X2)),X4)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__setsum_0) ).
cnf(cls_wf__induct__rule_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
cnf(cls_wf__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
cnf(cls_tfl__wf__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
cnf(cls_wf__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
cnf(cls_total__on__def_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_Relation_Ototal__on(X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
cnf(cls_eq__equiv__class__iff_1,axiom,
( c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
cnf(cls_Image__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X6,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
cnf(cls_rev__ImageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X6,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
cnf(cls_rtrancl__induct_2,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X3,X2,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
cnf(cls_converse__rtrancl__induct_2,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X2,X3,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
cnf(cls_equiv__class__eq__iff_0,axiom,
( c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
cnf(cls_equiv__class__eq_0,axiom,
( c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
cnf(cls_le__add__iff1_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4),X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
cnf(cls_le__add__iff2_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
cnf(cls_setprod__pos_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Finite__Set_Osetprod(X2,X3,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X3,X2,X4,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__pos_1) ).
cnf(cls_wf__union__compatible_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X3,X3),X1,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_Wellfounded_Owf(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
cnf(cls_Nitpick_Orefl_H__def_1,axiom,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X2)),c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),X2,X2)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
cnf(cls_acc_Oinduct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X4,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
cnf(cls_acc_Oinducts_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X4,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
cnf(cls_eq__equiv__class__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
cnf(cls_equiv__class__eq__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
cnf(cls_acc_Oinduct_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
cnf(cls_acc_Oinducts_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
cnf(cls_acc__downwards__aux_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
cnf(cls_acc__downwards_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
cnf(cls_setprod__Un__Int_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X5,tc_bool)),X5,X1)),c_Finite__Set_Osetprod(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X5,tc_bool)),X5,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X2,X3,X5,X1)),c_Finite__Set_Osetprod(X2,X4,X5,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X4,X5)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__Un__Int_0) ).
cnf(cls_congruent_Ocongruent_0,axiom,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),X5))
| ~ c_Equiv__Relations_Ocongruent(X5,X1,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
cnf(cls_acc_Ocases_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
cnf(cls_acc__downward_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
cnf(cls_Not__Domain__rtrancl_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X1),c_Relation_ODomain(X4,X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),c_Transitive__Closure_Ortrancl(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
cnf(cls_eq__equiv__class_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
cnf(cls_Image__subset__eq_1,axiom,
( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X3)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).
cnf(cls_in__measure_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),c_Wellfounded_Omeasure(X1,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__measure_0) ).
cnf(cls_DomainI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
cnf(cls_Domain__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
cnf(cls_le__add__iff1_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
cnf(cls_le__add__iff2_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
cnf(cls_converse__rel__comp_0,axiom,
c_Relation_Oconverse(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X4,X5),c_Relation_Oconverse(X1,X3,X4),X5,X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
cnf(cls_wf__comp__self_1,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
cnf(cls_equiv__class__eq__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
cnf(cls_equiv__class__eq__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X4,X2,X1,X1)),X5))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
cnf(cls_refl__onD1_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ c_Relation_Orefl__on(X3,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
cnf(cls_refl__onD2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X4,X2,X1,X1)),X5))
| ~ c_Relation_Orefl__on(X3,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
cnf(cls_Id__on__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_OId__on(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
cnf(cls_pred__subset__eq_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
cnf(cls_in__mkbot_1,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X2),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
cnf(cls_in__mktop_1,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X2),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
cnf(cls_in__mkbot_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
cnf(cls_in__mktop_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
cnf(cls_SigmaI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Product__Type_OSigma(X5,X6,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
cnf(cls_mem__Sigma__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Product__Type_OSigma(X5,X6,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
cnf(cls_Id__on__iff_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),c_Relation_OId__on(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
cnf(cls_irrefl__def_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Relation_Oirrefl(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_wf__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Wellfounded_Owf(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
cnf(cls_pair__in__Id__conv_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),c_Relation_OId(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
cnf(cls_acyclic__insert_2,axiom,
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),c_Transitive__Closure_Ortrancl(X4,X3)))
| ~ c_Wellfounded_Oacyclic(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
cnf(cls_wf__insert_2,axiom,
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),c_Transitive__Closure_Ortrancl(X4,X3)))
| ~ c_Wellfounded_Owf(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
cnf(cls_gt__half__sum_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)))),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
cnf(cls_acc_OaccI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X3,X2,X1),X2,X1,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
cnf(cls_not__acc__down_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X3,X1),X3,X1,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),c_Wellfounded_Oacc(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
cnf(cls_setsum__Un_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5))),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool))))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un_0) ).
cnf(cls_setprod__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Finite__Set_Osetprod(X2,X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X3,X2,X4,X1)),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__pos_0) ).
cnf(cls_of__nat__setprod_0,axiom,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Finite__Set_Osetprod(X2,X3,X4,tc_nat)) = c_Finite__Set_Osetprod(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X1),X2,tc_nat,X1,X4),X3,X4,X1)
| ~ class_Ring__and__Field_Osemiring__1(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__setprod_0) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
cnf(cls_vimage__singleton__eq_0,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X4,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
cnf(cls_Image__subset__eq_0,axiom,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).
cnf(cls_Image__Int__subset_0,axiom,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
cnf(cls_mlex__less_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omlex__prod(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X4,X2)),hAPP(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mlex__less_0) ).
cnf(cls_refl__on__comp__subset_0,axiom,
( c_lessequals(X1,c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Orefl__on(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
cnf(cls_in__measure_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omeasure(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X4,X2)),hAPP(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__measure_1) ).
cnf(cls_irrefl__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
cnf(cls_eq__add__iff2_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X2)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_eq__add__iff1_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_Not__Domain__rtrancl_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X3,X1,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
cnf(cls_single__valued__rel__comp_0,axiom,
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5)
| ~ c_Relation_Osingle__valued(X2,X4,X5)
| ~ c_Relation_Osingle__valued(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
cnf(cls_rtrancl__unfold_0,axiom,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
cnf(cls_refl__onD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Relation_Orefl__on(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
cnf(cls_refl__on__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Relation_Orefl__on(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
cnf(cls_setprod__zero__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X3,X2,X4,X1)),X3))
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Finite__Set_Osetprod(X2,X3,X4,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero__iff_0) ).
cnf(cls_Id__on__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId__on(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
cnf(cls_ATP__Linkup_OCOMBS__def_0,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
cnf(cls_r__comp__rtrancl__eq_0,axiom,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_pred__subset__eq_1,axiom,
( c_lessequals(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3),tc_fun(X1,tc_bool))
| ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
cnf(cls_wf__comp__self_0,axiom,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
cnf(cls_inf__period_I4_J_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X6))),X4),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
cnf(cls_rtrancl__eq__or__trancl_1,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
cnf(cls_rtrancl_Ortrancl__refl_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
cnf(cls_setprod__1_H_0,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X3,X2,X4,X1)),X3))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__1_H_0) ).
cnf(cls_Nitpick_Orefl_H__def_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Nitpick_Orefl_H(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
cnf(cls_IdI_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
cnf(cls_pair__in__Id__conv_1,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
cnf(cls_complete__Lin_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2)))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
cnf(cls_comp__equivI_0,axiom,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
cnf(cls_equiv__class__self_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Equiv__Relations_Oequiv(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
cnf(cls_setsum__0_H_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4) = c_HOL_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X4,X3,X2,X1)),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_H_0) ).
cnf(cls_setsum__Un__Int_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X2,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).
cnf(cls_setprod__Un__disjoint_0,axiom,
( c_Finite__Set_Osetprod(X5,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X5,X2,X4,X1)),c_Finite__Set_Osetprod(X5,X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__Un__disjoint_0) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(hAPP(X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X1,X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
cnf(cls_setprod__pos__nat__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X1,X4,X3,tc_nat)))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__pos__nat__iff_0) ).
cnf(cls_divide__less__eq_9,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
cnf(cls_divide__less__eq_8,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
cnf(cls_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
cnf(cls_power__Suc__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
cnf(cls_in__rtrancl__UnI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X1),tc_bool)),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
cnf(cls_in__rtrancl__UnI_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X1),tc_bool)),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
cnf(cls_diff__frac__eq_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
cnf(cls_add__frac__eq_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
cnf(cls_vimageE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
cnf(cls_vimageD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
cnf(cls_eq__add__iff1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( X4 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_less__half__sum_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)))))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
cnf(cls_combine__common__factor_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
cnf(cls_vimage__insert_0,axiom,
c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
cnf(cls_acyclic__insert_0,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
cnf(cls_wf__insert_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
cnf(cls_less__divide__eq_9,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
cnf(cls_less__divide__eq_8,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
cnf(cls_pred__equals__eq_0,axiom,
( X2 = X3
| hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) != hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
cnf(cls_inf__period_I4_J_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5))),X6),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X6),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
cnf(cls_Image__Int__eq_0,axiom,
( c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
| ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X1,X4,X5),X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
cnf(cls_divide__less__eq_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
cnf(cls_divide__less__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
cnf(cls_divide__less__eq_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
cnf(cls_divide__strict__left__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
cnf(cls_divide__strict__left__mono__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
cnf(cls_Un__Image_0,axiom,
c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
cnf(cls_Sigma__Un__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
cnf(cls_power__strict__increasing__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X4,X2,X1)),c_Power_Opower__class_Opower(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
cnf(cls_power__less__imp__less__exp_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X4,X2,X1)),c_Power_Opower__class_Opower(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
cnf(cls_Image__Un_0,axiom,
c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
cnf(cls_less__divide__eq_7,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
cnf(cls_vimage__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
cnf(cls_vimageI2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
cnf(cls_vimageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
cnf(cls_equiv__comp__eq_0,axiom,
( c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) = X1
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
cnf(cls_frac__less2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X5),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X5))
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).
cnf(cls_Image__mono_0,axiom,
( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),c_Relation_OImage(X5,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X6,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X5,tc_fun(tc_prod(X3,X4),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
cnf(cls_power__less__imp__less__base_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
cnf(cls_power__less__power__Suc_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
cnf(cls_mult__strict__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
cnf(cls_Domain__insert_0,axiom,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X1,c_Relation_ODomain(X5,X3,X4),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_divide__less__eq_7,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
cnf(cls_divide__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
cnf(cls_less__divide__eq_6,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
cnf(cls_mult__imp__less__div__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
cnf(cls_power__strict__decreasing_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X2,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
cnf(cls_mult__le__less__imp__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
cnf(cls_mult__less__le__imp__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
cnf(cls_frac__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).
cnf(cls_rtrancl__idemp__self__comp_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
cnf(cls_mult__strict__mono_H_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_sum__squares__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
cnf(cls_sum__squares__le__zero__iff_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
cnf(cls_less__divide__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
cnf(cls_divide__less__eq_6,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
cnf(cls_mult__imp__div__pos__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
cnf(cls_R__O__Id_0,axiom,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
cnf(cls_divide__less__eq_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
cnf(cls_setprod__dvd__setprod__subset_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Finite__Set_Osetprod(X2,X3,X4,X1),c_Finite__Set_Osetprod(X2,X5,X4,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_lessequals(X3,X5,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__dvd__setprod__subset_0) ).
cnf(cls_power__strict__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X4,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
cnf(cls_vimage__mono_0,axiom,
( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
| ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
cnf(cls_less__divide__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
cnf(cls_less__divide__eq_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
cnf(cls_less__divide__eq_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
cnf(cls_divide__less__0__1__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
cnf(cls_power__strict__increasing__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X2,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
cnf(cls_power__strict__increasing_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X2,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
cnf(cls_Id__onE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X3),c_Relation_OId__on(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
cnf(cls_divide__less__0__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
cnf(cls_divide__strict__right__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
cnf(cls_divide__less__0__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
cnf(cls_divide__less__0__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
cnf(cls_setprod__insert_0,axiom,
( c_Finite__Set_Osetprod(X2,c_Set_Oinsert(X3,X4,X5),X5,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(X2,X3)),c_Finite__Set_Osetprod(X2,X4,X5,X1))
| hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__insert_0) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
cnf(cls_divide__strict__right__mono__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
cnf(cls_divide__less__0__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
cnf(cls_acc_OaccI_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X3,X2,X1)),c_Wellfounded_Oacc(X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
cnf(cls_not__acc__down_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X3),c_Wellfounded_Oacc(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X3,X1)),c_Wellfounded_Oacc(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_add__strict__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_setprod__1_H_1,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X3,X2,X4,X1)) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__1_H_1) ).
cnf(cls_setsum__Un__disjoint_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X5),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X5),X2)),hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).
cnf(cls_Id__onE_1,axiom,
( X1 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),X1),c_Relation_OId__on(X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
cnf(cls_rtrancl__Un__subset_0,axiom,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
cnf(cls_sum__squares__le__zero__iff_2,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
cnf(cls_divide__less__eq_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
cnf(cls_divide__left__mono__neg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_divide__left__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
cnf(cls_power__gt1__lemma_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_wfE__pf_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Relation_OImage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
cnf(cls_setprod__zero__iff_1,axiom,
( hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X3,X2,X4,X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Finite__Set_Osetprod(X2,X3,X4,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero__iff_1) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_add__frac__num_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
cnf(cls_divide__less__0__iff_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
cnf(cls_divide__less__0__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_mult__neg__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
cnf(cls_mult__pos__neg2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
cnf(cls_mult__pos__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
cnf(cls_divide__neg__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
cnf(cls_divide__pos__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
cnf(cls_distrib__inf__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
cnf(cls_distrib__sup__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
cnf(cls_add__neg__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_setsum__0_H_1,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X2),X3) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X3,X2,X4,X1)) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_H_1) ).
cnf(cls_converse__inv__image_0,axiom,
c_Relation_Oconverse(c_Relation_Oinv__image(X1,X2,X3,X4),X4,X4) = c_Relation_Oinv__image(c_Relation_Oconverse(X1,X3,X3),X2,X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
cnf(cls_add__strict__left__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_less__divide__eq_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
cnf(cls_acc__induct__rule_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X4,X3)),c_Wellfounded_Oacc(X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Wellfounded_Oacc(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
cnf(cls_acc__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X4,X3)),c_Wellfounded_Oacc(X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Wellfounded_Oacc(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
cnf(cls_UnE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X1,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
cnf(cls_r__into__rtrancl_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
cnf(cls_divide__le__eq_8,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
cnf(cls_le__divide__eq_8,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
cnf(cls_add__num__frac_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))),X4)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( X1 = X5
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( X2 = X4
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( X1 = X5
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( X2 = X4
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
cnf(cls_singletonE_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
cnf(cls_divide__less__0__1__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
cnf(cls_add__nonpos__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
cnf(cls_add__neg__nonpos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
cnf(cls_IdE_0,axiom,
( X1 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),X2,X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X2)),X1),c_Relation_OId(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( c_lessequals(X4,X1,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
cnf(cls_zero__less__divide__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
cnf(cls_zero__less__divide__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
cnf(cls_zero__less__divide__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
cnf(cls_zero__less__divide__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
cnf(cls_sum__squares__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
cnf(cls_Pair__eq_0,axiom,
( X1 = X5
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
cnf(cls_Pair__eq_1,axiom,
( X2 = X6
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
cnf(cls_dvd__setprod_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(X2,X3),c_Finite__Set_Osetprod(X2,X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ c_Finite__Set_Ofinite(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__setprod_0) ).
cnf(cls_less__divide__eq_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
cnf(cls_zero__less__divide__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
cnf(cls_divide__le__eq_9,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
cnf(cls_le__divide__eq_9,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
cnf(cls_less__1__mult_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
cnf(cls_mult__pos__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
cnf(cls_add__pos__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_divide__pos__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
cnf(cls_IntE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
cnf(cls_IntE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
cnf(cls_zero__less__divide__1__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
cnf(cls_IntI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
cnf(cls_Int__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_frac__le_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X5))
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).
cnf(cls_divide__le__eq_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
cnf(cls_divide__le__eq_4,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
cnf(cls_le__divide__eq_1,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
cnf(cls_le__divide__eq_4,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
cnf(cls_mult__frac__frac_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_one__less__power_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_wfE__min_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ c_Wellfounded_Owf(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
cnf(cls_wf__eq__minimal_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ c_Wellfounded_Owf(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
cnf(cls_zero__less__divide__iff_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
cnf(cls_even__less__0__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_mult__neg__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
cnf(cls_divide__neg__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
cnf(cls_less__infI1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
cnf(cls_less__infI2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
cnf(cls_pos__add__strict_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_power__increasing__iff_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
cnf(cls_power__le__imp__le__exp_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
cnf(cls_minus__less__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(cls_minus__less__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
cnf(cls_power__minus_0,axiom,
( c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1)),X3,X1)),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ class_Ring__and__Field_Oring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_acc__induct__rule_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
cnf(cls_acc__induct_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
cnf(cls_converse__Un_0,axiom,
c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
cnf(cls_divide__le__eq_5,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
cnf(cls_le__divide__eq_5,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
cnf(cls_add__nonneg__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
cnf(cls_add__pos__nonneg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_rtrancl__Un__rtrancl_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
cnf(cls_neg__less__iff__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
cnf(cls_refl__on__Un_0,axiom,
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X2,X5,X3)
| ~ c_Relation_Orefl__on(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
cnf(cls_divide__le__eq_7,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
cnf(cls_le__divide__eq_7,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
cnf(cls_mult__mono_H_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
cnf(cls_mult__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
cnf(cls_of__nat__less__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
cnf(cls_Un__mono_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
cnf(cls_Int__mono_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
cnf(cls_le__divide__eq_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
cnf(cls_divide__le__eq_6,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
cnf(cls_divide__le__eq_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
cnf(cls_le__divide__eq_6,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_diff__divide__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
cnf(cls_add__divide__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
cnf(cls_setsum__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Set_Oinsert(X4,X5,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X3,X4)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).
cnf(cls_add__strict__increasing_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
cnf(cls_mult__imp__div__pos__le_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
cnf(cls_mult__imp__le__div__pos_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
cnf(cls_insertE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
cnf(cls_Int__Un__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
cnf(cls_Int__Un__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
cnf(cls_Compl__subset__Compl__iff_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
cnf(cls_zero__less__divide__1__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
cnf(cls_Domain__Un__eq_0,axiom,
c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
cnf(cls_add__strict__increasing2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
cnf(cls_subset__singletonD_0,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X1,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
cnf(cls_UnCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
cnf(cls_card__gt__0__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).
cnf(cls_divide__le__eq_2,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
cnf(cls_le__divide__eq_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
cnf(cls_power__increasing__iff_1,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
cnf(cls_neg__less__0__iff__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
cnf(cls_Int__insert__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
cnf(cls_Int__insert__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
cnf(cls_zero__less__power_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
cnf(cls_inf1E_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_Compl__Un_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
cnf(cls_Compl__Int_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X1,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
cnf(cls_power__decreasing_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_power__divide_0,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
cnf(cls_nonzero__power__divide_0,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
cnf(cls_power__eq__imp__eq__base_0,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
cnf(cls_power__mult__distrib_0,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
cnf(cls_add__sup__distrib__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
cnf(cls_wf__inv__image_0,axiom,
( c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
| ~ c_Wellfounded_Owf(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
cnf(cls_sym__inv__image_0,axiom,
( c_Relation_Osym(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
| ~ c_Relation_Osym(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_mult__frac__num_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_divide__le__eq_3,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
cnf(cls_le__divide__eq_3,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
cnf(cls_neg__less__iff__less_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_power__le__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_lessequals(X3,X5,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X5,X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_insert__inter__insert_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_less__supI1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
cnf(cls_less__supI2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
cnf(cls_Domain__mono_0,axiom,
( c_lessequals(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
cnf(cls_of__nat__less__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
cnf(cls_insertCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
cnf(cls_insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
cnf(cls_setprod__zero__iff_2,axiom,
( c_Finite__Set_Osetprod(X2,X5,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(X2,X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero__iff_2) ).
cnf(cls_neg__less__0__iff__less_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
cnf(cls_sym__Un__converse_0,axiom,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_setprod__zero_0,axiom,
( c_Finite__Set_Osetprod(X2,X5,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(X2,X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero_0) ).
cnf(cls_less__minus__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
cnf(cls_less__minus__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
cnf(cls_rtrancl__subset_0,axiom,
( c_Transitive__Closure_Ortrancl(X1,X2) = c_Transitive__Closure_Ortrancl(X3,X2)
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
cnf(cls_sgn__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Osgn__class_Osgn(X2,X1)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__less_0) ).
cnf(cls_dvd__mult__cancel__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
cnf(cls_Un__least_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
cnf(cls_Un__subset__iff_2,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
cnf(cls_Int__subset__iff_2,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
cnf(cls_Int__greatest_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
cnf(cls_insert__subset_2,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
cnf(cls_subset__insert_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
cnf(cls_subset__insert__iff_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_divide__nonpos__pos_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
cnf(cls_divide__nonneg__pos_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
cnf(cls_finite__UNIV__card__ge__0_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).
cnf(cls_add__le__cancel__right_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
cnf(cls_Int__assoc_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
cnf(cls_Int__left__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
cnf(cls_Compl__anti__mono_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
cnf(cls_Compl__subset__Compl__iff_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
cnf(cls_antisym__reflcl_0,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
cnf(cls_power__mono_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
cnf(cls_divide__right__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
cnf(cls_divide__right__mono__neg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
cnf(cls_power__increasing_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
cnf(cls_divide__nonneg__neg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
cnf(cls_divide__nonpos__neg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
cnf(cls_neg__0__less__iff__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
cnf(cls_mult__right__le__one__le_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
cnf(cls_mult__left__le__one__le_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
cnf(cls_order__less__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_mult__mono1_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
cnf(cls_mult__left__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
cnf(cls_mult__right__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
cnf(cls_mult__left__mono__neg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
cnf(cls_mult__right__mono__neg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
cnf(cls_less__eqI_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_dvd__power__le_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_lessequals(X3,X5,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
cnf(cls_Un__subset__iff_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
cnf(cls_Un__subset__iff_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
cnf(cls_Int__subset__iff_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
cnf(cls_Int__subset__iff_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
cnf(cls_mult__dvd__mono_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
cnf(cls_add__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
cnf(cls_wf__induct__rule_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
cnf(cls_wf__def_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
cnf(cls_tfl__wf__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
cnf(cls_wf__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
cnf(cls_power__commutes_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(X2,X3,X1)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
cnf(cls_add__eq__inf__sup_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
cnf(cls_mult__divide__mult__cancel__left_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
cnf(cls_mult__divide__mult__cancel__right_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
cnf(cls_disjoint__eq__subset__Compl_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
cnf(cls_acc__wfI_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2)),c_Wellfounded_Oacc(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
cnf(cls_wf__acc__iff_1,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2)),c_Wellfounded_Oacc(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
cnf(cls_sgn__greater_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Osgn__class_Osgn(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__greater_0) ).
cnf(cls_rtrancl__subset__rtrancl_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
cnf(cls_add__sup__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_sgn__less_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Osgn__class_Osgn(X2,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__less_1) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
cnf(cls_zero__less__two_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
cnf(cls_less__minus__self__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
cnf(cls_subset__insert_1,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
cnf(cls_subset__insert__iff_2,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
cnf(cls_insert__mono_0,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
cnf(cls_neg__0__less__iff__less_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
cnf(cls_sgn__greater_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Osgn__class_Osgn(X2,X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__greater_1) ).
cnf(cls_divide__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
cnf(cls_divide__le__0__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
cnf(cls_divide__le__0__iff_3,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
cnf(cls_zero__le__divide__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
cnf(cls_zero__le__divide__iff_3,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
cnf(cls_zero__le__divide__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
cnf(cls_zero__le__divide__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
cnf(cls_divide__le__0__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
cnf(cls_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_insert__ident_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X4))
| hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| X2 = X4
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
cnf(cls_power__inject__exp_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
cnf(cls_mult__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
cnf(cls_mult__le__0__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
cnf(cls_mult__le__0__iff_3,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
cnf(cls_zero__le__mult__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
cnf(cls_zero__le__mult__iff_3,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
cnf(cls_zero__le__mult__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
cnf(cls_zero__le__mult__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
cnf(cls_mult__le__0__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_add__cancel__21_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_rtrancl__mono_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
cnf(cls_acc_Oinduct_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X3,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
cnf(cls_acc_Oinducts_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X3,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
cnf(cls_bex__empty_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
cnf(cls_less__minus__self__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
cnf(cls_refl__reflcl_0,axiom,
c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).
cnf(cls_disjoint__eq__subset__Compl_0,axiom,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
cnf(cls_zero__le__divide__1__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
cnf(cls_divide__le__0__1__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
cnf(cls_divide__le__0__iff_5,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
cnf(cls_divide__le__0__iff_4,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
cnf(cls_zero__le__divide__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
cnf(cls_zero__le__divide__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
cnf(cls_Int__insert__left_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
cnf(cls_Int__insert__right_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
cnf(cls_order__le__less__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_insert__subset_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
cnf(cls_power__one__over_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),c_Power_Opower__class_Opower(X2,X3,X1)) = c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
cnf(cls_subset__Compl__self__eq_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
cnf(cls_mult__nonpos__nonneg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
cnf(cls_split__mult__neg__le_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
cnf(cls_mult__nonneg__nonpos_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
cnf(cls_split__mult__neg__le_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
cnf(cls_mult__le__0__iff_5,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
cnf(cls_mult__le__0__iff_4,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
cnf(cls_mult__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
cnf(cls_split__mult__pos__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
cnf(cls_zero__le__mult__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_split__mult__pos__le_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
cnf(cls_mult__nonpos__nonpos_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
cnf(cls_zero__le__mult__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
cnf(cls_dvd__power__same_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
cnf(cls_le__imp__power__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_lessequals(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
cnf(cls_le__eq__neg_1,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
cnf(cls_add__increasing2_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
cnf(cls_add__increasing_0,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
cnf(cls_dvd__mult__cancel__left_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
cnf(cls_dvd__mult__cancel__right_2,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
cnf(cls_add__left__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__right__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_Image__Id__on_0,axiom,
c_Relation_OImage(c_Relation_OId__on(X1,X2),X3,X2,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
cnf(cls_setsum__eq__0__iff_0,axiom,
( hAPP(X2,X4) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Finite__Set_Osetsum(X1,tc_nat),X2),X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__eq__0__iff_0) ).
cnf(cls_single__valued__subset_0,axiom,
( c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_less__add__one_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
cnf(cls_card__insert__le_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
cnf(cls_le__sup__iff_2,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
cnf(cls_sup__least_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
cnf(cls_le__supI_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
cnf(cls_le__infI_0,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
cnf(cls_le__inf__iff_2,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
cnf(cls_inf__greatest_0,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
cnf(cls_dvd__diff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
cnf(cls_dvd__add_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
cnf(cls_dvd__power_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).
cnf(cls_singleton__inject_0,axiom,
( X1 = X3
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
cnf(cls_acc__subset_0,axiom,
( c_lessequals(c_Wellfounded_Oacc(X1,X2),c_Wellfounded_Oacc(X3,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_sup__assoc_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
cnf(cls_inf__assoc_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_sup__left__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
cnf(cls_inf__left__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_vimage__UNIV_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
cnf(cls_Image__empty_0,axiom,
c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
cnf(cls_card__insert__if_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_divide__eq__eq_4,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
cnf(cls_eq__divide__eq_4,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2)),X2)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
cnf(cls_subset__trans_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
cnf(cls_insertCI_1,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
cnf(cls_insertI1_0,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
cnf(cls_le__eq__neg_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
cnf(cls_sym__Un_0,axiom,
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X2,X3)
| ~ c_Relation_Osym(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
cnf(cls_le__supE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
cnf(cls_le__sup__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__supE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
cnf(cls_le__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
cnf(cls_le__inf__iff_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_le__inf__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
cnf(cls_le__infE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_add__cancel__21_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_finite__compl_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).
cnf(cls_dvd__mult__cancel__left_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X3),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
cnf(cls_add__minus__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_sup__eq__if_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__if_0) ).
cnf(cls_card__seteq_0,axiom,
( X1 = X2
| ~ c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
cnf(cls_le__eqI_1,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_setprod__empty_0,axiom,
( c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__empty_0) ).
cnf(cls_dvd__mult__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
cnf(cls_dvd__mult__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
cnf(cls_total__on__converse_0,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
cnf(cls_refl__on__converse_0,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
cnf(cls_subset__insertI2_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
cnf(cls_antisym__reflcl_1,axiom,
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
cnf(cls_divide__le__0__1__iff_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
cnf(cls_zero__le__divide__1__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
cnf(cls_rtrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
cnf(cls_minus__add__distrib_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
cnf(cls_minus__add_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
cnf(cls_dvd__mult__cancel__right_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),c_HOL_Ozero__class_Ozero(X1)),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
cnf(cls_frac__eq__eq_0,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
cnf(cls_frac__eq__eq_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
cnf(cls_eq__divide__eq_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X3) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
cnf(cls_divide__eq__eq_3,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
cnf(cls_divide__eq__eq_0,axiom,
( X2 = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
cnf(cls_eq__divide__eq_3,axiom,
( X2 = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
cnf(cls_finite__Un_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
cnf(cls_finite__Un_1,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
cnf(cls_setprod__infinite_0,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Ofinite(X3,X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__infinite_0) ).
cnf(cls_setprod__def_1,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Ofinite(X3,X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__def_1) ).
cnf(cls_add__cancel__end_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4)
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_finite__compl_1,axiom,
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).
cnf(cls_one__le__power_0,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
cnf(cls_zero__le__power_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
cnf(cls_divide__eq__imp_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
cnf(cls_eq__divide__imp_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),X2)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
cnf(cls_of__nat__le__iff_0,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_compl__sup_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
cnf(cls_compl__inf_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_card__gt__0__iff_1,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
cnf(cls_minus__mult__left_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
cnf(cls_minus__divide__left_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
cnf(cls_less__le__not__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_le__infI1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
cnf(cls_le__infI2_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
cnf(cls_le__supI1_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
cnf(cls_le__supI2_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
cnf(cls_Image__Id_0,axiom,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
cnf(cls_sgn__times_0,axiom,
( c_HOL_Osgn__class_Osgn(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Osgn__class_Osgn(X2,X1)),c_HOL_Osgn__class_Osgn(X3,X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).
cnf(cls_dvd__mult2_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
cnf(cls_dvd__mult_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
cnf(cls_card__mono_0,axiom,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).
cnf(cls_total__on__converse_1,axiom,
( c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
cnf(cls_refl__on__converse_1,axiom,
( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
cnf(cls_set__eq__subset_2,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
cnf(cls_equalityI_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
cnf(cls_minus__le__iff_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_minus__le__iff_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_le__minus__iff_0,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_le__funD_0,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(cls_antisym__subset_0,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
cnf(cls_acyclic__subset_0,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Oacyclic(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
cnf(cls_wf__subset_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Owf(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
cnf(cls_minus__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_add__cancel__end_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_sgn__if_1,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osgn__if(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_1) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
cnf(cls_dvd__trans_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_order__trans_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_sgn__neg_0,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__neg_0) ).
cnf(cls_Compl__partition2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
cnf(cls_Compl__disjoint2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
cnf(cls_Compl__partition_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
cnf(cls_Compl__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
cnf(cls_minus__divide__divide_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
cnf(cls_not__one__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Ozero__class_Ozero(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
cnf(cls_subset__empty_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_sgn__pos_0,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
cnf(cls_nonzero__minus__divide__divide_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
cnf(cls_Int__lower1_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
cnf(cls_order__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_order__le__less_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_sup__eq__if_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__if_1) ).
cnf(cls_minus__divide__right_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
cnf(cls_square__eq__iff_1,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
cnf(cls_minus__mult__minus_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(cls_nonzero__minus__divide__right_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
cnf(cls_le__imp__neg__le_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
cnf(cls_neg__le__0__iff__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
cnf(cls_neg__0__le__iff__le_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_linorder__neqE_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_sup__left__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
cnf(cls_inf__left__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_of__nat__le__iff_1,axiom,
( c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X2,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
cnf(cls_minus__mult__right_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
cnf(cls_neg__less__eq__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
cnf(cls_minus__le__self__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
cnf(cls_less__eq__neg__nonpos_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
cnf(cls_le__minus__self__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
cnf(cls_mult__left__idem_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_compl__unique_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).
cnf(cls_finite__UnI_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
cnf(cls_finite__Un_2,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_card__gt__0__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X1,X2)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
cnf(cls_minus__dvd__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
cnf(cls_dvd__minus__iff_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
cnf(cls_Un__empty_2,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
cnf(cls_antisym__converse_0,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
cnf(cls_acyclic__converse_0,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
cnf(cls_finite__insert_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
cnf(cls_sym__converse_0,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_order__le__less_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_order__less__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__neq__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_neg__le__0__iff__le_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
cnf(cls_neg__0__le__iff__le_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
cnf(cls_nat__less__le_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
cnf(cls_rtrancl__converse_0,axiom,
c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
cnf(cls_subset__Un__eq_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
cnf(cls_Un__absorb2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
cnf(cls_Un__absorb1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
cnf(cls_Int__absorb2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
cnf(cls_Int__absorb1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_neg__less__eq__nonneg_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
cnf(cls_minus__le__self__iff_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
cnf(cls_less__eq__neg__nonpos_1,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
cnf(cls_le__minus__self__iff_1,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
cnf(cls_square__eq__iff_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_Un__empty_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
cnf(cls_Un__empty_1,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
cnf(cls_nat__neq__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_finite__Int_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
cnf(cls_finite__Int_1,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
cnf(cls_sgn__1__neg_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
cnf(cls_dvd__power_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
cnf(cls_minus__dvd__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
cnf(cls_dvd__minus__iff_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
cnf(cls_sgn__if_2,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osgn__if(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_2) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_minus__diff__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X2)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
cnf(cls_acc__wfD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ c_Wellfounded_Owf(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_nat__less__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
cnf(cls_le__neq__implies__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
cnf(cls_class__ring_Oneg__mul_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(cls_neq0__conv_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
cnf(cls_rtrancl__reflcl__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_zero__le__square_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__less_0,axiom,
( c_lessequals(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_linorder__not__le_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_not__leE_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_inf__le1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_inf__le2_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
cnf(cls_sup__ge1_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
cnf(cls_sup__ge2_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_sgn__1__pos_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
cnf(cls_sup__0__imp__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__0__imp__0_0) ).
cnf(cls_inf__0__imp__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).
cnf(cls_dvdI_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Odvd(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
cnf(cls_dvd__triv__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
cnf(cls_dvd__triv__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
cnf(cls_converse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
cnf(cls_not__less0_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
cnf(cls_gr__implies__not0_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_Un__UNIV__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
cnf(cls_Int__empty__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
cnf(cls_Un__UNIV__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
cnf(cls_Int__empty__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
cnf(cls_setsum__empty_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__empty_0) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
cnf(cls_Int__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_diff__eq_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
cnf(cls_zero__less__one_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Oone__class_Oone(X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_diff__minus_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
cnf(cls_ab__diff__minus_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
cnf(cls_diff__def_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
cnf(cls_le__iff__sup_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_sup__absorb1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_le__iff__sup_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_le__iff__inf_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_inf__absorb2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_nat__less__le_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_less__not__refl_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_Compl__UNIV__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
cnf(cls_antisym__converse_1,axiom,
( c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
cnf(cls_acyclic__converse_1,axiom,
( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
cnf(cls_wf__mlex_0,axiom,
( c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X1,X2,X3),X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__mlex_0) ).
cnf(cls_finite__insert_1,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
cnf(cls_sym__converse_1,axiom,
( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
cnf(cls_equiv_Orefl__on_0,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
cnf(cls_left__minus_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
cnf(cls_ab__left__minus_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_refl__rtrancl_0,axiom,
c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Ortrancl(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_Int__UNIV__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_subset__UNIV_0,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
cnf(cls_power__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
cnf(cls_power__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
cnf(cls_setsum__infinite_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4) = c_HOL_Ozero__class_Ozero(X1)
| c_Finite__Set_Ofinite(X4,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).
cnf(cls_setsum__def_1,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4) = c_HOL_Ozero__class_Ozero(X1)
| c_Finite__Set_Ofinite(X4,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__def_1) ).
cnf(cls_minus__unique_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_sup__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_inf__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_refl__Id_0,axiom,
c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__Id_0) ).
cnf(cls_not__one__le__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_gr0I_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
cnf(cls_dvd__0__left_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
cnf(cls_Domain__rtrancl_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__rtrancl_0) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
cnf(cls_total__on__empty_0,axiom,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_of__nat__0__le__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
cnf(cls_zero__le__imp__of__nat_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(cls_field__power__not__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( X3 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_compl__sup__top_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_sup__compl__top_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_right__inverse__eq_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
cnf(cls_sym__conv__converse__eq_1,axiom,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
cnf(cls_right__minus_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_equiv_Osym_0,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
cnf(cls_right__minus__eq_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_power__eq__0__iff_2,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
cnf(cls_converse__Id__on_0,axiom,
c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2) = c_Relation_OId__on(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
cnf(cls_le__0__eq_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
cnf(cls_group__add__class_Odiff__0_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
cnf(cls_divide__self__if_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
cnf(cls_Domain__Id_0,axiom,
c_Relation_ODomain(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
cnf(cls_power__0__left_1,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
cnf(cls_power__0__left_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
cnf(cls_double__eq__0__iff_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_Domain__Id__on_0,axiom,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
cnf(cls_single__valued__Id__on_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
cnf(cls_refl__on__Id__on_0,axiom,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_sym__conv__converse__eq_0,axiom,
( c_Relation_Oconverse(X1,X2,X2) = X1
| ~ c_Relation_Osym(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
cnf(cls_card__eq__0__iff_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
cnf(cls_divide__zero_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).
cnf(cls_divide__eq__eq_1,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
cnf(cls_eq__divide__eq_2,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
cnf(cls_divide__self__if_1,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X2) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
cnf(cls_mult__zero__left_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_divide__zero__left_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
cnf(cls_zero__le__one_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_finite__UNIV_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_mult__1_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
cnf(cls_mult__1__left_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_add__0__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(cls_sup__top__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_inf__bot__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_sup__top__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf__bot__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_mult__zero__right_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_divide__self_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X2) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
cnf(cls_right__inverse__eq_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(cls_power__0_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
cnf(cls_class__semiring_Opwr__0_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
cnf(cls_sup__bot__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_inf__top__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
cnf(cls_sup__bot__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_inf__top__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
cnf(cls_card__empty_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__empty_0) ).
cnf(cls_one__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_dvd__0__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
cnf(cls_top__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_diff__0__right_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_mult__1__right_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_divide__1_0,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_minus__minus_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_equation__minus__iff_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
cnf(cls_converse__Id_0,axiom,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
cnf(cls_diff__self_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
cnf(cls_right__minus__eq_1,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_acyclic__impl__antisym__rtrancl_0,axiom,
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
cnf(cls_sym__rtrancl_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
cnf(cls_sup__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_inf__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_dvd__refl_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_sgn__sgn_0,axiom,
( c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X2,X1),X1) = c_HOL_Osgn__class_Osgn(X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
cnf(cls_single__valued__Id_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
cnf(cls_mult__idem_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
cnf(cls_rtrancl__idemp_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
cnf(cls_neg__equal__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
cnf(clsarity_prod__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
cnf(cls_sgn__0__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
cnf(cls_antisym__Id__on_0,axiom,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
cnf(cls_wf__measure_0,axiom,
c_Wellfounded_Owf(c_Wellfounded_Omeasure(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__measure_0) ).
cnf(cls_sym__Id__on_0,axiom,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
cnf(cls_compl__top__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(cls_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_minus__zero_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
cnf(cls_neg__equal__zero_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(X1,X2))
| ~ class_HOL_Oord(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Orderings_Otop,axiom,
( class_Orderings_Otop(tc_fun(X1,X2))
| ~ class_Orderings_Otop(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Odistrib__lattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(cls_wf__acyclic_0,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
cnf(cls_of__nat__0_0,axiom,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
cnf(cls_sgn__0__0_1,axiom,
( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
cnf(cls_sgn0_0,axiom,
( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osgn__if(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
cnf(cls_card__eq__0__iff_2,axiom,
( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
cnf(cls_finite_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
cnf(cls_antisym__Id_0,axiom,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
cnf(cls_sym__Id_0,axiom,
c_Relation_Osym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
cnf(cls_one__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(i_0_1343,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_trancl__trans_0 ).
cnf(i_0_1344,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
cls_trancl__unfold__left_0 ).
cnf(i_0_1345,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X1,X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X1),X1,X1))) ),
cls_trancl__converseI_0 ).
cnf(i_0_1346,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X1),X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X1,X1),X1))) ),
cls_trancl__converseD_0 ).
cnf(i_0_1347,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1))) ),
cls_converse__tranclE_1 ).
cnf(i_0_1348,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_tranclE_0 ).
cnf(i_0_1349,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtrancl__trancl__trancl_0 ).
cnf(i_0_1350,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_trancl__rtrancl__trancl_0 ).
cnf(i_0_1351,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
cls_trancl__into__trancl2_0 ).
cnf(i_0_1352,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_Transitive__Closure_Otrancl__into__trancl_0 ).
cnf(i_0_1353,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a)),c_Transitive__Closure_Otrancl(X3,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Otrancl(X3,t_a))) ),
cls_trancl_Ocases_0 ).
cnf(i_0_1354,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_tranclE_1 ).
cnf(i_0_1355,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X3,X2,X4,X1),X1,X1)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1))) ),
cls_converse__tranclE_0 ).
cnf(i_0_1356,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1))) ),
cls_tranclD_1 ).
cnf(i_0_1357,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X3,X2,X4,X1),X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1))) ),
cls_tranclD2_0 ).
cnf(i_0_1358,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X3,X4,X1),X4,X1,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Otrancl(X2,X1))) ),
cls_tranclD2_1 ).
cnf(i_0_1359,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X3,X2,X4,X1),X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1))) ),
cls_tranclD_0 ).
cnf(i_0_1360,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Otrancl(X3,t_a))) ),
cls_trancl_Ocases_1 ).
cnf(i_0_1361,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
cls_rtrancl__into__trancl2_0 ).
cnf(i_0_1362,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtrancl__into__trancl1_0 ).
cnf(i_0_1363,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
cls_r__r__into__trancl_0 ).
cnf(i_0_1364,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_rtrancl__eq__or__trancl_2 ).
cnf(i_0_1365,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_trancl__into__rtrancl_0 ).
cnf(i_0_1366,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ c_lessequals(X4,X3,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X4,X1))) ),
cls_trancl__mono_0 ).
cnf(i_0_1367,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ c_Wellfounded_Oacyclic(X3,X1) ),
cls_acyclic__def_0 ).
cnf(i_0_1368,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X1),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X1),X1,X1)),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3)) ),
cls_irrefl__trancl__rD_0 ).
cnf(i_0_1369,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtranclD_0 ).
cnf(i_0_1370,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtrancl__eq__or__trancl_0 ).
cnf(i_0_1371,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Otrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
cls_trancl_Or__into__trancl_0 ).
cnf(i_0_1372,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
cls_trancl__unfold_0 ).
cnf(i_0_1373,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ORange(X4,X1,X2))) ),
cls_Range__iff_0 ).
cnf(i_0_1374,axiom,
c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),
cls_Range__def_0 ).
cnf(i_0_1375,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ORange(X4,X1,X2))) ),
cls_RangeE_0 ).
cnf(i_0_1376,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Otrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3)) ),
cls_r__into__trancl_H_0 ).
cnf(i_0_1377,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
cls_trancl__range_0 ).
cnf(i_0_1378,axiom,
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_wf__converse__trancl_0 ).
cnf(i_0_1379,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ORange(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X1)),c_Pair(X5,X2,X4,X1)),X3)) ),
cls_RangeI_0 ).
cnf(i_0_1380,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ORange(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X1)),c_Pair(X5,X2,X4,X1)),X3)) ),
cls_Range__iff_1 ).
cnf(i_0_1381,axiom,
c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),
cls_trancl__converse_0 ).
cnf(i_0_1382,axiom,
c_Relation_ORange(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X2,c_Relation_ORange(X5,X3,X4),X4),
cls_Range__insert_0 ).
cnf(i_0_1383,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_reflcl__trancl_0 ).
cnf(i_0_1384,axiom,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
cls_Nitpick_Ortrancl__def_0 ).
cnf(i_0_1385,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
cls_trancl__domain_0 ).
cnf(i_0_1386,axiom,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__trancl_0 ).
cnf(i_0_1387,axiom,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__trancl_0 ).
cnf(i_0_1388,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_trancl__rtrancl__absorb_0 ).
cnf(i_0_1389,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
cls_trancl__unfold__right_0 ).
cnf(i_0_1390,axiom,
( X1 = X2
| X2 = X1
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X1))) ),
cls_in__mkbot_4 ).
cnf(i_0_1391,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X2))) ),
inference(fof_simplification,[status(thm)],[cls_in__mktop_4]) ).
cnf(i_0_1392,axiom,
c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_trancl__reflcl_0 ).
cnf(i_0_1393,axiom,
c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),
cls_Range__Un__eq_0 ).
cnf(i_0_1394,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__trancl__absorb_0 ).
cnf(i_0_1395,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X3,X2,X2),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__Un_0 ).
cnf(i_0_1396,axiom,
c_Relation_ORange(c_Relation_Oconverse(X1,X2,X3),X3,X2) = c_Relation_ODomain(X1,X2,X3),
cls_Range__converse_0 ).
cnf(i_0_1397,axiom,
c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
cls_Range__rtrancl_0 ).
cnf(i_0_1398,axiom,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
cls_Range__Id__on_0 ).
cnf(i_0_1399,axiom,
c_Relation_ORange(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Range__Id_0 ).
cnf(i_0_1400,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonneg__eq__0__iff_2 ).
cnf(i_0_1401,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
cls_CHAINED_0_01,
[final] ).
cnf(i_0_1402,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ),
cls_CHAINED_1,
[final] ).
cnf(i_0_1403,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P____)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
cls_PW_1,
[final] ).
cnf(i_0_1404,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))),
cls_conjecture_0,
[final] ).
cnf(i_0_1405,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P____))) ),
cls_PW_0,
[final] ).
cnf(i_0_1406,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X1),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ c_lessequals(X1,v_n____,tc_nat) ),
cls_CHAINED_0,
[final] ).
cnf(i_0_1407,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,X6,X7,X2,X1),X4,X1,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X7,X2)),c_Pair(X3,X4,X7,X2)),c_Relation_Orel__comp(X5,X6,X7,X1,X2))) ),
cls_rel__compEpair_1,
[final] ).
cnf(i_0_1408,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,X6,X1,X7,X2),X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X7)),c_Pair(X3,X4,X1,X7)),c_Relation_Orel__comp(X5,X6,X1,X2,X7))) ),
cls_rel__compEpair_0,
[final] ).
cnf(i_0_1409,axiom,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5),X3,X4,X4)),X2)) ),
cls_cuts__eq_1,
[final] ).
cnf(i_0_1410,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X5),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X3,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
cls_setsum__restrict__set_0,
[final] ).
cnf(i_0_1411,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setsum__delta_0,
[final] ).
cnf(i_0_1412,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = c_HOL_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setsum__delta_1,
[final] ).
cnf(i_0_1413,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X6)) ),
cls_vimage__if_0,
[final] ).
cnf(i_0_1414,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3)
| hBOOL(hAPP(hAPP(c_in(X1),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X6)) ),
cls_vimage__if_2,
[final] ).
cnf(i_0_1415,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = X3
| hBOOL(hAPP(hAPP(c_in(X1),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X6)) ),
cls_vimage__if_1,
[final] ).
cnf(i_0_1416,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X2,X1,tc_fun(X1,X1)),X4),X2,X1,X1),X5),X6,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X1),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X6)) ),
cls_vimage__if_3,
[final] ).
cnf(i_0_1417,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setsum__delta_H_0,
[final] ).
cnf(i_0_1418,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Ozero__class_Ozero(X1))),X5) = c_HOL_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setsum__delta_H_1,
[final] ).
cnf(i_0_1419,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_in(X2),X2,tc_fun(X2,tc_bool),tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X5,X2,X1,X1)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X4),c_Lattices_Olower__semilattice__class_Oinf(X6,X3,tc_fun(X2,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X6,X2) ),
cls_setsum__cases_0,
[final] ).
cnf(i_0_1420,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X3,X1),X4,tc_fun(X3,X1),tc_fun(tc_fun(X3,tc_bool),X1),X2),X2,tc_fun(X3,tc_bool),X1),X5)),X6) = hAPP(hAPP(c_Finite__Set_Osetsum(X3,X1),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X2,X1),c_COMBC(X4,X2,X3,X1),tc_fun(X2,X1),tc_fun(tc_fun(X2,tc_bool),X1),X3),X3,tc_fun(X2,tc_bool),X1),X6)),X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__commute_0,
[final] ).
cnf(i_0_1421,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setprod__delta_0,
[final] ).
cnf(i_0_1422,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),X5),X6,X2,X1) = c_Power_Opower__class_Opower(X5,c_Finite__Set_Ocard(X6,X2),X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X6))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X6,X2) ),
cls_setprod__gen__delta_1,
[final] ).
cnf(i_0_1423,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = c_HOL_Oone__class_Oone(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setprod__delta_1,
[final] ).
cnf(i_0_1424,axiom,
( c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6)
| hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6)) != hAPP(X2,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6)) ),
cls_cuts__eq_2,
[final] ).
cnf(i_0_1425,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = hAPP(X4,X3)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setprod__delta_H_0,
[final] ).
cnf(i_0_1426,axiom,
( c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X1),hAPP(c_fequal(X2),X3),tc_bool,tc_fun(X1,tc_fun(X1,X1)),X2),X4,X2,X1,tc_fun(X1,X1)),X2,X1,X1),c_HOL_Oone__class_Oone(X1)),X5,X2,X1) = c_HOL_Oone__class_Oone(X1)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setprod__delta_H_1,
[final] ).
cnf(i_0_1427,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
cls_wf__union__merge_1,
[final] ).
cnf(i_0_1428,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1343,c_0_1344]),c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1429,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(c_Relation_Oconverse(X4,X1,X1),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X1,X1),X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oconverse(c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1),X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1345,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1430,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oconverse(c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1),X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(c_Relation_Oconverse(X4,X1,X1),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X1,X1),X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1346,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1431,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1347,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1432,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1348,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1433,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X4,X5,X1,X2),X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,X3,X1,X2))) ),
cls_Image__iff_1,
[final] ).
cnf(i_0_1434,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X4,X5,X1,X2),X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,X3,X1,X2))) ),
cls_ImageE_0,
[final] ).
cnf(i_0_1435,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X2,X1,X1),X5)),X4)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__left__distrib_0,
[final] ).
cnf(i_0_1436,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),hAPP(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(X1),X3,X1,tc_fun(X1,X1),X2),X2,X1,X1),X5)),X4)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_setsum__divide__distrib_0,
[final] ).
cnf(i_0_1437,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1349,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1438,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1350,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1439,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1351,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1440,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1352,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1441,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,t_a),t_a,t_a,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,t_a),t_a,t_a,t_a))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1353,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1442,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
cls_wf__union__merge_0,
[final] ).
cnf(i_0_1443,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1354,c_0_1344]),
[final] ).
cnf(i_0_1444,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X3,X2,X4,X1),X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1355,c_0_1344]),
[final] ).
cnf(i_0_1445,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1356,c_0_1344]),
[final] ).
cnf(i_0_1446,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X3,X2,X4,X1),X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1357,c_0_1344]),
[final] ).
cnf(i_0_1447,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X3,X4,X1),X4,X1,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1358,c_0_1344]),
[final] ).
cnf(i_0_1448,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X3,X2,X4,X1),X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1359,c_0_1344]),
[final] ).
cnf(i_0_1449,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)) ),
cls_less__add__iff1_1,
[final] ).
cnf(i_0_1450,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X4),X5)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(X3,X5,X6,X6)),X7))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X8,X8)),c_Pair(X2,X4,X8,X8)),X9))
| ~ c_Equiv__Relations_Ocongruent2(X9,X7,X1,X8,X6,X10) ),
cls_congruent2_Ocongruent2_0,
[final] ).
cnf(i_0_1451,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,t_a),t_a,t_a,t_a))) ),
inference(rw,[status(thm)],[i_0_1360,c_0_1344]),
[final] ).
cnf(i_0_1452,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X4),X5))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_setsum__subtractf_0,
[final] ).
cnf(i_0_1453,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X4),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__addf_0,
[final] ).
cnf(i_0_1454,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),tc_fun(X1,tc_bool))))
| ~ c_Equiv__Relations_Oequiv(X6,X4,X1) ),
cls_equiv__class__nondisjoint_0,
[final] ).
cnf(i_0_1455,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
inference(rw,[status(thm)],[i_0_1361,c_0_1344]),
[final] ).
cnf(i_0_1456,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
inference(rw,[status(thm)],[i_0_1362,c_0_1344]),
[final] ).
cnf(i_0_1457,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
inference(rw,[status(thm)],[i_0_1363,c_0_1344]),
[final] ).
cnf(i_0_1458,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Orel__comp(X5,X6,X1,X7,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X7,X2)),c_Pair(X8,X4,X7,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X7)),c_Pair(X3,X8,X1,X7)),X5)) ),
cls_rel__compI_0,
[final] ).
cnf(i_0_1459,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X4,X5,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X1,X4,X5,X3),X3,X3)),X5))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X2,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
cls_rtrancl__induct_1,
[final] ).
cnf(i_0_1460,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X1,X4,X5,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X4,X5,X3),X3,X3)),X5))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
cls_converse__rtrancl__induct_0,
[final] ).
cnf(i_0_1461,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
cls_less__add__iff1_0,
[final] ).
cnf(i_0_1462,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1364,c_0_1344]),
[final] ).
cnf(i_0_1463,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1365,c_0_1344]),
[final] ).
cnf(i_0_1464,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1)))
| ~ c_lessequals(X4,X3,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1366,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1465,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Relation_Osingle__valued(X4,X1,X1) ),
cls_single__valued__confluent_0,
[final] ).
cnf(i_0_1466,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X5)),X4),c_Product__Type_OSigma(X2,X3,X1,X5))) ),
cls_SigmaE_0,
[final] ).
cnf(i_0_1467,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Relation_OImage(X4,X2,X1,X5))) ),
cls_Image__iff_0,
[final] ).
cnf(i_0_1468,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Relation_OImage(X4,X2,X1,X5))) ),
cls_ImageE_1,
[final] ).
cnf(i_0_1469,plain,
( ~ c_Wellfounded_Oacyclic(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1))) ),
inference(rw,[status(thm)],[i_0_1367,c_0_1344]),
[final] ).
cnf(i_0_1470,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X1),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X1),X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3)) ),
inference(rw,[status(thm)],[i_0_1368,c_0_1344]),
[final] ).
cnf(i_0_1471,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
inference(rw,[status(thm)],[i_0_1369,c_0_1344]),
[final] ).
cnf(i_0_1472,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
inference(rw,[status(thm)],[i_0_1370,c_0_1344]),
[final] ).
cnf(i_0_1473,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
inference(rw,[status(thm)],[i_0_1371,c_0_1344]),
[final] ).
cnf(i_0_1474,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))) ),
cls_less__add__iff2_1,
[final] ).
cnf(i_0_1475,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X4,X5,X3),X4,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
cls_converse__rtrancl__induct_1,
[final] ).
cnf(i_0_1476,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X4,X5,X3),X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X2,X3,X3)),c_Transitive__Closure_Ortrancl(X5,X3))) ),
cls_rtrancl__induct_0,
[final] ).
cnf(i_0_1477,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X3,X4,X1),X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1)))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X2,X1))) ),
cls_converse__rtranclE_1,
[final] ).
cnf(i_0_1478,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X3,X4,X1),X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtranclE_0,
[final] ).
cnf(i_0_1479,axiom,
( c_Equiv__Relations_Ocongruent(X1,hAPP(X2,X3),X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X6),X3),X7))
| ~ c_Equiv__Relations_Ocongruent2(X8,X1,X2,X6,X4,X5)
| ~ c_Equiv__Relations_Oequiv(X7,X8,X6) ),
cls_congruent2__implies__congruent_0,
[final] ).
cnf(i_0_1480,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X3,X4,X1),X3,X1,X1)),X4))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtranclE_1,
[final] ).
cnf(i_0_1481,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X3,X2,X4,X1),X1,X1)),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
cls_converse__rtranclE_0,
[final] ).
cnf(i_0_1482,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtrancl__trans_0,
[final] ).
cnf(i_0_1483,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),X4)) ),
cls_converse__rtrancl__into__rtrancl_0,
[final] ).
cnf(i_0_1484,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtrancl_Ortrancl__into__rtrancl_0,
[final] ).
cnf(i_0_1485,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
cls_less__add__iff2_0,
[final] ).
cnf(i_0_1486,axiom,
( c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_Finite__Set_Osetprod(X2,X5,X3,X1)),c_Finite__Set_Osetprod(X4,X5,X3,X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_Finite__Set_Ofinite(X5,X3) ),
cls_setprod__dividef_0,
[final] ).
cnf(i_0_1487,axiom,
( c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X2,X5,X3,X1)),c_Finite__Set_Osetprod(X4,X5,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_setprod__timesf_0,
[final] ).
cnf(i_0_1488,plain,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1372,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1489,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(hAPP(X2,X3),hAPP(X2,X4),X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(X3,X4,X6,X6)),c_Relation_Oinv__image(X5,X2,X1,X6))) ),
cls_in__inv__image_0,
[final] ).
cnf(i_0_1490,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oinv__image(X4,X5,X6,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(hAPP(X5,X2),hAPP(X5,X3),X6,X6)),X4)) ),
cls_in__inv__image_1,
[final] ).
cnf(i_0_1491,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ODomain(c_Relation_Oconverse(X4,X1,X2),X2,X1))) ),
inference(rw,[status(thm)],[i_0_1373,c_0_1374]),
[final] ).
cnf(i_0_1492,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ODomain(c_Relation_Oconverse(X4,X1,X2),X2,X1))) ),
inference(rw,[status(thm)],[i_0_1375,c_0_1374]),
[final] ).
cnf(i_0_1493,axiom,
( hAPP(X1,X7) = hAPP(X6,X7)
| c_Recdef_Ocut(X1,X2,X3,X4,X5) != c_Recdef_Ocut(X6,X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X7,X3,X4,X4)),X2)) ),
cls_cuts__eq_0,
[final] ).
cnf(i_0_1494,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X4)),c_Pair(X5,X2,X3,X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X4)),c_Pair(X5,X1,X3,X4)),X6))
| ~ c_Relation_Osingle__valued(X6,X3,X4) ),
cls_single__valuedD_0,
[final] ).
cnf(i_0_1495,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
cls_O__assoc_0,
[final] ).
cnf(i_0_1496,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),X4))
| ~ c_Relation_Oantisym(X4,X3) ),
cls_antisymD_0,
[final] ).
cnf(i_0_1497,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),X4))
| ~ c_Relation_Oantisym(X4,X3) ),
cls_antisym__def_0,
[final] ).
cnf(i_0_1498,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Wellfounded_Owf(X4,X1) ),
cls_wf__asym_0,
[final] ).
cnf(i_0_1499,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X3,X4,X1,X2),X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X4,X1,X2))) ),
cls_Domain__iff_0,
[final] ).
cnf(i_0_1500,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X3,X4,X1,X2),X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X4,X1,X2))) ),
cls_DomainE_0,
[final] ).
cnf(i_0_1501,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X1,X1),X1))) ),
cls_rtrancl__converseD_0,
[final] ).
cnf(i_0_1502,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a)),c_Transitive__Closure_Ortrancl(X3,t_a)))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Ortrancl(X3,t_a))) ),
cls_rtrancl_Ocases_0,
[final] ).
cnf(i_0_1503,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a)),X3))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X1,X2,t_a,t_a)),c_Transitive__Closure_Ortrancl(X3,t_a))) ),
cls_rtrancl_Ocases_1,
[final] ).
cnf(i_0_1504,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X1,X1),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_rtrancl__converseI_0,
[final] ).
cnf(i_0_1505,axiom,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)),
cls_rel__comp__distrib2_0,
[final] ).
cnf(i_0_1506,axiom,
c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
cls_rel__comp__distrib_0,
[final] ).
cnf(i_0_1507,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omlex__prod(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X5))
| ~ c_lessequals(hAPP(X4,X2),hAPP(X4,X3),tc_nat) ),
cls_mlex__leq_0,
[final] ).
cnf(i_0_1508,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2))) ),
cls_converseD_0,
[final] ).
cnf(i_0_1509,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5)) ),
cls_converseI_0,
[final] ).
cnf(i_0_1510,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(X5,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),X5)) ),
cls_converse__iff_1,
[final] ).
cnf(i_0_1511,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X6,X3,X4,X4)),X2)) ),
cls_tfl__cut__apply_0,
[final] ).
cnf(i_0_1512,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X6,X3,X4,X4)),X2)) ),
cls_cut__apply_0,
[final] ).
cnf(i_0_1513,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4))) ),
cls_in__mkbot_2,
[final] ).
cnf(i_0_1514,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4))) ),
cls_in__mktop_2,
[final] ).
cnf(i_0_1515,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Relation_Osym(X4,X1) ),
cls_symD_0,
[final] ).
cnf(i_0_1516,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Relation_Osym(X4,X1) ),
cls_sym__def_0,
[final] ).
cnf(i_0_1517,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
| X1 = X2
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
cls_in__mktop_5,
[final] ).
cnf(i_0_1518,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
| X1 = X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
cls_in__mkbot_5,
[final] ).
cnf(i_0_1519,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X4)))
| X1 = X4
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
cls_in__mkbot_3,
[final] ).
cnf(i_0_1520,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X4)))
| X2 = X4
| X1 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3)) ),
cls_in__mktop_3,
[final] ).
cnf(i_0_1521,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3)) ),
inference(rw,[status(thm)],[i_0_1376,c_0_1344]),
[final] ).
cnf(i_0_1522,axiom,
( c_lessequals(c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_equiv__class__subset_0,
[final] ).
cnf(i_0_1523,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),tc_fun(X1,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1) ),
cls_subset__equiv__class_0,
[final] ).
cnf(i_0_1524,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),X3)) ),
cls_Image__singleton__iff_1,
[final] ).
cnf(i_0_1525,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X4,tc_prod(X1,X1)),X1) ),
cls_acyclic__insert_1,
[final] ).
cnf(i_0_1526,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X4,tc_prod(X1,X1)),X1) ),
cls_wf__insert_1,
[final] ).
cnf(i_0_1527,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X3,X2,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
cls_rtrancl__induct_3,
[final] ).
cnf(i_0_1528,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X2,X3,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
cls_converse__rtrancl__induct_3,
[final] ).
cnf(i_0_1529,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Relation_Orel__comp(X6,X7,X3,X4,X5),tc_fun(tc_prod(X3,X5),tc_bool))
| ~ c_lessequals(X2,X7,tc_fun(tc_prod(X4,X5),tc_bool))
| ~ c_lessequals(X1,X6,tc_fun(tc_prod(X3,X4),tc_bool)) ),
cls_rel__comp__mono_0,
[final] ).
cnf(i_0_1530,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X2))) ),
cls_Image__singleton__iff_0,
[final] ).
cnf(i_0_1531,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X4,X2,X5,X1)),c_Product__Type_OSigma(X6,X3,X5,X1))) ),
cls_SigmaD2_0,
[final] ).
cnf(i_0_1532,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Finite__Set_Osetsum(X3,X1),X4),X5)) = hAPP(hAPP(c_Finite__Set_Osetsum(X3,X1),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4,X1,X1,X3)),X5)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__right__distrib_0,
[final] ).
cnf(i_0_1533,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X3,X4,X1),X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ c_Wellfounded_Owf(X4,X1) ),
cls_wfE__min_1,
[final] ).
cnf(i_0_1534,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X3,X4,X1),X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ c_Wellfounded_Owf(X4,X1) ),
cls_wf__eq__minimal_1,
[final] ).
cnf(i_0_1535,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),c_Product__Type_OSigma(X3,X6,X1,X4))) ),
cls_SigmaD1_0,
[final] ).
cnf(i_0_1536,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X5,X4),X4,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X5,X4))) ),
cls_acc__induct__rule_1,
[final] ).
cnf(i_0_1537,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X5,X4),X4,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X5,X4))) ),
cls_acc__induct_1,
[final] ).
cnf(i_0_1538,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),X2,X2) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X2),X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1377,c_0_1344]),c_0_1374]),c_0_1374]),
[final] ).
cnf(i_0_1539,plain,
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(rw,[status(thm)],[i_0_1378,c_0_1344]),
[final] ).
cnf(i_0_1540,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X3,X1,X1,X2)),X4) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_setsum__negf_0,
[final] ).
cnf(i_0_1541,axiom,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,tc_nat),X3),X4)) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X1),X3,tc_nat,X1,X2)),X4)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__setsum_0,
[final] ).
cnf(i_0_1542,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
cls_wf__induct__rule_0,
[final] ).
cnf(i_0_1543,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
cls_wf__def_0,
[final] ).
cnf(i_0_1544,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
cls_tfl__wf__induct_0,
[final] ).
cnf(i_0_1545,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X5,X4),X4,X4)),X5))
| ~ c_Wellfounded_Owf(X5,X4) ),
cls_wf__induct_0,
[final] ).
cnf(i_0_1546,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_Relation_Ototal__on(X5,X4,X1) ),
cls_total__on__def_0,
[final] ).
cnf(i_0_1547,axiom,
( c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_eq__equiv__class__iff_1,
[final] ).
cnf(i_0_1548,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X6,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X4)) ),
cls_Image__iff_2,
[final] ).
cnf(i_0_1549,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X1)),c_Pair(X6,X2,X5,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X6),X4)) ),
cls_rev__ImageI_0,
[final] ).
cnf(i_0_1550,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X3,X2,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
cls_rtrancl__induct_2,
[final] ).
cnf(i_0_1551,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X3,X4,X5)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X5,X5)),c_Pair(X2,X3,X5,X5)),c_Transitive__Closure_Ortrancl(X4,X5))) ),
cls_converse__rtrancl__induct_2,
[final] ).
cnf(i_0_1552,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1))) ),
cls_not__sum__squares__lt__zero_0,
[final] ).
cnf(i_0_1553,axiom,
( c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_equiv__class__eq__iff_0,
[final] ).
cnf(i_0_1554,axiom,
( c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_equiv__class__eq_0,
[final] ).
cnf(i_0_1555,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4),X6,X1) ),
cls_le__add__iff1_1,
[final] ).
cnf(i_0_1556,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6),X1) ),
cls_le__add__iff2_1,
[final] ).
cnf(i_0_1557,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Finite__Set_Osetprod(X2,X3,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X3,X2,X4,X1)))) ),
cls_setprod__pos_1,
[final] ).
cnf(i_0_1558,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(c_Relation_Oconverse(X3,X4,X1),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X1)),c_Pair(X5,X2,X4,X1)),X3)) ),
inference(rw,[status(thm)],[i_0_1379,c_0_1374]),
[final] ).
cnf(i_0_1559,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(c_Relation_Oconverse(X3,X4,X1),X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X1)),c_Pair(X5,X2,X4,X1)),X3)) ),
inference(rw,[status(thm)],[i_0_1380,c_0_1374]),
[final] ).
cnf(i_0_1560,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X3,X3),X1,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_Wellfounded_Owf(X1,X3) ),
cls_wf__union__compatible_0,
[final] ).
cnf(i_0_1561,axiom,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X2)),c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),X2,X2)),X1)) ),
cls_Nitpick_Orefl_H__def_1,
[final] ).
cnf(i_0_1562,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X4,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
cls_acc_Oinduct_0,
[final] ).
cnf(i_0_1563,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X4,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
cls_acc_Oinducts_0,
[final] ).
cnf(i_0_1564,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_eq__equiv__class__iff_0,
[final] ).
cnf(i_0_1565,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X5)) ),
cls_equiv__class__eq__iff_3,
[final] ).
cnf(i_0_1566,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
cls_acc_Oinduct_1,
[final] ).
cnf(i_0_1567,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X4,t_a))) ),
cls_acc_Oinducts_1,
[final] ).
cnf(i_0_1568,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
cls_acc__downwards__aux_0,
[final] ).
cnf(i_0_1569,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1))) ),
cls_acc__downwards_0,
[final] ).
cnf(i_0_1570,plain,
c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2),X2,X2,X2) = c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1381,c_0_1344]),c_0_1344]),
[final] ).
cnf(i_0_1571,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X5,tc_bool)),X5,X1)),c_Finite__Set_Osetprod(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X5,tc_bool)),X5,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X2,X3,X5,X1)),c_Finite__Set_Osetprod(X2,X4,X5,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X4,X5)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
cls_setprod__Un__Int_0,
[final] ).
cnf(i_0_1572,axiom,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),X5))
| ~ c_Equiv__Relations_Ocongruent(X5,X1,X4,X6) ),
cls_congruent_Ocongruent_0,
[final] ).
cnf(i_0_1573,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1))) ),
cls_acc_Ocases_0,
[final] ).
cnf(i_0_1574,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),c_Wellfounded_Oacc(X3,X1))) ),
cls_acc__downward_0,
[final] ).
cnf(i_0_1575,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X1),c_Relation_ODomain(X4,X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),c_Transitive__Closure_Ortrancl(X4,X3))) ),
cls_Not__Domain__rtrancl_0,
[final] ).
cnf(i_0_1576,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X1))
| c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_eq__equiv__class_0,
[final] ).
cnf(i_0_1577,axiom,
( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X3,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X3)),tc_fun(X3,tc_bool)) ),
cls_Image__subset__eq_1,
[final] ).
cnf(i_0_1578,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),c_Wellfounded_Omeasure(X1,X4))) ),
cls_in__measure_0,
[final] ).
cnf(i_0_1579,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X3)) ),
cls_DomainI_0,
[final] ).
cnf(i_0_1580,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X3)) ),
cls_Domain__iff_1,
[final] ).
cnf(i_0_1581,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6),X1) ),
cls_le__add__iff1_0,
[final] ).
cnf(i_0_1582,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6),X1) ),
cls_le__add__iff2_0,
[final] ).
cnf(i_0_1583,axiom,
c_Relation_Oconverse(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X4,X5),c_Relation_Oconverse(X1,X3,X4),X5,X4,X3),
cls_converse__rel__comp_0,
[final] ).
cnf(i_0_1584,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
cls_wf__comp__self_1,
[final] ).
cnf(i_0_1585,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1) ),
cls_equiv__class__eq__iff_1,
[final] ).
cnf(i_0_1586,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X4,X2,X1,X1)),X5))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X1) ),
cls_equiv__class__eq__iff_2,
[final] ).
cnf(i_0_1587,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X5))
| ~ c_Relation_Orefl__on(X3,X5,X1) ),
cls_refl__onD1_0,
[final] ).
cnf(i_0_1588,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X4,X2,X1,X1)),X5))
| ~ c_Relation_Orefl__on(X3,X5,X1) ),
cls_refl__onD2_0,
[final] ).
cnf(i_0_1589,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_OId__on(X3,X1))) ),
cls_Id__on__iff_1,
[final] ).
cnf(i_0_1590,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X1),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X2),tc_fun(X3,tc_bool)) ),
cls_pred__subset__eq_0,
[final] ).
cnf(i_0_1591,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X2),X1))),
cls_in__mkbot_1,
[final] ).
cnf(i_0_1592,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X2),X1))),
cls_in__mktop_1,
[final] ).
cnf(i_0_1593,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
cls_in__mkbot_0,
[final] ).
cnf(i_0_1594,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
cls_in__mktop_0,
[final] ).
cnf(i_0_1595,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Product__Type_OSigma(X5,X6,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5)) ),
cls_SigmaI_0,
[final] ).
cnf(i_0_1596,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Product__Type_OSigma(X5,X6,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),hAPP(X6,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5)) ),
cls_mem__Sigma__iff_2,
[final] ).
cnf(i_0_1597,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),c_Relation_OId__on(X4,X3))) ),
cls_Id__on__iff_0,
[final] ).
cnf(i_0_1598,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Relation_Oirrefl(X3,X1) ),
cls_irrefl__def_0,
[final] ).
cnf(i_0_1599,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Wellfounded_Owf(X3,X1) ),
cls_wf__irrefl_0,
[final] ).
cnf(i_0_1600,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X1,X2,X3,X3)),c_Relation_OId(X3))) ),
cls_pair__in__Id__conv_0,
[final] ).
cnf(i_0_1601,axiom,
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),c_Transitive__Closure_Ortrancl(X4,X3)))
| ~ c_Wellfounded_Oacyclic(X4,X3) ),
cls_acyclic__insert_2,
[final] ).
cnf(i_0_1602,axiom,
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),c_Transitive__Closure_Ortrancl(X4,X3)))
| ~ c_Wellfounded_Owf(X4,X3) ),
cls_wf__insert_2,
[final] ).
cnf(i_0_1603,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)))),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_gt__half__sum_0,
[final] ).
cnf(i_0_1604,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X3,X2,X1),X2,X1,X1)),X3)) ),
cls_acc_OaccI_0,
[final] ).
cnf(i_0_1605,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X3,X1),X3,X1,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),c_Wellfounded_Oacc(X2,X1))) ),
cls_not__acc__down_0,
[final] ).
cnf(i_0_1606,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X2,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5))),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool))))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
cls_setsum__Un_0,
[final] ).
cnf(i_0_1607,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Finite__Set_Osetprod(X2,X3,X4,X1)))
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X3,X2,X4,X1)),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_setprod__pos_0,
[final] ).
cnf(i_0_1608,axiom,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Finite__Set_Osetprod(X2,X3,X4,tc_nat)) = c_Finite__Set_Osetprod(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X1),X2,tc_nat,X1,X4),X3,X4,X1)
| ~ class_Ring__and__Field_Osemiring__1(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_of__nat__setprod_0,
[final] ).
cnf(i_0_1609,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))))) ),
cls_sum__squares__gt__zero__iff_0,
[final] ).
cnf(i_0_1610,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X4,X5))) ),
cls_vimage__singleton__eq_0,
[final] ).
cnf(i_0_1611,axiom,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool))
| ~ c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool)) ),
cls_Image__subset__eq_0,
[final] ).
cnf(i_0_1612,axiom,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
cls_Image__Int__subset_0,
[final] ).
cnf(i_0_1613,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omlex__prod(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X4,X2)),hAPP(X4,X3))) ),
cls_mlex__less_0,
[final] ).
cnf(i_0_1614,axiom,
( c_lessequals(X1,c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Orefl__on(X3,X1,X2) ),
cls_refl__on__comp__subset_0,
[final] ).
cnf(i_0_1615,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4),X4,X3) = c_Set_Oinsert(X2,c_Relation_ODomain(c_Relation_Oconverse(X5,X3,X4),X4,X3),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1382,c_0_1374]),c_0_1374]),
[final] ).
cnf(i_0_1616,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omeasure(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X4,X2)),hAPP(X4,X3))) ),
cls_in__measure_1,
[final] ).
cnf(i_0_1617,axiom,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2)),X1)) ),
cls_irrefl__def_1,
[final] ).
cnf(i_0_1618,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X2)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff2_1,
[final] ).
cnf(i_0_1619,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff1_1,
[final] ).
cnf(i_0_1620,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X3,X1,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
cls_Not__Domain__rtrancl_1,
[final] ).
cnf(i_0_1621,axiom,
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X3,X5)
| ~ c_Relation_Osingle__valued(X2,X4,X5)
| ~ c_Relation_Osingle__valued(X1,X3,X4) ),
cls_single__valued__rel__comp_0,
[final] ).
cnf(i_0_1622,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_1383,c_0_1344]),
[final] ).
cnf(i_0_1623,plain,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(rw,[status(thm)],[i_0_1384,c_0_1344]),
[final] ).
cnf(i_0_1624,axiom,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
cls_rtrancl__unfold_0,
[final] ).
cnf(i_0_1625,plain,
c_Relation_ODomain(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
inference(rw,[status(thm)],[i_0_1385,c_0_1344]),
[final] ).
cnf(i_0_1626,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Relation_Orefl__on(X4,X3,X1) ),
cls_refl__onD_0,
[final] ).
cnf(i_0_1627,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Relation_Orefl__on(X4,X3,X1) ),
cls_refl__on__def_1,
[final] ).
cnf(i_0_1628,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X3,X2,X4,X1)),X3))
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Finite__Set_Osetprod(X2,X3,X4,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
cls_setprod__zero__iff_0,
[final] ).
cnf(i_0_1629,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId__on(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_Id__on__eqI_0,
[final] ).
cnf(i_0_1630,plain,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(rw,[status(thm)],[i_0_1386,c_0_1344]),
[final] ).
cnf(i_0_1631,plain,
( c_Relation_Osym(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(rw,[status(thm)],[i_0_1387,c_0_1344]),
[final] ).
cnf(i_0_1632,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
cls_ATP__Linkup_OCOMBS__def_0,
[final] ).
cnf(i_0_1633,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
cls_COMBS__def_0,
[final] ).
cnf(i_0_1634,plain,
c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_1388,c_0_1344]),
[final] ).
cnf(i_0_1635,plain,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
inference(rw,[status(thm)],[i_0_1389,c_0_1344]),
[final] ).
cnf(i_0_1636,axiom,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
cls_r__comp__rtrancl__eq_0,
[final] ).
cnf(i_0_1637,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_ATP__Linkup_OCOMBB__def_0,
[final] ).
cnf(i_0_1638,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0,
[final] ).
cnf(i_0_1639,axiom,
( c_lessequals(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3),tc_fun(X1,tc_bool))
| ~ c_lessequals(X2,X3,tc_fun(X1,tc_bool)) ),
cls_pred__subset__eq_1,
[final] ).
cnf(i_0_1640,axiom,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__comp__self_0,
[final] ).
cnf(i_0_1641,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X6))),X4),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X6,X1) ),
cls_inf__period_I4_J_1,
[final] ).
cnf(i_0_1642,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X1))) ),
inference(cn,[status(thm)],[i_0_1390]),
[final] ).
cnf(i_0_1643,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X2))) ),
c_0_1391,
[final] ).
cnf(i_0_1644,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
cls_rtrancl__eq__or__trancl_1,
[final] ).
cnf(i_0_1645,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
cls_rtrancl_Ortrancl__refl_0,
[final] ).
cnf(i_0_1646,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| hBOOL(hAPP(hAPP(c_in(X4),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X3,X2,X4,X1)),X3))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_setprod__1_H_0,
[final] ).
cnf(i_0_1647,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Nitpick_Orefl_H(X3,X1) ),
cls_Nitpick_Orefl_H__def_0,
[final] ).
cnf(i_0_1648,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
cls_IdI_0,
[final] ).
cnf(i_0_1649,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
cls_pair__in__Id__conv_1,
[final] ).
cnf(i_0_1650,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2)))
| X1 = X2 ),
cls_complete__Lin_1,
[final] ).
cnf(i_0_1651,axiom,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1 ),
cls_comp__equivI_0,
[final] ).
cnf(i_0_1652,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Equiv__Relations_Oequiv(X4,X3,X1) ),
cls_equiv__class__self_0,
[final] ).
cnf(i_0_1653,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4) = c_HOL_Ozero__class_Ozero(X1)
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X4,X3,X2,X1)),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__0_H_0,
[final] ).
cnf(i_0_1654,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X2,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X2,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
cls_setsum__Un__Int_0,
[final] ).
cnf(i_0_1655,axiom,
( c_Finite__Set_Osetprod(X5,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetprod(X5,X2,X4,X1)),c_Finite__Set_Osetprod(X5,X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
cls_setprod__Un__disjoint_0,
[final] ).
cnf(i_0_1656,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(hAPP(X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X1,X4))),
cls_vimage__singleton__eq_1,
[final] ).
cnf(i_0_1657,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X1,X4,X3,tc_nat)))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setprod__pos__nat__iff_0,
[final] ).
cnf(i_0_1658,plain,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_1392,c_0_1344]),
[final] ).
cnf(i_0_1659,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
cls_divide__less__eq_9,
[final] ).
cnf(i_0_1660,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
cls_divide__less__eq_8,
[final] ).
cnf(i_0_1661,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Un__Int__crazy_0,
[final] ).
cnf(i_0_1662,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_power__Suc__less_0,
[final] ).
cnf(i_0_1663,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X1),tc_bool)),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X3,X1))) ),
cls_in__rtrancl__UnI_0,
[final] ).
cnf(i_0_1664,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X1),tc_bool)),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X4,X1))) ),
cls_in__rtrancl__UnI_1,
[final] ).
cnf(i_0_1665,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_diff__frac__eq_0,
[final] ).
cnf(i_0_1666,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_add__frac__eq_0,
[final] ).
cnf(i_0_1667,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
cls_vimageE_0,
[final] ).
cnf(i_0_1668,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
cls_vimageD_0,
[final] ).
cnf(i_0_1669,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
cls_eq__add__iff1_0,
[final] ).
cnf(i_0_1670,axiom,
( X4 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
cls_eq__add__iff2_0,
[final] ).
cnf(i_0_1671,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)))))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__half__sum_0,
[final] ).
cnf(i_0_1672,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
cls_combine__common__factor_0,
[final] ).
cnf(i_0_1673,axiom,
c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
cls_vimage__insert_0,
[final] ).
cnf(i_0_1674,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
cls_acyclic__insert_0,
[final] ).
cnf(i_0_1675,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
cls_wf__insert_0,
[final] ).
cnf(i_0_1676,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
cls_less__divide__eq_9,
[final] ).
cnf(i_0_1677,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
cls_less__divide__eq_8,
[final] ).
cnf(i_0_1678,axiom,
( X2 = X3
| hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) != hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X3) ),
cls_pred__equals__eq_0,
[final] ).
cnf(i_0_1679,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5))),X6),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X6),X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X1) ),
cls_inf__period_I4_J_0,
[final] ).
cnf(i_0_1680,axiom,
( c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool))
| ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X1,X4,X5),X5,X4) ),
cls_Image__Int__eq_0,
[final] ).
cnf(i_0_1681,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
cls_vimage__code_0,
[final] ).
cnf(i_0_1682,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2)) ),
cls_divide__less__eq_5,
[final] ).
cnf(i_0_1683,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)),X2)) ),
cls_divide__less__eq_1,
[final] ).
cnf(i_0_1684,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X2)) ),
cls_divide__less__eq_4,
[final] ).
cnf(i_0_1685,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_divide__strict__left__mono_0,
[final] ).
cnf(i_0_1686,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_divide__strict__left__mono__neg_0,
[final] ).
cnf(i_0_1687,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__gt__zero__iff_1,
[final] ).
cnf(i_0_1688,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__gt__zero__iff_2,
[final] ).
cnf(i_0_1689,axiom,
c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)),
cls_Un__Image_0,
[final] ).
cnf(i_0_1690,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
cls_Sigma__Un__distrib1_0,
[final] ).
cnf(i_0_1691,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X4,X2,X1)),c_Power_Opower__class_Opower(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
cls_power__strict__increasing__iff_0,
[final] ).
cnf(i_0_1692,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X4,X2,X1)),c_Power_Opower__class_Opower(X4,X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
cls_power__less__imp__less__exp_0,
[final] ).
cnf(i_0_1693,axiom,
c_Set_Ovimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
cls_vimage__Un_0,
[final] ).
cnf(i_0_1694,axiom,
c_Set_Ovimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X1,X2,X5,X4),c_Set_Ovimage(X1,X3,X5,X4),tc_fun(X5,tc_bool)),
cls_vimage__Int_0,
[final] ).
cnf(i_0_1695,axiom,
c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
cls_Image__Un_0,
[final] ).
cnf(i_0_1696,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
cls_mult__less__cancel__left__pos_0,
[final] ).
cnf(i_0_1697,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
cls_less__divide__eq_7,
[final] ).
cnf(i_0_1698,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__less__cancel__left__neg_0,
[final] ).
cnf(i_0_1699,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
cls_vimage__eq_1,
[final] ).
cnf(i_0_1700,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
cls_vimageI2_0,
[final] ).
cnf(i_0_1701,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X5),hAPP(X3,X2)),X4)) ),
cls_vimageI_0,
[final] ).
cnf(i_0_1702,axiom,
( c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) = X1
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
cls_equiv__comp__eq_0,
[final] ).
cnf(i_0_1703,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X5),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X5))
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_frac__less2_0,
[final] ).
cnf(i_0_1704,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(c_Relation_Oconverse(X1,X3,X4),X4,X3),c_Relation_ODomain(c_Relation_Oconverse(X2,X3,X4),X4,X3),tc_fun(X4,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1393,c_0_1374]),c_0_1374]),c_0_1374]),
[final] ).
cnf(i_0_1705,axiom,
( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),c_Relation_OImage(X5,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X6,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X5,tc_fun(tc_prod(X3,X4),tc_bool)) ),
cls_Image__mono_0,
[final] ).
cnf(i_0_1706,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_mult__less__cancel__left__disj_0,
[final] ).
cnf(i_0_1707,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
cls_mult__less__cancel__right__disj_0,
[final] ).
cnf(i_0_1708,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))) ),
cls_power__less__imp__less__base_0,
[final] ).
cnf(i_0_1709,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_power__less__power__Suc_0,
[final] ).
cnf(i_0_1710,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_mult__less__cancel__right__disj_1,
[final] ).
cnf(i_0_1711,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
cls_mult__less__cancel__left__disj_1,
[final] ).
cnf(i_0_1712,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_mult__strict__mono_0,
[final] ).
cnf(i_0_1713,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_mult__less__cancel__left__disj_2,
[final] ).
cnf(i_0_1714,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
cls_mult__less__cancel__right__disj_2,
[final] ).
cnf(i_0_1715,axiom,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X1,c_Relation_ODomain(X5,X3,X4),X3),
cls_Domain__insert_0,
[final] ).
cnf(i_0_1716,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_mult__less__cancel__right__disj_3,
[final] ).
cnf(i_0_1717,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
cls_mult__less__cancel__left__disj_3,
[final] ).
cnf(i_0_1718,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
cls_divide__less__eq_7,
[final] ).
cnf(i_0_1719,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)),X3)) ),
cls_divide__less__eq_0,
[final] ).
cnf(i_0_1720,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)) ),
cls_less__divide__eq_6,
[final] ).
cnf(i_0_1721,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))) ),
cls_mult__right__less__imp__less_0,
[final] ).
cnf(i_0_1722,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
cls_mult__left__less__imp__less_0,
[final] ).
cnf(i_0_1723,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))) ),
cls_mult__less__imp__less__right_0,
[final] ).
cnf(i_0_1724,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
cls_mult__less__imp__less__left_0,
[final] ).
cnf(i_0_1725,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
cls_mult__imp__less__div__pos_0,
[final] ).
cnf(i_0_1726,plain,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_1394,c_0_1344]),
[final] ).
cnf(i_0_1727,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X2,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Oone__class_Oone(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X4),X3)) ),
cls_power__strict__decreasing_0,
[final] ).
cnf(i_0_1728,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__le__less__imp__less_0,
[final] ).
cnf(i_0_1729,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_mult__less__le__imp__less_0,
[final] ).
cnf(i_0_1730,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_frac__less_0,
[final] ).
cnf(i_0_1731,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__idemp__self__comp_0,
[final] ).
cnf(i_0_1732,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_mult__strict__mono_H_0,
[final] ).
cnf(i_0_1733,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_1734,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_1735,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__squares__le__zero__iff_0,
[final] ).
cnf(i_0_1736,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__squares__le__zero__iff_1,
[final] ).
cnf(i_0_1737,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3))) ),
cls_less__divide__eq_0,
[final] ).
cnf(i_0_1738,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
cls_divide__less__eq_6,
[final] ).
cnf(i_0_1739,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
cls_mult__imp__div__pos__less_0,
[final] ).
cnf(i_0_1740,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
cls_Id__O__R_0,
[final] ).
cnf(i_0_1741,axiom,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
cls_R__O__Id_0,
[final] ).
cnf(i_0_1742,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)),X2)) ),
cls_divide__less__eq_2,
[final] ).
cnf(i_0_1743,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Finite__Set_Osetprod(X2,X3,X4,X1),c_Finite__Set_Osetprod(X2,X5,X4,X1),X1)
| ~ class_Ring__and__Field_Odvd(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_lessequals(X3,X5,tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
cls_setprod__dvd__setprod__subset_0,
[final] ).
cnf(i_0_1744,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X4,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_power__strict__mono_0,
[final] ).
cnf(i_0_1745,axiom,
( c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,X5,X3,X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X4,tc_bool)) ),
cls_vimage__mono_0,
[final] ).
cnf(i_0_1746,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X2,X2),c_Relation_ODomain(c_Relation_Oconverse(X3,X2,X2),X2,X2),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(rw,[status(thm)],[i_0_1395,c_0_1374]),
[final] ).
cnf(i_0_1747,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
cls_class__ringb_Onoteq__reduce_0,
[final] ).
cnf(i_0_1748,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
cls_class__ringb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_1749,axiom,
( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
| ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
cls_vimage__code_1,
[final] ).
cnf(i_0_1750,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4))) ),
cls_less__divide__eq_1,
[final] ).
cnf(i_0_1751,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_less__divide__eq_5,
[final] ).
cnf(i_0_1752,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_less__divide__eq_4,
[final] ).
cnf(i_0_1753,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__1__iff_0,
[final] ).
cnf(i_0_1754,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X2,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_power__strict__increasing__iff_1,
[final] ).
cnf(i_0_1755,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X3,X1)),c_Power_Opower__class_Opower(X2,X4,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X4)) ),
cls_power__strict__increasing_0,
[final] ).
cnf(i_0_1756,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X3),c_Relation_OId__on(X2,X1))) ),
cls_Id__onE_0,
[final] ).
cnf(i_0_1757,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__iff_1,
[final] ).
cnf(i_0_1758,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_mult__strict__left__mono__comm_0,
[final] ).
cnf(i_0_1759,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_mult__strict__left__mono_0,
[final] ).
cnf(i_0_1760,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_mult__less__cancel__left__pos_1,
[final] ).
cnf(i_0_1761,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_mult__less__cancel__left__disj_4,
[final] ).
cnf(i_0_1762,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_mult__strict__right__mono_0,
[final] ).
cnf(i_0_1763,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
cls_mult__less__cancel__right__disj_4,
[final] ).
cnf(i_0_1764,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_divide__strict__right__mono_0,
[final] ).
cnf(i_0_1765,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__iff_0,
[final] ).
cnf(i_0_1766,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__iff_3,
[final] ).
cnf(i_0_1767,axiom,
( c_Finite__Set_Osetprod(X2,c_Set_Oinsert(X3,X4,X5),X5,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(X2,X3)),c_Finite__Set_Osetprod(X2,X4,X5,X1))
| hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| ~ c_Finite__Set_Ofinite(X4,X5) ),
cls_setprod__insert_0,
[final] ).
cnf(i_0_1768,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__less__cancel__left__neg_1,
[final] ).
cnf(i_0_1769,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_mult__strict__left__mono__neg_0,
[final] ).
cnf(i_0_1770,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__less__cancel__left__disj_5,
[final] ).
cnf(i_0_1771,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2)) ),
cls_mult__strict__right__mono__neg_0,
[final] ).
cnf(i_0_1772,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__less__cancel__right__disj_5,
[final] ).
cnf(i_0_1773,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2)) ),
cls_divide__strict__right__mono__neg_0,
[final] ).
cnf(i_0_1774,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__iff_2,
[final] ).
cnf(i_0_1775,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X3,X2,X1)),c_Wellfounded_Oacc(X3,X1))) ),
cls_acc_OaccI_1,
[final] ).
cnf(i_0_1776,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X3),c_Wellfounded_Oacc(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X3,X1)),c_Wellfounded_Oacc(X2,X1))) ),
cls_not__acc__down_1,
[final] ).
cnf(i_0_1777,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_ATP__Linkup_OCOMBC__def_0,
[final] ).
cnf(i_0_1778,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0,
[final] ).
cnf(i_0_1779,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_1780,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X3,X2,X4,X1)) != c_HOL_Oone__class_Oone(X1) ),
cls_setprod__1_H_1,
[final] ).
cnf(i_0_1781,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X5),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X5),X2)),hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
cls_setsum__Un__disjoint_0,
[final] ).
cnf(i_0_1782,axiom,
( X1 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X3,X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),X1),c_Relation_OId__on(X2,X3))) ),
cls_Id__onE_1,
[final] ).
cnf(i_0_1783,axiom,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
cls_rtrancl__Un__subset_0,
[final] ).
cnf(i_0_1784,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__le__zero__iff_2,
[final] ).
cnf(i_0_1785,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
cls_divide__less__eq_3,
[final] ).
cnf(i_0_1786,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_divide__left__mono__neg_0,
[final] ).
cnf(i_0_1787,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__less__mono_0,
[final] ).
cnf(i_0_1788,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__less__le__mono_0,
[final] ).
cnf(i_0_1789,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_divide__left__mono_0,
[final] ).
cnf(i_0_1790,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_power__gt1__lemma_0,
[final] ).
cnf(i_0_1791,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_even__less__0__iff_0,
[final] ).
cnf(i_0_1792,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_double__add__less__zero__iff__single__less__zero_0,
[final] ).
cnf(i_0_1793,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Relation_OImage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X3,X2) ),
cls_wfE__pf_0,
[final] ).
cnf(i_0_1794,axiom,
( hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X3,X2,X4,X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Finite__Set_Osetprod(X2,X3,X4,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
cls_setprod__zero__iff_1,
[final] ).
cnf(i_0_1795,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_less__iff__diff__less__0_1,
[final] ).
cnf(i_0_1796,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_add__frac__num_0,
[final] ).
cnf(i_0_1797,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
cls_vimage__Compl_0,
[final] ).
cnf(i_0_1798,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__iff_5,
[final] ).
cnf(i_0_1799,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_divide__less__0__iff_4,
[final] ).
cnf(i_0_1800,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_1801,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__neg__pos_0,
[final] ).
cnf(i_0_1802,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
cls_mult__pos__neg2_0,
[final] ).
cnf(i_0_1803,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_mult__pos__neg_0,
[final] ).
cnf(i_0_1804,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__neg__pos_0,
[final] ).
cnf(i_0_1805,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_divide__pos__neg_0,
[final] ).
cnf(i_0_1806,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_distrib__inf__le_0,
[final] ).
cnf(i_0_1807,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_distrib__sup__le_0,
[final] ).
cnf(i_0_1808,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_add__neg__neg_0,
[final] ).
cnf(i_0_1809,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X4,X1),X2),X3) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(X2,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X3,X2,X4,X1)) != c_HOL_Ozero__class_Ozero(X1) ),
cls_setsum__0_H_1,
[final] ).
cnf(i_0_1810,axiom,
c_Relation_Oconverse(c_Relation_Oinv__image(X1,X2,X3,X4),X4,X4) = c_Relation_Oinv__image(c_Relation_Oconverse(X1,X3,X3),X2,X3,X4),
cls_converse__inv__image_0,
[final] ).
cnf(i_0_1811,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_1812,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_1813,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_1814,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_1815,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3))) ),
cls_less__divide__eq_2,
[final] ).
cnf(i_0_1816,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
cls_zero__less__mult__pos2_0,
[final] ).
cnf(i_0_1817,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2))) ),
cls_zero__less__mult__pos_0,
[final] ).
cnf(i_0_1818,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X4,X3)),c_Wellfounded_Oacc(X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Wellfounded_Oacc(X4,X3))) ),
cls_acc__induct__rule_0,
[final] ).
cnf(i_0_1819,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X4,X3)),c_Wellfounded_Oacc(X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Wellfounded_Oacc(X4,X3))) ),
cls_acc__induct_0,
[final] ).
cnf(i_0_1820,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X1,tc_bool)))) ),
cls_UnE_0,
[final] ).
cnf(i_0_1821,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3)) ),
cls_r__into__rtrancl_0,
[final] ).
cnf(i_0_1822,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
cls_divide__le__eq_8,
[final] ).
cnf(i_0_1823,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
cls_le__divide__eq_8,
[final] ).
cnf(i_0_1824,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))),X4)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_add__num__frac_0,
[final] ).
cnf(i_0_1825,axiom,
( X1 = X5
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_0,
[final] ).
cnf(i_0_1826,axiom,
( X2 = X4
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_1,
[final] ).
cnf(i_0_1827,axiom,
( X1 = X5
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_2,
[final] ).
cnf(i_0_1828,axiom,
( X2 = X4
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_3,
[final] ).
cnf(i_0_1829,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_not__square__less__zero_0,
[final] ).
cnf(i_0_1830,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
cls_singletonE_0,
[final] ).
cnf(i_0_1831,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__less__0__1__iff_1,
[final] ).
cnf(i_0_1832,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__neg_0,
[final] ).
cnf(i_0_1833,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_add__neg__nonpos_0,
[final] ).
cnf(i_0_1834,axiom,
( X1 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),X2,X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X2)),X1),c_Relation_OId(X2))) ),
cls_IdE_0,
[final] ).
cnf(i_0_1835,axiom,
( c_lessequals(X4,X1,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
cls_Un__Int__assoc__eq_0,
[final] ).
cnf(i_0_1836,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3))) ),
cls_zero__less__divide__iff_0,
[final] ).
cnf(i_0_1837,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2))) ),
cls_zero__less__divide__iff_3,
[final] ).
cnf(i_0_1838,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3))) ),
cls_zero__less__divide__iff_2,
[final] ).
cnf(i_0_1839,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2))) ),
cls_zero__less__divide__iff_1,
[final] ).
cnf(i_0_1840,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__ge__zero_0,
[final] ).
cnf(i_0_1841,axiom,
( X1 = X5
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
cls_Pair__eq_0,
[final] ).
cnf(i_0_1842,axiom,
( X2 = X6
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
cls_Pair__eq_1,
[final] ).
cnf(i_0_1843,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(X2,X3),c_Finite__Set_Osetprod(X2,X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),X4))
| ~ c_Finite__Set_Ofinite(X4,X5) ),
cls_dvd__setprod_0,
[final] ).
cnf(i_0_1844,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_less__divide__eq_3,
[final] ).
cnf(i_0_1845,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_zero__less__divide__iff_4,
[final] ).
cnf(i_0_1846,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
cls_divide__le__eq_9,
[final] ).
cnf(i_0_1847,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
cls_le__divide__eq_9,
[final] ).
cnf(i_0_1848,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_less__1__mult_0,
[final] ).
cnf(i_0_1849,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_mult__pos__pos_0,
[final] ).
cnf(i_0_1850,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_add__pos__pos_0,
[final] ).
cnf(i_0_1851,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_divide__pos__pos_0,
[final] ).
cnf(i_0_1852,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)))) ),
cls_IntE_0,
[final] ).
cnf(i_0_1853,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)))) ),
cls_IntE_1,
[final] ).
cnf(i_0_1854,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2))) ),
cls_zero__less__divide__1__iff_0,
[final] ).
cnf(i_0_1855,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_IntI_0,
[final] ).
cnf(i_0_1856,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_Int__iff_2,
[final] ).
cnf(i_0_1857,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplD_0,
[final] ).
cnf(i_0_1858,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X5,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X5))
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_frac__le_0,
[final] ).
cnf(i_0_1859,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X2,X1) ),
cls_divide__le__eq_1,
[final] ).
cnf(i_0_1860,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1) ),
cls_divide__le__eq_4,
[final] ).
cnf(i_0_1861,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X1) ),
cls_le__divide__eq_1,
[final] ).
cnf(i_0_1862,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
cls_le__divide__eq_4,
[final] ).
cnf(i_0_1863,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__frac__frac_0,
[final] ).
cnf(i_0_1864,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_1865,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Onoteq__reduce_1,
[final] ).
cnf(i_0_1866,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_one__less__power_0,
[final] ).
cnf(i_0_1867,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_1868,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_1869,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_1870,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ c_Wellfounded_Owf(X3,X1) ),
cls_wfE__min_0,
[final] ).
cnf(i_0_1871,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ c_Wellfounded_Owf(X3,X1) ),
cls_wf__eq__minimal_0,
[final] ).
cnf(i_0_1872,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_zero__less__divide__iff_5,
[final] ).
cnf(i_0_1873,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_even__less__0__iff_1,
[final] ).
cnf(i_0_1874,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_double__add__less__zero__iff__single__less__zero_1,
[final] ).
cnf(i_0_1875,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__neg__neg_0,
[final] ).
cnf(i_0_1876,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_divide__neg__neg_0,
[final] ).
cnf(i_0_1877,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_less__infI1_0,
[final] ).
cnf(i_0_1878,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_less__infI2_0,
[final] ).
cnf(i_0_1879,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__iff__diff__less__0_0,
[final] ).
cnf(i_0_1880,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
cls_pos__add__strict_0,
[final] ).
cnf(i_0_1881,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
cls_power__increasing__iff_0,
[final] ).
cnf(i_0_1882,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_Power_Opower__class_Opower(X4,X2,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X4)) ),
cls_power__le__imp__le__exp_0,
[final] ).
cnf(i_0_1883,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1) ),
cls_mult__right__le__imp__le_0,
[final] ).
cnf(i_0_1884,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
cls_mult__left__le__imp__le_0,
[final] ).
cnf(i_0_1885,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
cls_mult__le__cancel__left__pos_0,
[final] ).
cnf(i_0_1886,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
cls_minus__less__iff_1,
[final] ).
cnf(i_0_1887,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
cls_minus__less__iff_0,
[final] ).
cnf(i_0_1888,axiom,
( c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1)),X3,X1)),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ class_Ring__and__Field_Oring__1(X1) ),
cls_power__minus_0,
[final] ).
cnf(i_0_1889,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2))) ),
cls_zero__less__double__add__iff__zero__less__single__add_0,
[final] ).
cnf(i_0_1890,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X3,X4))) ),
cls_acc__induct__rule_2,
[final] ).
cnf(i_0_1891,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),c_Wellfounded_Oacc(X3,X4))) ),
cls_acc__induct_2,
[final] ).
cnf(i_0_1892,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__le__cancel__left__neg_0,
[final] ).
cnf(i_0_1893,axiom,
c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
cls_converse__Un_0,
[final] ).
cnf(i_0_1894,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X2,X1) ),
cls_divide__le__eq_5,
[final] ).
cnf(i_0_1895,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1) ),
cls_le__divide__eq_5,
[final] ).
cnf(i_0_1896,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__pos_0,
[final] ).
cnf(i_0_1897,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_add__pos__nonneg_0,
[final] ).
cnf(i_0_1898,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
cls_rtrancl__Un__rtrancl_0,
[final] ).
cnf(i_0_1899,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_neg__less__iff__less_0,
[final] ).
cnf(i_0_1900,axiom,
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X2,X5,X3)
| ~ c_Relation_Orefl__on(X1,X4,X3) ),
cls_refl__on__Un_0,
[final] ).
cnf(i_0_1901,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
cls_divide__le__eq_7,
[final] ).
cnf(i_0_1902,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
cls_le__divide__eq_7,
[final] ).
cnf(i_0_1903,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__mono_H_0,
[final] ).
cnf(i_0_1904,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__mono_0,
[final] ).
cnf(i_0_1905,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))) ),
cls_of__nat__less__iff_0,
[final] ).
cnf(i_0_1906,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
cls_Un__mono_0,
[final] ).
cnf(i_0_1907,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
cls_Int__mono_0,
[final] ).
cnf(i_0_1908,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1) ),
cls_le__divide__eq_0,
[final] ).
cnf(i_0_1909,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
cls_divide__le__eq_6,
[final] ).
cnf(i_0_1910,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4),X3,X1) ),
cls_divide__le__eq_0,
[final] ).
cnf(i_0_1911,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
cls_le__divide__eq_6,
[final] ).
cnf(i_0_1912,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_1913,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
cls_comm__semiring__class_Odistrib_0,
[final] ).
cnf(i_0_1914,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_1915,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_diff__divide__distrib_0,
[final] ).
cnf(i_0_1916,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4))
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_add__divide__distrib_0,
[final] ).
cnf(i_0_1917,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Set_Oinsert(X4,X5,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X3,X4)),hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X2) ),
cls_setsum__insert_0,
[final] ).
cnf(i_0_1918,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
cls_add__strict__increasing_0,
[final] ).
cnf(i_0_1919,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
cls_mult__imp__div__pos__le_0,
[final] ).
cnf(i_0_1920,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4)) ),
cls_mult__imp__le__div__pos_0,
[final] ).
cnf(i_0_1921,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1))) ),
cls_insertE_0,
[final] ).
cnf(i_0_1922,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Un__Int__distrib2_0,
[final] ).
cnf(i_0_1923,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Int__Un__distrib2_0,
[final] ).
cnf(i_0_1924,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Un__Int__distrib_0,
[final] ).
cnf(i_0_1925,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Int__Un__distrib_0,
[final] ).
cnf(i_0_1926,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X1),tc_fun(X3,tc_bool)) ),
cls_Compl__subset__Compl__iff_0,
[final] ).
cnf(i_0_1927,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2)))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_zero__less__divide__1__iff_1,
[final] ).
cnf(i_0_1928,axiom,
c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),
cls_Domain__Un__eq_0,
[final] ).
cnf(i_0_1929,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing2_0,
[final] ).
cnf(i_0_1930,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
cls_subset__singletonD_0,
[final] ).
cnf(i_0_1931,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
cls_sup1E_0,
[final] ).
cnf(i_0_1932,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_0,
[final] ).
cnf(i_0_1933,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_1,
[final] ).
cnf(i_0_1934,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X1,tc_fun(X3,tc_bool)) ),
cls_Un__Int__assoc__eq_1,
[final] ).
cnf(i_0_1935,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_UnCI_1,
[final] ).
cnf(i_0_1936,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
cls_UnCI_0,
[final] ).
cnf(i_0_1937,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
cls_card__gt__0__iff_0,
[final] ).
cnf(i_0_1938,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X2,X1) ),
cls_divide__le__eq_2,
[final] ).
cnf(i_0_1939,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1) ),
cls_le__divide__eq_2,
[final] ).
cnf(i_0_1940,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_power__increasing__iff_1,
[final] ).
cnf(i_0_1941,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_neg__less__0__iff__less_0,
[final] ).
cnf(i_0_1942,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
cls_Int__insert__left_0,
[final] ).
cnf(i_0_1943,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
cls_Int__insert__right_0,
[final] ).
cnf(i_0_1944,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_mult__le__cancel__left__pos_1,
[final] ).
cnf(i_0_1945,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_zero__less__power_0,
[final] ).
cnf(i_0_1946,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
cls_inf1E_0,
[final] ).
cnf(i_0_1947,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
cls_inf1E_1,
[final] ).
cnf(i_0_1948,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X1,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)),
cls_Compl__Un_0,
[final] ).
cnf(i_0_1949,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X1,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool)),
cls_Compl__Int_0,
[final] ).
cnf(i_0_1950,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X4,X3,tc_nat) ),
cls_power__decreasing_0,
[final] ).
cnf(i_0_1951,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_zero__less__double__add__iff__zero__less__single__add_1,
[final] ).
cnf(i_0_1952,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I2_J_0,
[final] ).
cnf(i_0_1953,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__divide_0,
[final] ).
cnf(i_0_1954,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__power__divide_0,
[final] ).
cnf(i_0_1955,axiom,
( X2 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_power__eq__imp__eq__base_0,
[final] ).
cnf(i_0_1956,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_mult__le__cancel__left__neg_1,
[final] ).
cnf(i_0_1957,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_power__mult__distrib_0,
[final] ).
cnf(i_0_1958,axiom,
( c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__mul_0,
[final] ).
cnf(i_0_1959,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
cls_add__sup__distrib__right_0,
[final] ).
cnf(i_0_1960,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),X4) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,
[final] ).
cnf(i_0_1961,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
cls_add__inf__distrib__right_0,
[final] ).
cnf(i_0_1962,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)),X4) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,
[final] ).
cnf(i_0_1963,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
cls_doubleton__eq__iff_4,
[final] ).
cnf(i_0_1964,axiom,
( c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
| ~ c_Wellfounded_Owf(X1,X3) ),
cls_wf__inv__image_0,
[final] ).
cnf(i_0_1965,axiom,
( c_Relation_Osym(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
| ~ c_Relation_Osym(X1,X3) ),
cls_sym__inv__image_0,
[final] ).
cnf(i_0_1966,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
cls_singleton__iff_1,
[final] ).
cnf(i_0_1967,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__frac__num_0,
[final] ).
cnf(i_0_1968,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__d_0,
[final] ).
cnf(i_0_1969,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_1970,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_1971,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X4,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_divide__le__eq_3,
[final] ).
cnf(i_0_1972,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4),X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__divide__eq_3,
[final] ).
cnf(i_0_1973,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_neg__less__iff__less_1,
[final] ).
cnf(i_0_1974,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)) ),
cls_class__ringb_Oadd__scale__eq__noteq_0,
[final] ).
cnf(i_0_1975,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_lessequals(X3,X5,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X5,X1),X4,X1) ),
cls_power__le__dvd_0,
[final] ).
cnf(i_0_1976,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__iff__not__equal_0,
[final] ).
cnf(i_0_1977,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3),
cls_insert__inter__insert_0,
[final] ).
cnf(i_0_1978,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5),X1) ),
cls_le__add__right__mono_0,
[final] ).
cnf(i_0_1979,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__supI1_0,
[final] ).
cnf(i_0_1980,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_less__supI2_0,
[final] ).
cnf(i_0_1981,axiom,
( c_lessequals(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
cls_Domain__mono_0,
[final] ).
cnf(i_0_1982,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3)) ),
cls_of__nat__less__iff_1,
[final] ).
cnf(i_0_1983,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
cls_insertCI_0,
[final] ).
cnf(i_0_1984,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
cls_insert__iff_2,
[final] ).
cnf(i_0_1985,axiom,
( c_Finite__Set_Osetprod(X2,X5,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(X2,X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
cls_setprod__zero__iff_2,
[final] ).
cnf(i_0_1986,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_neg__less__0__iff__less_1,
[final] ).
cnf(i_0_1987,axiom,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
cls_sym__Un__converse_0,
[final] ).
cnf(i_0_1988,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__eq__zero__iff_2,
[final] ).
cnf(i_0_1989,axiom,
( c_Finite__Set_Osetprod(X2,X5,X4,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(X2,X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
cls_setprod__zero_0,
[final] ).
cnf(i_0_1990,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_less__minus__iff_1,
[final] ).
cnf(i_0_1991,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_less__minus__iff_0,
[final] ).
cnf(i_0_1992,axiom,
( c_Transitive__Closure_Ortrancl(X1,X2) = c_Transitive__Closure_Ortrancl(X3,X2)
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_rtrancl__subset_0,
[final] ).
cnf(i_0_1993,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Osgn__class_Osgn(X2,X1)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_sgn__less_0,
[final] ).
cnf(i_0_1994,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1) ),
cls_dvd__mult__cancel__right_0,
[final] ).
cnf(i_0_1995,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1) ),
cls_dvd__mult__cancel__left_0,
[final] ).
cnf(i_0_1996,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
cls_Un__least_0,
[final] ).
cnf(i_0_1997,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
cls_Un__subset__iff_2,
[final] ).
cnf(i_0_1998,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
cls_Int__subset__iff_2,
[final] ).
cnf(i_0_1999,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
cls_Int__greatest_0,
[final] ).
cnf(i_0_2000,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
cls_insert__subset_2,
[final] ).
cnf(i_0_2001,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
cls_subset__insert_0,
[final] ).
cnf(i_0_2002,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
cls_subset__insert__iff_1,
[final] ).
cnf(i_0_2003,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_ComplI_0,
[final] ).
cnf(i_0_2004,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__nonpos__pos_0,
[final] ).
cnf(i_0_2005,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__nonneg__pos_0,
[final] ).
cnf(i_0_2006,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
cls_finite__UNIV__card__ge__0_0,
[final] ).
cnf(i_0_2007,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
cls_add__le__cancel__right_0,
[final] ).
cnf(i_0_2008,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
cls_add__le__cancel__left_0,
[final] ).
cnf(i_0_2009,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Un__assoc_0,
[final] ).
cnf(i_0_2010,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Int__assoc_0,
[final] ).
cnf(i_0_2011,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Un__left__commute_0,
[final] ).
cnf(i_0_2012,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Int__left__commute_0,
[final] ).
cnf(i_0_2013,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
cls_Compl__anti__mono_0,
[final] ).
cnf(i_0_2014,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X1,tc_bool)) ),
cls_Compl__subset__Compl__iff_1,
[final] ).
cnf(i_0_2015,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
cls_antisym__reflcl_0,
[final] ).
cnf(i_0_2016,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_power__mono_0,
[final] ).
cnf(i_0_2017,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_divide__right__mono_0,
[final] ).
cnf(i_0_2018,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_divide__right__mono__neg_0,
[final] ).
cnf(i_0_2019,axiom,
( c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(X3,X4,tc_nat) ),
cls_power__increasing_0,
[final] ).
cnf(i_0_2020,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__nonneg__neg_0,
[final] ).
cnf(i_0_2021,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__nonpos__neg_0,
[final] ).
cnf(i_0_2022,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_neg__0__less__iff__less_0,
[final] ).
cnf(i_0_2023,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__right__le__one__le_0,
[final] ).
cnf(i_0_2024,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__left__le__one__le_0,
[final] ).
cnf(i_0_2025,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_2026,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_2027,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_mult__mono1_0,
[final] ).
cnf(i_0_2028,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_mult__left__mono_0,
[final] ).
cnf(i_0_2029,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__right__mono_0,
[final] ).
cnf(i_0_2030,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_mult__left__mono__neg_0,
[final] ).
cnf(i_0_2031,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_mult__right__mono__neg_0,
[final] ).
cnf(i_0_2032,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5)) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_2033,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_2034,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_lessequals(X3,X5,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__power__le_0,
[final] ).
cnf(i_0_2035,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I3_J_0,
[final] ).
cnf(i_0_2036,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2))) ),
cls_of__nat__0__less__iff_0,
[final] ).
cnf(i_0_2037,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
cls_Un__subset__iff_0,
[final] ).
cnf(i_0_2038,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
cls_Un__subset__iff_1,
[final] ).
cnf(i_0_2039,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
cls_Int__subset__iff_0,
[final] ).
cnf(i_0_2040,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
cls_Int__subset__iff_1,
[final] ).
cnf(i_0_2041,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_mult__dvd__mono_0,
[final] ).
cnf(i_0_2042,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__mono_0,
[final] ).
cnf(i_0_2043,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
cls_wf__induct__rule_1,
[final] ).
cnf(i_0_2044,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
cls_wf__def_1,
[final] ).
cnf(i_0_2045,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
cls_tfl__wf__induct_1,
[final] ).
cnf(i_0_2046,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X3,X4)))
| ~ c_Wellfounded_Owf(X3,X4) ),
cls_wf__induct_1,
[final] ).
cnf(i_0_2047,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib2_0,
[final] ).
cnf(i_0_2048,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib2_0,
[final] ).
cnf(i_0_2049,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib1_0,
[final] ).
cnf(i_0_2050,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib1_0,
[final] ).
cnf(i_0_2051,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_of__nat__less__0__iff_0,
[final] ).
cnf(i_0_2052,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Power_Opower__class_Opower(X2,X3,X1)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__commutes_0,
[final] ).
cnf(i_0_2053,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_add__eq__inf__sup_0,
[final] ).
cnf(i_0_2054,axiom,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_inf1I_0,
[final] ).
cnf(i_0_2055,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X4)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__divide__mult__cancel__left_0,
[final] ).
cnf(i_0_2056,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X4)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_mult__divide__mult__cancel__right_0,
[final] ).
cnf(i_0_2057,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)) ),
cls_disjoint__eq__subset__Compl_1,
[final] ).
cnf(i_0_2058,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2),X2,X3) = c_Relation_ODomain(X1,X2,X3),
inference(rw,[status(thm)],[i_0_1396,c_0_1374]),
[final] ).
cnf(i_0_2059,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2)),c_Wellfounded_Oacc(X1,X2))) ),
cls_acc__wfI_0,
[final] ).
cnf(i_0_2060,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2)),c_Wellfounded_Oacc(X1,X2))) ),
cls_wf__acc__iff_1,
[final] ).
cnf(i_0_2061,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Osgn__class_Osgn(X2,X1))) ),
cls_sgn__greater_0,
[final] ).
cnf(i_0_2062,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_rtrancl__subset__rtrancl_0,
[final] ).
cnf(i_0_2063,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
cls_add__sup__distrib__left_0,
[final] ).
cnf(i_0_2064,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,
[final] ).
cnf(i_0_2065,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
cls_add__inf__distrib__left_0,
[final] ).
cnf(i_0_2066,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,
[final] ).
cnf(i_0_2067,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_2068,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_2069,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_2070,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_2071,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_2072,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_2073,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_2074,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_2075,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_2076,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Osgn__class_Osgn(X2,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_sgn__less_1,
[final] ).
cnf(i_0_2077,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
cls_insert__code_0,
[final] ).
cnf(i_0_2078,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__two_0,
[final] ).
cnf(i_0_2079,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_less__minus__self__iff_0,
[final] ).
cnf(i_0_2080,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
cls_subset__insert_1,
[final] ).
cnf(i_0_2081,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
cls_subset__insert__iff_2,
[final] ).
cnf(i_0_2082,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
cls_insert__mono_0,
[final] ).
cnf(i_0_2083,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_neg__0__less__iff__less_1,
[final] ).
cnf(i_0_2084,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
cls_set__mp_0,
[final] ).
cnf(i_0_2085,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
cls_subsetD_0,
[final] ).
cnf(i_0_2086,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
cls_set__rev__mp_0,
[final] ).
cnf(i_0_2087,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
cls_subset__iff_0,
[final] ).
cnf(i_0_2088,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) ),
cls_insert__subset_0,
[final] ).
cnf(i_0_2089,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Osgn__class_Osgn(X2,X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_sgn__greater_1,
[final] ).
cnf(i_0_2090,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_1,
[final] ).
cnf(i_0_2091,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_0,
[final] ).
cnf(i_0_2092,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_3,
[final] ).
cnf(i_0_2093,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1) ),
cls_zero__le__divide__iff_0,
[final] ).
cnf(i_0_2094,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),X1) ),
cls_zero__le__divide__iff_3,
[final] ).
cnf(i_0_2095,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1) ),
cls_zero__le__divide__iff_2,
[final] ).
cnf(i_0_2096,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2),X1) ),
cls_zero__le__divide__iff_1,
[final] ).
cnf(i_0_2097,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_2,
[final] ).
cnf(i_0_2098,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
cls_Un__insert__left_0,
[final] ).
cnf(i_0_2099,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
cls_Un__insert__right_0,
[final] ).
cnf(i_0_2100,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I4_J_0,
[final] ).
cnf(i_0_2101,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X4))
| hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| X2 = X4
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
cls_insert__ident_0,
[final] ).
cnf(i_0_2102,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Power_Opower__class_Opower(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),X2)) ),
cls_power__inject__exp_0,
[final] ).
cnf(i_0_2103,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_1,
[final] ).
cnf(i_0_2104,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_0,
[final] ).
cnf(i_0_2105,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_3,
[final] ).
cnf(i_0_2106,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
cls_zero__le__mult__iff_0,
[final] ).
cnf(i_0_2107,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1) ),
cls_zero__le__mult__iff_3,
[final] ).
cnf(i_0_2108,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) ),
cls_zero__le__mult__iff_2,
[final] ).
cnf(i_0_2109,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1) ),
cls_zero__le__mult__iff_1,
[final] ).
cnf(i_0_2110,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_2,
[final] ).
cnf(i_0_2111,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_2112,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_rtrancl__mono_0,
[final] ).
cnf(i_0_2113,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_sup1CI_1,
[final] ).
cnf(i_0_2114,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_sup1CI_0,
[final] ).
cnf(i_0_2115,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)))
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
cls_of__nat__0__less__iff_1,
[final] ).
cnf(i_0_2116,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X3,t_a))) ),
cls_acc_Oinduct_2,
[final] ).
cnf(i_0_2117,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X2),c_Wellfounded_Oacc(X3,t_a))) ),
cls_acc_Oinducts_2,
[final] ).
cnf(i_0_2118,axiom,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
cls_bex__empty_0,
[final] ).
cnf(i_0_2119,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_less__minus__self__iff_1,
[final] ).
cnf(i_0_2120,axiom,
c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
cls_refl__reflcl_0,
[final] ).
cnf(i_0_2121,axiom,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_disjoint__eq__subset__Compl_0,
[final] ).
cnf(i_0_2122,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),X1) ),
cls_zero__le__divide__1__iff_0,
[final] ).
cnf(i_0_2123,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__1__iff_0,
[final] ).
cnf(i_0_2124,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__iff_5,
[final] ).
cnf(i_0_2125,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_divide__le__0__iff_4,
[final] ).
cnf(i_0_2126,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__divide__iff_4,
[final] ).
cnf(i_0_2127,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__le__divide__iff_5,
[final] ).
cnf(i_0_2128,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X1),X4)) ),
cls_Int__insert__left_1,
[final] ).
cnf(i_0_2129,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X1)) ),
cls_Int__insert__right_1,
[final] ).
cnf(i_0_2130,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ c_lessequals(X2,X4,X1) ),
cls_order__le__less__trans_0,
[final] ).
cnf(i_0_2131,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_order__less__le__trans_0,
[final] ).
cnf(i_0_2132,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_xt1_I7_J_0,
[final] ).
cnf(i_0_2133,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I8_J_0,
[final] ).
cnf(i_0_2134,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
cls_insert__subset_1,
[final] ).
cnf(i_0_2135,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),c_Power_Opower__class_Opower(X2,X3,X1)) = c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),X3,X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__one__over_0,
[final] ).
cnf(i_0_2136,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),
cls_subset__Compl__self__eq_1,
[final] ).
cnf(i_0_2137,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__nonneg__nonpos2_0,
[final] ).
cnf(i_0_2138,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__nonpos__nonneg_0,
[final] ).
cnf(i_0_2139,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_split__mult__neg__le_1,
[final] ).
cnf(i_0_2140,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__nonneg__nonpos_0,
[final] ).
cnf(i_0_2141,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_split__mult__neg__le_0,
[final] ).
cnf(i_0_2142,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_5,
[final] ).
cnf(i_0_2143,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__le__0__iff_4,
[final] ).
cnf(i_0_2144,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__nonpos_0,
[final] ).
cnf(i_0_2145,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__nonneg__nonneg_0,
[final] ).
cnf(i_0_2146,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_split__mult__pos__le_0,
[final] ).
cnf(i_0_2147,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__mult__iff_4,
[final] ).
cnf(i_0_2148,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__nonneg_0,
[final] ).
cnf(i_0_2149,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_split__mult__pos__le_1,
[final] ).
cnf(i_0_2150,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__nonpos__nonpos_0,
[final] ).
cnf(i_0_2151,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__le__mult__iff_5,
[final] ).
cnf(i_0_2152,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__power__same_0,
[final] ).
cnf(i_0_2153,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
cls_ball__empty_0,
[final] ).
cnf(i_0_2154,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_lessequals(X3,X4,tc_nat) ),
cls_le__imp__power__dvd_0,
[final] ).
cnf(i_0_2155,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__eq__neg_1,
[final] ).
cnf(i_0_2156,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
cls_subset__Compl__self__eq_0,
[final] ).
cnf(i_0_2157,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_add__increasing2_0,
[final] ).
cnf(i_0_2158,axiom,
( c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__increasing_0,
[final] ).
cnf(i_0_2159,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
cls_dvd__mult__cancel__left_2,
[final] ).
cnf(i_0_2160,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult__cancel__right_2,
[final] ).
cnf(i_0_2161,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__left__mono_0,
[final] ).
cnf(i_0_2162,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__le__cancel__left_1,
[final] ).
cnf(i_0_2163,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__right__mono_0,
[final] ).
cnf(i_0_2164,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__cancel__right_1,
[final] ).
cnf(i_0_2165,axiom,
c_Relation_OImage(c_Relation_OId__on(X1,X2),X3,X2,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),
cls_Image__Id__on_0,
[final] ).
cnf(i_0_2166,axiom,
( hAPP(X2,X4) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_Finite__Set_Osetsum(X1,tc_nat),X2),X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
cls_setsum__eq__0__iff_0,
[final] ).
cnf(i_0_2167,axiom,
( c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Relation_Osingle__valued(X4,X2,X3)
| ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
cls_single__valued__subset_0,
[final] ).
cnf(i_0_2168,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_2169,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_2170,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_2171,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_2172,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1))))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_less__add__one_0,
[final] ).
cnf(i_0_2173,axiom,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
cls_insert__is__Un_0,
[final] ).
cnf(i_0_2174,axiom,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2),tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
cls_card__insert__le_0,
[final] ).
cnf(i_0_2175,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__sup__iff_2,
[final] ).
cnf(i_0_2176,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_sup__least_0,
[final] ).
cnf(i_0_2177,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__supI_0,
[final] ).
cnf(i_0_2178,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__infI_0,
[final] ).
cnf(i_0_2179,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__inf__iff_2,
[final] ).
cnf(i_0_2180,axiom,
( c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_inf__greatest_0,
[final] ).
cnf(i_0_2181,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_sup__eq__neg__inf_0,
[final] ).
cnf(i_0_2182,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_inf__eq__neg__sup_0,
[final] ).
cnf(i_0_2183,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__diff_0,
[final] ).
cnf(i_0_2184,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__add_0,
[final] ).
cnf(i_0_2185,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3)) ),
cls_dvd__power_0,
[final] ).
cnf(i_0_2186,axiom,
( X1 = X3
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
cls_singleton__inject_0,
[final] ).
cnf(i_0_2187,axiom,
( c_lessequals(c_Wellfounded_Oacc(X1,X2),c_Wellfounded_Oacc(X3,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_acc__subset_0,
[final] ).
cnf(i_0_2188,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
cls_emptyE_0,
[final] ).
cnf(i_0_2189,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
cls_empty__iff_0,
[final] ).
cnf(i_0_2190,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
cls_ex__in__conv_0,
[final] ).
cnf(i_0_2191,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__assoc_0,
[final] ).
cnf(i_0_2192,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I6_J_0,
[final] ).
cnf(i_0_2193,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__assoc_0,
[final] ).
cnf(i_0_2194,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I2_J_0,
[final] ).
cnf(i_0_2195,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__commute_0,
[final] ).
cnf(i_0_2196,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I7_J_0,
[final] ).
cnf(i_0_2197,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__commute_0,
[final] ).
cnf(i_0_2198,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I3_J_0,
[final] ).
cnf(i_0_2199,axiom,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
cls_vimage__UNIV_0,
[final] ).
cnf(i_0_2200,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_vimage__empty_0,
[final] ).
cnf(i_0_2201,axiom,
c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_Image__empty_0,
[final] ).
cnf(i_0_2202,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__insert__if_0,
[final] ).
cnf(i_0_2203,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_0,
[final] ).
cnf(i_0_2204,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_0,
[final] ).
cnf(i_0_2205,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_4,
[final] ).
cnf(i_0_2206,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2)),X2)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_4,
[final] ).
cnf(i_0_2207,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
cls_insert__commute_0,
[final] ).
cnf(i_0_2208,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
cls_subset__trans_0,
[final] ).
cnf(i_0_2209,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
cls_insertCI_1,
[final] ).
cnf(i_0_2210,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
cls_insertI1_0,
[final] ).
cnf(i_0_2211,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
cls_insert__iff_1,
[final] ).
cnf(i_0_2212,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__iff__diff__le__0_1,
[final] ).
cnf(i_0_2213,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) ),
cls_le__eq__neg_0,
[final] ).
cnf(i_0_2214,axiom,
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X2,X3)
| ~ c_Relation_Osym(X1,X3) ),
cls_sym__Un_0,
[final] ).
cnf(i_0_2215,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
cls_le__supE_0,
[final] ).
cnf(i_0_2216,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X1),X3,X1) ),
cls_le__sup__iff_0,
[final] ).
cnf(i_0_2217,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
cls_le__supE_1,
[final] ).
cnf(i_0_2218,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X1),X3,X1) ),
cls_le__sup__iff_1,
[final] ).
cnf(i_0_2219,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
cls_le__inf__iff_0,
[final] ).
cnf(i_0_2220,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1),X1) ),
cls_le__infE_0,
[final] ).
cnf(i_0_2221,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
cls_le__inf__iff_1,
[final] ).
cnf(i_0_2222,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X1),X1) ),
cls_le__infE_1,
[final] ).
cnf(i_0_2223,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_2224,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_2225,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_2226,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_2227,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__compl_0,
[final] ).
cnf(i_0_2228,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X3),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_dvd__mult__cancel__left_1,
[final] ).
cnf(i_0_2229,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__minus__cancel_0,
[final] ).
cnf(i_0_2230,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_sup__eq__if_0,
[final] ).
cnf(i_0_2231,axiom,
( X1 = X2
| ~ c_lessequals(c_Finite__Set_Ocard(X2,X3),c_Finite__Set_Ocard(X1,X3),tc_nat)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__seteq_0,
[final] ).
cnf(i_0_2232,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ c_lessequals(X5,X4,X1) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_2233,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_2234,axiom,
( c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_setprod__empty_0,
[final] ).
cnf(i_0_2235,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X3,X1) ),
cls_dvd__mult__left_0,
[final] ).
cnf(i_0_2236,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2),X3,X1) ),
cls_dvd__mult__right_0,
[final] ).
cnf(i_0_2237,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
cls_total__on__converse_0,
[final] ).
cnf(i_0_2238,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
cls_refl__on__converse_0,
[final] ).
cnf(i_0_2239,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
cls_Un__left__absorb_0,
[final] ).
cnf(i_0_2240,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
cls_Int__left__absorb_0,
[final] ).
cnf(i_0_2241,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
cls_subset__insertI2_0,
[final] ).
cnf(i_0_2242,axiom,
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
cls_antisym__reflcl_1,
[final] ).
cnf(i_0_2243,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_divide__le__0__1__iff_1,
[final] ).
cnf(i_0_2244,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Oone__class_Oone(X1)),X2),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__divide__1__iff_1,
[final] ).
cnf(i_0_2245,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__reflcl_0,
[final] ).
cnf(i_0_2246,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__add__distrib_0,
[final] ).
cnf(i_0_2247,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add_0,
[final] ).
cnf(i_0_2248,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_0,
[final] ).
cnf(i_0_2249,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_1,
[final] ).
cnf(i_0_2250,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_insert__code_2,
[final] ).
cnf(i_0_2251,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),c_HOL_Ozero__class_Ozero(X1)),X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_dvd__mult__cancel__right_1,
[final] ).
cnf(i_0_2252,axiom,
( X5 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X5) ),
cls_frac__eq__eq_0,
[final] ).
cnf(i_0_2253,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X4),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5) ),
cls_frac__eq__eq_1,
[final] ).
cnf(i_0_2254,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X3) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_0,
[final] ).
cnf(i_0_2255,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3) = X2
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_3,
[final] ).
cnf(i_0_2256,axiom,
( X2 = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_0,
[final] ).
cnf(i_0_2257,axiom,
( X2 = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_3,
[final] ).
cnf(i_0_2258,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
cls_finite__Un_0,
[final] ).
cnf(i_0_2259,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)),X2) ),
cls_finite__Un_1,
[final] ).
cnf(i_0_2260,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2)) ),
cls_nat__less__cases_0,
[final] ).
cnf(i_0_2261,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Ofinite(X3,X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_setprod__infinite_0,
[final] ).
cnf(i_0_2262,axiom,
( c_Finite__Set_Osetprod(X2,X3,X4,X1) = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Ofinite(X3,X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_setprod__def_1,
[final] ).
cnf(i_0_2263,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4)
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != X3 ),
cls_add__cancel__end_0,
[final] ).
cnf(i_0_2264,axiom,
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__compl_1,
[final] ).
cnf(i_0_2265,axiom,
( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_one__le__power_0,
[final] ).
cnf(i_0_2266,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__power_0,
[final] ).
cnf(i_0_2267,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__eq__imp_0,
[final] ).
cnf(i_0_2268,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),X2)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_eq__divide__imp_0,
[final] ).
cnf(i_0_2269,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_neg__le__iff__le_0,
[final] ).
cnf(i_0_2270,axiom,
( c_lessequals(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3),X1) ),
cls_of__nat__le__iff_0,
[final] ).
cnf(i_0_2271,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_1,
[final] ).
cnf(i_0_2272,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_1,
[final] ).
cnf(i_0_2273,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup_0,
[final] ).
cnf(i_0_2274,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_neg__sup__eq__inf_0,
[final] ).
cnf(i_0_2275,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf_0,
[final] ).
cnf(i_0_2276,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_neg__inf__eq__sup_0,
[final] ).
cnf(i_0_2277,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_2278,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_2279,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X1,X2))) ),
cls_card__gt__0__iff_1,
[final] ).
cnf(i_0_2280,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_less__le__not__le_1,
[final] ).
cnf(i_0_2281,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_linorder__antisym__conv2_1,
[final] ).
cnf(i_0_2282,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_linorder__not__le_1,
[final] ).
cnf(i_0_2283,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ c_lessequals(X3,X2,X1) ),
cls_linorder__not__less_1,
[final] ).
cnf(i_0_2284,axiom,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
cls_card__eq__UNIV__imp__eq__UNIV_0,
[final] ).
cnf(i_0_2285,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_2286,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_minus__divide__left_0,
[final] ).
cnf(i_0_2287,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__diff__le__0_0,
[final] ).
cnf(i_0_2288,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_less__le__not__le_2,
[final] ).
cnf(i_0_2289,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__infI1_0,
[final] ).
cnf(i_0_2290,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_le__infI2_0,
[final] ).
cnf(i_0_2291,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__supI1_0,
[final] ).
cnf(i_0_2292,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_le__supI2_0,
[final] ).
cnf(i_0_2293,axiom,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
cls_Image__Id_0,
[final] ).
cnf(i_0_2294,axiom,
( c_HOL_Osgn__class_Osgn(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Osgn__class_Osgn(X2,X1)),c_HOL_Osgn__class_Osgn(X3,X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sgn__times_0,
[final] ).
cnf(i_0_2295,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__mult2_0,
[final] ).
cnf(i_0_2296,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__mult_0,
[final] ).
cnf(i_0_2297,axiom,
( c_lessequals(c_Finite__Set_Ocard(X1,X2),c_Finite__Set_Ocard(X3,X2),tc_nat)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_card__mono_0,
[final] ).
cnf(i_0_2298,axiom,
( c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
cls_total__on__converse_1,
[final] ).
cnf(i_0_2299,axiom,
( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
cls_refl__on__converse_1,
[final] ).
cnf(i_0_2300,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_set__eq__subset_2,
[final] ).
cnf(i_0_2301,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_equalityI_0,
[final] ).
cnf(i_0_2302,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
cls_minus__le__iff_1,
[final] ).
cnf(i_0_2303,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
cls_minus__le__iff_0,
[final] ).
cnf(i_0_2304,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_le__minus__iff_1,
[final] ).
cnf(i_0_2305,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_le__minus__iff_0,
[final] ).
cnf(i_0_2306,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1,
[final] ).
cnf(i_0_2307,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
cls_le__funD_0,
[final] ).
cnf(i_0_2308,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_antisym__subset_0,
[final] ).
cnf(i_0_2309,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Oacyclic(X3,X2) ),
cls_acyclic__subset_0,
[final] ).
cnf(i_0_2310,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Owf(X3,X2) ),
cls_wf__subset_0,
[final] ).
cnf(i_0_2311,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[i_0_1397,c_0_1374]),
[final] ).
cnf(i_0_2312,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0,
[final] ).
cnf(i_0_2313,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__end_1,
[final] ).
cnf(i_0_2314,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osgn__if(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_sgn__if_1,
[final] ).
cnf(i_0_2315,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X1),X2))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_comm__monoid__add_Ononempty__iff_2,
[final] ).
cnf(i_0_2316,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
cls_dvd__trans_0,
[final] ).
cnf(i_0_2317,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__trans_0,
[final] ).
cnf(i_0_2318,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0,
[final] ).
cnf(i_0_2319,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
cls_sgn__neg_0,
[final] ).
cnf(i_0_2320,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__partition2_0,
[final] ).
cnf(i_0_2321,axiom,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__disjoint2_0,
[final] ).
cnf(i_0_2322,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
cls_Compl__partition_0,
[final] ).
cnf(i_0_2323,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Compl__disjoint_0,
[final] ).
cnf(i_0_2324,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_minus__divide__divide_0,
[final] ).
cnf(i_0_2325,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Ozero__class_Ozero(X1))) ),
cls_not__one__less__zero_0,
[final] ).
cnf(i_0_2326,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
cls_subset__empty_0,
[final] ).
cnf(i_0_2327,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
cls_sgn__pos_0,
[final] ).
cnf(i_0_2328,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__minus__divide__divide_0,
[final] ).
cnf(i_0_2329,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
cls_Int__lower1_0,
[final] ).
cnf(i_0_2330,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
cls_Int__lower2_0,
[final] ).
cnf(i_0_2331,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Un__upper1_0,
[final] ).
cnf(i_0_2332,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Un__upper2_0,
[final] ).
cnf(i_0_2333,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_order__less__imp__le_0,
[final] ).
cnf(i_0_2334,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_order__le__less_1,
[final] ).
cnf(i_0_2335,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_sup__eq__if_1,
[final] ).
cnf(i_0_2336,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_minus__divide__right_0,
[final] ).
cnf(i_0_2337,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_2338,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_2339,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_2340,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__minus__divide__right_0,
[final] ).
cnf(i_0_2341,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__neg__le_0,
[final] ).
cnf(i_0_2342,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__le__0__iff__le_0,
[final] ).
cnf(i_0_2343,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_neg__0__le__iff__le_0,
[final] ).
cnf(i_0_2344,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
cls_insert__absorb_0,
[final] ).
cnf(i_0_2345,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_2346,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_2347,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_2348,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_2349,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_2350,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__idem_0,
[final] ).
cnf(i_0_2351,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I8_J_0,
[final] ).
cnf(i_0_2352,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__idem_0,
[final] ).
cnf(i_0_2353,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I4_J_0,
[final] ).
cnf(i_0_2354,axiom,
( c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X2,X3,tc_nat) ),
cls_of__nat__le__iff_1,
[final] ).
cnf(i_0_2355,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_le__trans_0,
[final] ).
cnf(i_0_2356,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_2357,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
cls_insert__absorb2_0,
[final] ).
cnf(i_0_2358,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) ),
cls_neg__less__eq__nonneg_0,
[final] ).
cnf(i_0_2359,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) ),
cls_minus__le__self__iff_0,
[final] ).
cnf(i_0_2360,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_less__eq__neg__nonpos_0,
[final] ).
cnf(i_0_2361,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_le__minus__self__iff_0,
[final] ).
cnf(i_0_2362,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2) = X1,
inference(rw,[status(thm)],[i_0_1398,c_0_1374]),
[final] ).
cnf(i_0_2363,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_2364,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_compl__unique_0,
[final] ).
cnf(i_0_2365,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
cls_finite__UnI_0,
[final] ).
cnf(i_0_2366,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
cls_finite__Un_2,
[final] ).
cnf(i_0_2367,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0,
[final] ).
cnf(i_0_2368,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
cls_UNIV__I_0,
[final] ).
cnf(i_0_2369,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X1,X2)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
cls_card__gt__0__iff_2,
[final] ).
cnf(i_0_2370,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
cls_Compl__eq__Compl__iff_0,
[final] ).
cnf(i_0_2371,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1) ),
cls_minus__dvd__iff_0,
[final] ).
cnf(i_0_2372,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) ),
cls_dvd__minus__iff_0,
[final] ).
cnf(i_0_2373,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Un__empty_2,
[final] ).
cnf(i_0_2374,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_antisym__converse_0,
[final] ).
cnf(i_0_2375,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_acyclic__converse_0,
[final] ).
cnf(i_0_2376,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
cls_finite__insert_0,
[final] ).
cnf(i_0_2377,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_sym__converse_0,
[final] ).
cnf(i_0_2378,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0,
[final] ).
cnf(i_0_2379,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I12_J_0,
[final] ).
cnf(i_0_2380,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__less_0,
[final] ).
cnf(i_0_2381,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__less__le_2,
[final] ).
cnf(i_0_2382,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__neq__trans_0,
[final] ).
cnf(i_0_2383,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__neq__le__trans_0,
[final] ).
cnf(i_0_2384,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv1_0,
[final] ).
cnf(i_0_2385,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv2_0,
[final] ).
cnf(i_0_2386,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__le__0__iff__le_1,
[final] ).
cnf(i_0_2387,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__0__le__iff__le_1,
[final] ).
cnf(i_0_2388,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_termination__basic__simps_I5_J_0,
[final] ).
cnf(i_0_2389,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_nat__less__le_0,
[final] ).
cnf(i_0_2390,axiom,
c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),
cls_rtrancl__converse_0,
[final] ).
cnf(i_0_2391,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
cls_subset__Un__eq_1,
[final] ).
cnf(i_0_2392,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
cls_Un__absorb2_0,
[final] ).
cnf(i_0_2393,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_Un__absorb1_0,
[final] ).
cnf(i_0_2394,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_Int__absorb2_0,
[final] ).
cnf(i_0_2395,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
cls_Int__absorb1_0,
[final] ).
cnf(i_0_2396,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_rev__predicate1D_0,
[final] ).
cnf(i_0_2397,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
cls_predicate1D_0,
[final] ).
cnf(i_0_2398,plain,
c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId(X1),X1,X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[i_0_1399,c_0_1374]),
[final] ).
cnf(i_0_2399,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
cls_mem__def_0,
[final] ).
cnf(i_0_2400,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0,
[final] ).
cnf(i_0_2401,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__less__eq__nonneg_1,
[final] ).
cnf(i_0_2402,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_minus__le__self__iff_1,
[final] ).
cnf(i_0_2403,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__eq__neg__nonpos_1,
[final] ).
cnf(i_0_2404,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__minus__self__iff_1,
[final] ).
cnf(i_0_2405,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_2406,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_Un__empty_0,
[final] ).
cnf(i_0_2407,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_Un__empty_1,
[final] ).
cnf(i_0_2408,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
cls_nat__neq__iff_0,
[final] ).
cnf(i_0_2409,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
cls_linorder__neqE__nat_0,
[final] ).
cnf(i_0_2410,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
cls_finite__Int_0,
[final] ).
cnf(i_0_2411,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_finite__Int_1,
[final] ).
cnf(i_0_2412,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1)) ),
cls_sgn__1__neg_0,
[final] ).
cnf(i_0_2413,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(cn,[status(thm)],[i_0_1400]),
[final] ).
cnf(i_0_2414,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__power_1,
[final] ).
cnf(i_0_2415,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_minus__dvd__iff_1,
[final] ).
cnf(i_0_2416,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
cls_dvd__minus__iff_1,
[final] ).
cnf(i_0_2417,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
cls_subset__insertI_0,
[final] ).
cnf(i_0_2418,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osgn__if(X1) ),
cls_sgn__if_2,
[final] ).
cnf(i_0_2419,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0,
[final] ).
cnf(i_0_2420,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__antisym_0,
[final] ).
cnf(i_0_2421,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2,
[final] ).
cnf(i_0_2422,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X2)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__diff__eq_0,
[final] ).
cnf(i_0_2423,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
cls_subset__empty_1,
[final] ).
cnf(i_0_2424,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(X3,X1)))
| ~ c_Wellfounded_Owf(X3,X1) ),
cls_acc__wfD_0,
[final] ).
cnf(i_0_2425,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_2426,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_nat__less__le_2,
[final] ).
cnf(i_0_2427,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__eq__less__or__eq_0,
[final] ).
cnf(i_0_2428,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__neq__implies__less_0,
[final] ).
cnf(i_0_2429,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Oone__class_Oone(X1))),X2)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Oneg__mul_0,
[final] ).
cnf(i_0_2430,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
cls_neq0__conv_1,
[final] ).
cnf(i_0_2431,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__reflcl__absorb_0,
[final] ).
cnf(i_0_2432,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_2433,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_2434,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_2435,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X4) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_2436,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_2437,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_2438,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_2439,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_2440,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_zero__le__square_0,
[final] ).
cnf(i_0_2441,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__antisym_0,
[final] ).
cnf(i_0_2442,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_2443,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0,
[final] ).
cnf(i_0_2444,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0,
[final] ).
cnf(i_0_2445,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv1_1,
[final] ).
cnf(i_0_2446,axiom,
( c_lessequals(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0,
[final] ).
cnf(i_0_2447,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__le_0,
[final] ).
cnf(i_0_2448,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0,
[final] ).
cnf(i_0_2449,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le1_0,
[final] ).
cnf(i_0_2450,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0,
[final] ).
cnf(i_0_2451,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le2_0,
[final] ).
cnf(i_0_2452,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I2_J_0,
[final] ).
cnf(i_0_2453,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge1_0,
[final] ).
cnf(i_0_2454,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I3_J_0,
[final] ).
cnf(i_0_2455,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge2_0,
[final] ).
cnf(i_0_2456,axiom,
( c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I4_J_0,
[final] ).
cnf(i_0_2457,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Oone__class_Oone(X1) ),
cls_sgn__1__pos_0,
[final] ).
cnf(i_0_2458,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sup__0__imp__0_0,
[final] ).
cnf(i_0_2459,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_inf__0__imp__0_0,
[final] ).
cnf(i_0_2460,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Odvd(X1) ),
cls_dvdI_0,
[final] ).
cnf(i_0_2461,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__triv__left_0,
[final] ).
cnf(i_0_2462,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__triv__right_0,
[final] ).
cnf(i_0_2463,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
cls_converse__converse_0,
[final] ).
cnf(i_0_2464,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_rev__finite__subset_0,
[final] ).
cnf(i_0_2465,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
cls_finite__subset_0,
[final] ).
cnf(i_0_2466,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
cls_not__less0_0,
[final] ).
cnf(i_0_2467,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
cls_gr__implies__not0_0,
[final] ).
cnf(i_0_2468,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Un__UNIV__left_0,
[final] ).
cnf(i_0_2469,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Int__empty__left_0,
[final] ).
cnf(i_0_2470,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
cls_Un__UNIV__right_0,
[final] ).
cnf(i_0_2471,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Int__empty__right_0,
[final] ).
cnf(i_0_2472,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__empty_0,
[final] ).
cnf(i_0_2473,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
cls_Un__commute_0,
[final] ).
cnf(i_0_2474,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
cls_Int__commute_0,
[final] ).
cnf(i_0_2475,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1,
[final] ).
cnf(i_0_2476,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_diff__eq_0,
[final] ).
cnf(i_0_2477,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Oone__class_Oone(X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__one_0,
[final] ).
cnf(i_0_2478,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus__eq__add_0,
[final] ).
cnf(i_0_2479,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus_0,
[final] ).
cnf(i_0_2480,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__diff__minus_0,
[final] ).
cnf(i_0_2481,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__def_0,
[final] ).
cnf(i_0_2482,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Osub__add_0,
[final] ).
cnf(i_0_2483,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != X3 ),
cls_le__iff__sup_1,
[final] ).
cnf(i_0_2484,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != X2 ),
cls_le__iff__inf_1,
[final] ).
cnf(i_0_2485,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0,
[final] ).
cnf(i_0_2486,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__sup_0,
[final] ).
cnf(i_0_2487,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0,
[final] ).
cnf(i_0_2488,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0,
[final] ).
cnf(i_0_2489,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
cls_nat__less__le_1,
[final] ).
cnf(i_0_2490,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
cls_less__not__refl_0,
[final] ).
cnf(i_0_2491,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__UNIV__eq_0,
[final] ).
cnf(i_0_2492,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0,
[final] ).
cnf(i_0_2493,axiom,
( c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
cls_antisym__converse_1,
[final] ).
cnf(i_0_2494,axiom,
( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
cls_acyclic__converse_1,
[final] ).
cnf(i_0_2495,axiom,
( c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X1,X2,X3),X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
cls_wf__mlex_0,
[final] ).
cnf(i_0_2496,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_finite__insert_1,
[final] ).
cnf(i_0_2497,axiom,
( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__converse_1,
[final] ).
cnf(i_0_2498,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
cls_equiv_Orefl__on_0,
[final] ).
cnf(i_0_2499,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_eq__neg__iff__add__eq__0_0,
[final] ).
cnf(i_0_2500,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_left__minus_0,
[final] ).
cnf(i_0_2501,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__left__minus_0,
[final] ).
cnf(i_0_2502,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0,
[final] ).
cnf(i_0_2503,axiom,
c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Transitive__Closure_Ortrancl(X2,X1),X1),
cls_refl__rtrancl_0,
[final] ).
cnf(i_0_2504,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
cls_Un__empty__left_0,
[final] ).
cnf(i_0_2505,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
cls_Int__UNIV__left_0,
[final] ).
cnf(i_0_2506,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Un__empty__right_0,
[final] ).
cnf(i_0_2507,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Int__UNIV__right_0,
[final] ).
cnf(i_0_2508,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0,
[final] ).
cnf(i_0_2509,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
cls_subset__UNIV_0,
[final] ).
cnf(i_0_2510,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
cls_empty__not__insert_0,
[final] ).
cnf(i_0_2511,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_insert__not__empty_0,
[final] ).
cnf(i_0_2512,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_0,
[final] ).
cnf(i_0_2513,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_power__eq__0__iff_1,
[final] ).
cnf(i_0_2514,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4) = c_HOL_Ozero__class_Ozero(X1)
| c_Finite__Set_Ofinite(X4,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__infinite_0,
[final] ).
cnf(i_0_2515,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(X2,X1),X3),X4) = c_HOL_Ozero__class_Ozero(X1)
| c_Finite__Set_Ofinite(X4,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__def_1,
[final] ).
cnf(i_0_2516,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_minus__unique_0,
[final] ).
cnf(i_0_2517,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__neg__iff__add__eq__0_1,
[final] ).
cnf(i_0_2518,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_2519,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__commute_0,
[final] ).
cnf(i_0_2520,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0,
[final] ).
cnf(i_0_2521,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__commute_0,
[final] ).
cnf(i_0_2522,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0,
[final] ).
cnf(i_0_2523,axiom,
c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),c_Relation_OId(X1),X1),
cls_refl__Id_0,
[final] ).
cnf(i_0_2524,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__one__le__zero_0,
[final] ).
cnf(i_0_2525,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_2526,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_2527,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_2528,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_2529,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_2530,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_gr0I_0,
[final] ).
cnf(i_0_2531,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_dvd__0__left_0,
[final] ).
cnf(i_0_2532,axiom,
c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
cls_Domain__rtrancl_0,
[final] ).
cnf(i_0_2533,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
cls_nat__le__linear_0,
[final] ).
cnf(i_0_2534,axiom,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1),
cls_total__on__empty_0,
[final] ).
cnf(i_0_2535,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_2536,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divirors__neq0_0,
[final] ).
cnf(i_0_2537,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divisors_0,
[final] ).
cnf(i_0_2538,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_mult__eq__0__iff_0,
[final] ).
cnf(i_0_2539,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_of__nat__0__le__iff_0,
[final] ).
cnf(i_0_2540,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__le__imp__of__nat_0,
[final] ).
cnf(i_0_2541,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_class__ringb_Osubr0__iff_0,
[final] ).
cnf(i_0_2542,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq1_0,
[final] ).
cnf(i_0_2543,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq1_0,
[final] ).
cnf(i_0_2544,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_field__power__not__zero_0,
[final] ).
cnf(i_0_2545,axiom,
( X3 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X1) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq2_0,
[final] ).
cnf(i_0_2546,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq2_0,
[final] ).
cnf(i_0_2547,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup__top_0,
[final] ).
cnf(i_0_2548,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0,
[final] ).
cnf(i_0_2549,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_sup__compl__top_0,
[final] ).
cnf(i_0_2550,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0,
[final] ).
cnf(i_0_2551,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_2552,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X3) != c_HOL_Oone__class_Oone(X1) ),
cls_right__inverse__eq_0,
[final] ).
cnf(i_0_2553,axiom,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
cls_sym__conv__converse__eq_1,
[final] ).
cnf(i_0_2554,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus_0,
[final] ).
cnf(i_0_2555,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_2556,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
cls_equiv_Osym_0,
[final] ).
cnf(i_0_2557,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_right__minus__eq_0,
[final] ).
cnf(i_0_2558,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__iff__diff__eq__0_1,
[final] ).
cnf(i_0_2559,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| ~ class_Ring__and__Field_Omult__zero(X1)
| ~ class_Power_Opower(X1) ),
cls_power__eq__0__iff_2,
[final] ).
cnf(i_0_2560,axiom,
c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2) = c_Relation_OId__on(X1,X2),
cls_converse__Id__on_0,
[final] ).
cnf(i_0_2561,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
cls_le__0__eq_0,
[final] ).
cnf(i_0_2562,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_group__add__class_Odiff__0_0,
[final] ).
cnf(i_0_2563,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__self__if_0,
[final] ).
cnf(i_0_2564,axiom,
c_Relation_ODomain(c_Relation_OId(X1),X1,X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Domain__Id_0,
[final] ).
cnf(i_0_2565,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_UNIV__not__empty_0,
[final] ).
cnf(i_0_2566,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__left_1,
[final] ).
cnf(i_0_2567,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__0(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0__left_0,
[final] ).
cnf(i_0_2568,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_2569,axiom,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
cls_Domain__Id__on_0,
[final] ).
cnf(i_0_2570,axiom,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
cls_single__valued__Id__on_0,
[final] ).
cnf(i_0_2571,axiom,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
cls_refl__on__Id__on_0,
[final] ).
cnf(i_0_2572,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
cls_Un__absorb_0,
[final] ).
cnf(i_0_2573,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
cls_Int__absorb_0,
[final] ).
cnf(i_0_2574,axiom,
( c_Relation_Oconverse(X1,X2,X2) = X1
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__conv__converse__eq_0,
[final] ).
cnf(i_0_2575,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
cls_subset__refl_0,
[final] ).
cnf(i_0_2576,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
cls_equalityE_0,
[final] ).
cnf(i_0_2577,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
cls_card__eq__0__iff_0,
[final] ).
cnf(i_0_2578,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__zero_0,
[final] ).
cnf(i_0_2579,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_1,
[final] ).
cnf(i_0_2580,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_2,
[final] ).
cnf(i_0_2581,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X2) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__self__if_1,
[final] ).
cnf(i_0_2582,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__left_0,
[final] ).
cnf(i_0_2583,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_1,
[final] ).
cnf(i_0_2584,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__0_0,
[final] ).
cnf(i_0_2585,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I9_J_0,
[final] ).
cnf(i_0_2586,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__zero__left_0,
[final] ).
cnf(i_0_2587,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__le__one_0,
[final] ).
cnf(i_0_2588,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_2589,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
cls_finite__UNIV_0,
[final] ).
cnf(i_0_2590,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3) ),
cls_of__nat__eq__iff_0,
[final] ).
cnf(i_0_2591,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_2592,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_2593,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_mult__1_0,
[final] ).
cnf(i_0_2594,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__left_0,
[final] ).
cnf(i_0_2595,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I11_J_0,
[final] ).
cnf(i_0_2596,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Oone__class_Oone(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__1_0,
[final] ).
cnf(i_0_2597,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_2598,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_2599,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_2600,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_2601,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one_0,
[final] ).
cnf(i_0_2602,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X2,X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0,
[final] ).
cnf(i_0_2603,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__left_0,
[final] ).
cnf(i_0_2604,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Otop__class_Otop(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0,
[final] ).
cnf(i_0_2605,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__right_0,
[final] ).
cnf(i_0_2606,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Osubr0__iff_1,
[final] ).
cnf(i_0_2607,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__right_0,
[final] ).
cnf(i_0_2608,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_2,
[final] ).
cnf(i_0_2609,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I10_J_0,
[final] ).
cnf(i_0_2610,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X2) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__self_0,
[final] ).
cnf(i_0_2611,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_right__inverse__eq_1,
[final] ).
cnf(i_0_2612,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
cls_power__0_0,
[final] ).
cnf(i_0_2613,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__0_0,
[final] ).
cnf(i_0_2614,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__left_0,
[final] ).
cnf(i_0_2615,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__left_0,
[final] ).
cnf(i_0_2616,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,c_Orderings_Obot__class_Obot(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0,
[final] ).
cnf(i_0_2617,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Otop__class_Otop(X1),X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__right_0,
[final] ).
cnf(i_0_2618,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_card__empty_0,
[final] ).
cnf(i_0_2619,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_one__dvd_0,
[final] ).
cnf(i_0_2620,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0,
[final] ).
cnf(i_0_2621,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__0__right_0,
[final] ).
cnf(i_0_2622,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0,
[final] ).
cnf(i_0_2623,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__0__right_0,
[final] ).
cnf(i_0_2624,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__right_0,
[final] ).
cnf(i_0_2625,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I12_J_0,
[final] ).
cnf(i_0_2626,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_2627,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_2628,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_2629,axiom,
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X2),c_HOL_Oone__class_Oone(X1)) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__1_0,
[final] ).
cnf(i_0_2630,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_2631,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_2632,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_2633,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_2634,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_2635,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_finite_OemptyI_0,
[final] ).
cnf(i_0_2636,axiom,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
cls_converse__Id_0,
[final] ).
cnf(i_0_2637,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__self_0,
[final] ).
cnf(i_0_2638,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1,
[final] ).
cnf(i_0_2639,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0,
[final] ).
cnf(i_0_2640,axiom,
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
cls_acyclic__impl__antisym__rtrancl_0,
[final] ).
cnf(i_0_2641,axiom,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__rtrancl_0,
[final] ).
cnf(i_0_2642,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0,
[final] ).
cnf(i_0_2643,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0,
[final] ).
cnf(i_0_2644,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_dvd__refl_0,
[final] ).
cnf(i_0_2645,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_2646,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_2647,axiom,
( c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X2,X1),X1) = c_HOL_Osgn__class_Osgn(X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sgn__sgn_0,
[final] ).
cnf(i_0_2648,axiom,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
cls_single__valued__Id_0,
[final] ).
cnf(i_0_2649,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_2650,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_le__0__eq_1,
[final] ).
cnf(i_0_2651,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
cls_le0_0,
[final] ).
cnf(i_0_2652,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__idemp_0,
[final] ).
cnf(i_0_2653,axiom,
c_lessequals(X1,X1,tc_nat),
cls_eq__imp__le_0,
[final] ).
cnf(i_0_2654,axiom,
c_lessequals(X1,X1,tc_nat),
cls_le__refl_0,
[final] ).
cnf(i_0_2655,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) ),
cls_neg__0__equal__iff__equal_0,
[final] ).
cnf(i_0_2656,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_neg__equal__0__iff__equal_0,
[final] ).
cnf(i_0_2657,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != X2 ),
cls_neg__equal__zero_0,
[final] ).
cnf(i_0_2658,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
clsarity_prod__Finite__Set_Ofinite_Ofinite,
[final] ).
cnf(i_0_2659,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
clsarity_fun__Finite__Set_Ofinite_Ofinite,
[final] ).
cnf(i_0_2660,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sgn__0__0_0,
[final] ).
cnf(i_0_2661,axiom,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
cls_antisym__Id__on_0,
[final] ).
cnf(i_0_2662,axiom,
c_Wellfounded_Owf(c_Wellfounded_Omeasure(X1,X2),X2),
cls_wf__measure_0,
[final] ).
cnf(i_0_2663,axiom,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
cls_sym__Id__on_0,
[final] ).
cnf(i_0_2664,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__top__eq_0,
[final] ).
cnf(i_0_2665,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0,
[final] ).
cnf(i_0_2666,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__zero_0,
[final] ).
cnf(i_0_2667,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
cls_neg__equal__zero_1,
[final] ).
cnf(i_0_2668,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1,
[final] ).
cnf(i_0_2669,axiom,
( class_HOL_Oord(tc_fun(X1,X2))
| ~ class_HOL_Oord(X2) ),
clsarity_fun__HOL_Oord,
[final] ).
cnf(i_0_2670,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
clsarity_fun__Orderings_Opreorder,
[final] ).
cnf(i_0_2671,axiom,
( class_Orderings_Otop(tc_fun(X1,X2))
| ~ class_Orderings_Otop(X2) ),
clsarity_fun__Orderings_Otop,
[final] ).
cnf(i_0_2672,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder,
[final] ).
cnf(i_0_2673,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_2674,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Odistrib__lattice(X2) ),
clsarity_fun__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_2675,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
clsarity_fun__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_2676,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_2677,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olattice,
[final] ).
cnf(i_0_2678,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
clsarity_fun__Orderings_Obot,
[final] ).
cnf(i_0_2679,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
clsarity_fun__Lattices_Obounded__lattice,
[final] ).
cnf(i_0_2680,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__acyclic_0,
[final] ).
cnf(i_0_2681,axiom,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__0_0,
[final] ).
cnf(i_0_2682,axiom,
( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_sgn__0__0_1,
[final] ).
cnf(i_0_2683,axiom,
( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osgn__if(X1) ),
cls_sgn0_0,
[final] ).
cnf(i_0_2684,axiom,
( c_Finite__Set_Ocard(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(X1,X2) ),
cls_card__eq__0__iff_2,
[final] ).
cnf(i_0_2685,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
cls_finite_0,
[final] ).
cnf(i_0_2686,axiom,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
cls_antisym__Id_0,
[final] ).
cnf(i_0_2687,axiom,
c_Relation_Osym(c_Relation_OId(X1),X1),
cls_sym__Id_0,
[final] ).
cnf(i_0_2688,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_one__neq__zero_0,
[final] ).
cnf(i_0_2689,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0,
[final] ).
cnf(i_0_2690,axiom,
class_Nat_Osemiring__char__0(tc_nat),
clsarity_nat__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_2691,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_2692,axiom,
class_HOL_Oord(tc_nat),
clsarity_nat__HOL_Oord,
[final] ).
cnf(i_0_2693,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord,
[final] ).
cnf(i_0_2694,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_2695,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_2696,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_2697,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_2698,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_2699,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_2700,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_2701,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder,
[final] ).
cnf(i_0_2702,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
clsarity_bool__Finite__Set_Ofinite_Ofinite,
[final] ).
cnf(i_0_2703,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
clsarity_nat__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_2704,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
clsarity_nat__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_2705,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop,
[final] ).
cnf(i_0_2706,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_2707,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_2708,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_2709,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_2710,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_2711,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder,
[final] ).
cnf(i_0_2712,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
clsarity_nat__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_2713,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
clsarity_nat__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_2714,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_2715,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_2716,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_2717,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
clsarity_nat__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_2718,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
clsarity_bool__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_2719,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_2720,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_2721,axiom,
class_Power_Opower(tc_nat),
clsarity_nat__Power_Opower,
[final] ).
cnf(i_0_2722,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_2723,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_2724,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_2725,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_2726,axiom,
class_Lattices_Olattice(tc_nat),
clsarity_nat__Lattices_Olattice,
[final] ).
cnf(i_0_2727,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice,
[final] ).
cnf(i_0_2728,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
clsarity_nat__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_2729,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_2730,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_2731,axiom,
class_Ring__and__Field_Odvd(tc_nat),
clsarity_nat__Ring__and__Field_Odvd,
[final] ).
cnf(i_0_2732,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_2733,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_2734,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_2735,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot,
[final] ).
cnf(i_0_2736,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot,
[final] ).
cnf(i_0_2737,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_2738,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_2739,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice,
[final] ).
cnf(i_0_2740,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_2741,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_2742,axiom,
X1 = X1 ).
cnf(i_0_2743,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2744,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2745,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_2746,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_2747,axiom,
( X1 != X2
| c_Relation_Orel__comp(X1,X3,X4,X5,X6) = c_Relation_Orel__comp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2748,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X1,X4,X5,X6) = c_Relation_Orel__comp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2749,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X1,X5,X6) = c_Relation_Orel__comp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2750,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X1,X6) = c_Relation_Orel__comp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2751,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X6,X1) = c_Relation_Orel__comp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2752,axiom,
( X1 != X2
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2753,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X1,X4,X5,X6) = c_Recdef_Ocut(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2754,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X1,X5,X6) = c_Recdef_Ocut(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2755,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X1,X6) = c_Recdef_Ocut(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2756,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X6,X1) = c_Recdef_Ocut(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2757,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_2758,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_2759,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_2760,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_2761,axiom,
( X1 != X2
| c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).
cnf(i_0_2762,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).
cnf(i_0_2763,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).
cnf(i_0_2764,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).
cnf(i_0_2765,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_2766,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_2767,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X1,X3,X4,X5) = c_Finite__Set_Osetprod(X2,X3,X4,X5) ) ).
cnf(i_0_2768,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X3,X1,X4,X5) = c_Finite__Set_Osetprod(X3,X2,X4,X5) ) ).
cnf(i_0_2769,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X3,X4,X1,X5) = c_Finite__Set_Osetprod(X3,X4,X2,X5) ) ).
cnf(i_0_2770,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X3,X4,X5,X1) = c_Finite__Set_Osetprod(X3,X4,X5,X2) ) ).
cnf(i_0_2771,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_2772,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_2773,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_2774,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_2775,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_2776,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_2777,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).
cnf(i_0_2778,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).
cnf(i_0_2779,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).
cnf(i_0_2780,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_2781,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_2782,axiom,
( X1 != X2
| c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).
cnf(i_0_2783,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).
cnf(i_0_2784,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).
cnf(i_0_2785,axiom,
( X1 != X2
| c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).
cnf(i_0_2786,axiom,
( X1 != X2
| c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).
cnf(i_0_2787,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).
cnf(i_0_2788,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).
cnf(i_0_2789,axiom,
( X1 != X2
| c_Pair(X1,X3,X4,X5) = c_Pair(X2,X3,X4,X5) ) ).
cnf(i_0_2790,axiom,
( X1 != X2
| c_Pair(X3,X1,X4,X5) = c_Pair(X3,X2,X4,X5) ) ).
cnf(i_0_2791,axiom,
( X1 != X2
| c_Pair(X3,X4,X1,X5) = c_Pair(X3,X4,X2,X5) ) ).
cnf(i_0_2792,axiom,
( X1 != X2
| c_Pair(X3,X4,X5,X1) = c_Pair(X3,X4,X5,X2) ) ).
cnf(i_0_2793,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_2794,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_2795,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_2796,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_2797,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_2798,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_2799,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_2800,axiom,
( X1 != X2
| c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).
cnf(i_0_2801,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).
cnf(i_0_2802,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).
cnf(i_0_2803,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).
cnf(i_0_2804,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_2805,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_2806,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_2807,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_2808,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_2809,axiom,
( X1 != X2
| c_Relation_OId(X1) = c_Relation_OId(X2) ) ).
cnf(i_0_2810,axiom,
( X1 != X2
| c_HOL_Osgn__class_Osgn(X1,X3) = c_HOL_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_2811,axiom,
( X1 != X2
| c_HOL_Osgn__class_Osgn(X3,X1) = c_HOL_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_2812,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2813,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X1,X3,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2814,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X1,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2815,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X1,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2816,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X1,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2817,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X1,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2818,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X1)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2819,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_2820,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_2821,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_2822,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_2823,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_2824,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_2825,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_2826,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_2827,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_2828,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_2829,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_2830,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_2831,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_2832,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_2833,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X1,X3)
| c_Relation_Oantisym(X2,X3) ) ).
cnf(i_0_2834,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X3,X1)
| c_Relation_Oantisym(X3,X2) ) ).
cnf(i_0_2835,axiom,
( X1 != X2
| ~ c_Relation_Osym(X1,X3)
| c_Relation_Osym(X2,X3) ) ).
cnf(i_0_2836,axiom,
( X1 != X2
| ~ c_Relation_Osym(X3,X1)
| c_Relation_Osym(X3,X2) ) ).
cnf(i_0_2837,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_2838,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_2839,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_2840,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_2841,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_2842,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_2843,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_2844,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_2845,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_2846,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_2847,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_2848,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_2849,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_2850,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_2851,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_2852,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_2853,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__field(X2) ) ).
cnf(i_0_2854,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_2855,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_2856,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_2857,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_2858,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_2859,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_2860,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_2861,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odvd(X1)
| class_Ring__and__Field_Odvd(X2) ) ).
cnf(i_0_2862,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_2863,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_2864,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_2865,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_2866,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_2867,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_2868,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_2869,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_2870,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_2871,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_2872,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2873,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_2874,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_2875,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_2876,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2877,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_2878,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_2879,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_2880,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_2881,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_2882,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_2883,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).
cnf(i_0_2884,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).
cnf(i_0_2885,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_2886,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2887,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2888,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_2889,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_2890,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_2891,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_2892,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_2893,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_2894,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_2895,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_2896,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_2897,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_2898,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2899,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_2900,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_2901,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_2902,axiom,
( X1 != X2
| ~ class_HOL_Oord(X1)
| class_HOL_Oord(X2) ) ).
cnf(i_0_2903,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osgn__if(X1)
| class_Ring__and__Field_Osgn__if(X2) ) ).
cnf(i_0_2904,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_2905,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_2906,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_2907,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_2908,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2909,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_2910,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_2911,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_2912,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_2913,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2914,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_2915,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(X2) ) ).
cnf(i_0_2916,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_2917,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_2918,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_2919,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2920,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_2921,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_2742_001,axiom,
X1 = X1 ).
cnf(i_0_2743_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2744_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2745_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_2746_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_2747_006,axiom,
( X1 != X2
| c_Relation_Orel__comp(X1,X3,X4,X5,X6) = c_Relation_Orel__comp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2748_007,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X1,X4,X5,X6) = c_Relation_Orel__comp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2749_008,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X1,X5,X6) = c_Relation_Orel__comp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2750_009,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X1,X6) = c_Relation_Orel__comp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2751_010,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X6,X1) = c_Relation_Orel__comp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2752_011,axiom,
( X1 != X2
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2753_012,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X1,X4,X5,X6) = c_Recdef_Ocut(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2754_013,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X1,X5,X6) = c_Recdef_Ocut(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2755_014,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X1,X6) = c_Recdef_Ocut(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2756_015,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X6,X1) = c_Recdef_Ocut(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2757_016,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_2758_017,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_2759_018,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_2760_019,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_2761_020,axiom,
( X1 != X2
| c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).
cnf(i_0_2762_021,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).
cnf(i_0_2763_022,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).
cnf(i_0_2764_023,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).
cnf(i_0_2765_024,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_2766_025,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_2767_026,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X1,X3,X4,X5) = c_Finite__Set_Osetprod(X2,X3,X4,X5) ) ).
cnf(i_0_2768_027,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X3,X1,X4,X5) = c_Finite__Set_Osetprod(X3,X2,X4,X5) ) ).
cnf(i_0_2769_028,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X3,X4,X1,X5) = c_Finite__Set_Osetprod(X3,X4,X2,X5) ) ).
cnf(i_0_2770_029,axiom,
( X1 != X2
| c_Finite__Set_Osetprod(X3,X4,X5,X1) = c_Finite__Set_Osetprod(X3,X4,X5,X2) ) ).
cnf(i_0_2771_030,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_2772_031,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_2773_032,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_2774_033,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_2775_034,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_2776_035,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_2777_036,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).
cnf(i_0_2778_037,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).
cnf(i_0_2779_038,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).
cnf(i_0_2780_039,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_2781_040,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_2782_041,axiom,
( X1 != X2
| c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).
cnf(i_0_2783_042,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).
cnf(i_0_2784_043,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).
cnf(i_0_2785_044,axiom,
( X1 != X2
| c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).
cnf(i_0_2786_045,axiom,
( X1 != X2
| c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).
cnf(i_0_2787_046,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).
cnf(i_0_2788_047,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).
cnf(i_0_2789_048,axiom,
( X1 != X2
| c_Pair(X1,X3,X4,X5) = c_Pair(X2,X3,X4,X5) ) ).
cnf(i_0_2790_049,axiom,
( X1 != X2
| c_Pair(X3,X1,X4,X5) = c_Pair(X3,X2,X4,X5) ) ).
cnf(i_0_2791_050,axiom,
( X1 != X2
| c_Pair(X3,X4,X1,X5) = c_Pair(X3,X4,X2,X5) ) ).
cnf(i_0_2792_051,axiom,
( X1 != X2
| c_Pair(X3,X4,X5,X1) = c_Pair(X3,X4,X5,X2) ) ).
cnf(i_0_2793_052,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_2794_053,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_2795_054,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_2796_055,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_2797_056,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_2798_057,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_2799_058,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_2800_059,axiom,
( X1 != X2
| c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).
cnf(i_0_2801_060,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).
cnf(i_0_2802_061,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).
cnf(i_0_2803_062,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).
cnf(i_0_2804_063,axiom,
( X1 != X2
| c_Relation_ODomain(X1,X3,X4) = c_Relation_ODomain(X2,X3,X4) ) ).
cnf(i_0_2805_064,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X1,X4) = c_Relation_ODomain(X3,X2,X4) ) ).
cnf(i_0_2806_065,axiom,
( X1 != X2
| c_Relation_ODomain(X3,X4,X1) = c_Relation_ODomain(X3,X4,X2) ) ).
cnf(i_0_2807_066,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_2808_067,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_2809_068,axiom,
( X1 != X2
| c_Relation_OId(X1) = c_Relation_OId(X2) ) ).
cnf(i_0_2810_069,axiom,
( X1 != X2
| c_HOL_Osgn__class_Osgn(X1,X3) = c_HOL_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_2811_070,axiom,
( X1 != X2
| c_HOL_Osgn__class_Osgn(X3,X1) = c_HOL_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_2812_071,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2813_072,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X1,X3,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2814_073,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X1,X4,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2815_074,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X1,X5,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2816_075,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X1,X6,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2817_076,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X1,X7)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2818_077,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X1)
| c_Equiv__Relations_Ocongruent2(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2819_078,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_2820_079,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_2821_080,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_2822_081,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_2823_082,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_2824_083,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_2825_084,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_2826_085,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_2827_086,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_2828_087,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_2829_088,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_2830_089,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_2831_090,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_2832_091,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_2833_092,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X1,X3)
| c_Relation_Oantisym(X2,X3) ) ).
cnf(i_0_2834_093,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X3,X1)
| c_Relation_Oantisym(X3,X2) ) ).
cnf(i_0_2835_094,axiom,
( X1 != X2
| ~ c_Relation_Osym(X1,X3)
| c_Relation_Osym(X2,X3) ) ).
cnf(i_0_2836_095,axiom,
( X1 != X2
| ~ c_Relation_Osym(X3,X1)
| c_Relation_Osym(X3,X2) ) ).
cnf(i_0_2837_096,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_2838_097,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_2839_098,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_2840_099,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_2841_100,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_2842_101,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_2843_102,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_2844_103,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_2845_104,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_2846_105,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_2847_106,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_2848_107,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_2849_108,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_2850_109,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_2851_110,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_2852_111,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_2853_112,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__field(X1)
| class_Ring__and__Field_Oordered__field(X2) ) ).
cnf(i_0_2854_113,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_2855_114,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_2856_115,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_2857_116,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_2858_117,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_2859_118,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X4)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_2860_119,axiom,
( X1 != X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_2861_120,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odvd(X1)
| class_Ring__and__Field_Odvd(X2) ) ).
cnf(i_0_2862_121,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_2863_122,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_2864_123,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_2865_124,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_2866_125,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_2867_126,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_2868_127,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_2869_128,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_2870_129,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_2871_130,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_2872_131,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2873_132,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_2874_133,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_2875_134,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_2876_135,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2877_136,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_2878_137,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_2879_138,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1(X1)
| class_Ring__and__Field_Oring__1(X2) ) ).
cnf(i_0_2880_139,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_2881_140,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_2882_141,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_2883_142,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).
cnf(i_0_2884_143,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).
cnf(i_0_2885_144,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_2886_145,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2887_146,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2888_147,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_2889_148,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_2890_149,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_2891_150,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_2892_151,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_2893_152,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_2894_153,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_2895_154,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_2896_155,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_2897_156,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_2898_157,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2899_158,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_2900_159,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_2901_160,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_2902_161,axiom,
( X1 != X2
| ~ class_HOL_Oord(X1)
| class_HOL_Oord(X2) ) ).
cnf(i_0_2903_162,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osgn__if(X1)
| class_Ring__and__Field_Osgn__if(X2) ) ).
cnf(i_0_2904_163,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_2905_164,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_2906_165,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_2907_166,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_2908_167,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2909_168,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_2910_169,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_2911_170,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_2912_171,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_2913_172,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2914_173,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_2915_174,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(X2) ) ).
cnf(i_0_2916_175,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_2917_176,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_2918_177,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_2919_178,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2920_179,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_2921_180,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_2922,plain,
c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X1,X2,X3,X4,X5),
inference(equality_inference,[],[1424]) ).
cnf(i_0_2923,plain,
( hAPP(X1,X2) = hAPP(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X4,X3,X3)),X5)) ),
inference(equality_inference,[],[1493]) ).
cnf(i_0_2924,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X4,X4,X3,X3)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X1)) ),
inference(equality_inference,[],[1576]) ).
cnf(i_0_2925,plain,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2)),X3)),X4) = X4 ),
inference(equality_inference,[],[1669]) ).
cnf(i_0_2926,plain,
( ~ class_Ring__and__Field_Oring(X1)
| X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X3)),X4)),X2) ),
inference(equality_inference,[],[1670]) ).
cnf(i_0_2927,plain,
X1 = X1,
inference(equality_inference,[],[1678]) ).
cnf(i_0_2928,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = X4
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[1748]) ).
cnf(i_0_2929,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1825]) ).
cnf(i_0_2930,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1826]) ).
cnf(i_0_2931,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1827]) ).
cnf(i_0_2932,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1828]) ).
cnf(i_0_2933,plain,
X1 = X1,
inference(equality_inference,[],[1841]) ).
cnf(i_0_2934,plain,
X1 = X1,
inference(equality_inference,[],[1842]) ).
cnf(i_0_2935,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X3)) ),
inference(equality_inference,[],[1955]) ).
cnf(i_0_2936,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[1974]) ).
cnf(i_0_2937,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(equality_inference,[],[2101]) ).
cnf(i_0_2938,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Oone__class_Oone(X2)),X3)) ),
inference(equality_inference,[],[2102]) ).
cnf(i_0_2939,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
inference(equality_inference,[],[2111]) ).
cnf(i_0_2940,plain,
X1 = X1,
inference(equality_inference,[],[2186]) ).
cnf(i_0_2941,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2) ),
inference(equality_inference,[],[2252]) ).
cnf(i_0_2942,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X1),X3),X2) ),
inference(equality_inference,[],[2253]) ).
cnf(i_0_2943,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
inference(equality_inference,[],[2284]) ).
cnf(i_0_2944,plain,
X1 = X1,
inference(equality_inference,[],[2370]) ).
cnf(i_0_2945,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1) ),
inference(equality_inference,[],[2405]) ).
cnf(i_0_2946,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[2425]) ).
cnf(i_0_2947,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[2435]) ).
cnf(i_0_2948,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[2436]) ).
cnf(i_0_2949,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[2437]) ).
cnf(i_0_2950,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[2438]) ).
cnf(i_0_2951,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[2439]) ).
cnf(i_0_2952,plain,
( X1 = X1
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(equality_inference,[],[2590]) ).
cnf(i_0_2953,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[2591]) ).
cnf(i_0_2954,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[2592]) ).
cnf(i_0_2955,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))),
inference(scs_inference,[],[i_0_1404,i_0_1402]) ).
cnf(i_0_2956,plain,
c_Recdef_Ocut(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X3,X2,X4) = c_Recdef_Ocut(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X3,X2,X4),
inference(scs_inference,[],[i_0_2190,i_0_1409]) ).
cnf(i_0_2957,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2958,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X2,X3,X4,X5,X1,X6),X5,X1,X1)),X4))
| c_Recdef_Ocut(X2,X4,X5,X1,X6) = c_Recdef_Ocut(X3,X4,X5,X1,X6) ),
inference(rename_variables,[],[i_0_1409]) ).
cnf(i_0_2959,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X1),tc_bool)),X2,X1))),
inference(scs_inference,[],[i_0_2190,i_0_2957,i_0_1409,i_0_1508]) ).
cnf(i_0_2960,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2961,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2))) ),
inference(rename_variables,[],[i_0_1508]) ).
cnf(i_0_2962,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X5,X1,X2))),
inference(scs_inference,[],[i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535]) ).
cnf(i_0_2963,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),c_Product__Type_OSigma(X3,X6,X1,X4))) ),
inference(rename_variables,[],[i_0_1535]) ).
cnf(i_0_2964,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
inference(scs_inference,[],[i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589]) ).
cnf(i_0_2965,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_OId__on(X3,X1))) ),
inference(rename_variables,[],[i_0_1589]) ).
cnf(i_0_2966,plain,
~ c_lessequals(c_Set_Oinsert(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088]) ).
cnf(i_0_2967,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) ),
inference(rename_variables,[],[i_0_2088]) ).
cnf(i_0_2968,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128]) ).
cnf(i_0_2969,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) ),
inference(rename_variables,[],[i_0_2128]) ).
cnf(i_0_2970,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X3,tc_fun(X1,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129]) ).
cnf(i_0_2971,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)) ),
inference(rename_variables,[],[i_0_2129]) ).
cnf(i_0_2972,plain,
hBOOL(hAPP(c_Relation_OId(X1),c_Pair(X2,X2,X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399]) ).
cnf(i_0_2973,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_2399]) ).
cnf(i_0_2974,plain,
~ hBOOL(hAPP(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475]) ).
cnf(i_0_2975,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_2475]) ).
cnf(i_0_2976,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Orel__comp(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X2),tc_bool)),X1,X6,X2))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407]) ).
cnf(i_0_2977,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2978,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,X6,X7,X2,X1),X4,X1,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X7,X2)),c_Pair(X3,X4,X7,X2)),c_Relation_Orel__comp(X5,X6,X7,X1,X2))) ),
inference(rename_variables,[],[i_0_1407]) ).
cnf(i_0_2979,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X5),tc_bool)),X6,X1,X5,X2))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408]) ).
cnf(i_0_2980,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2981,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,X6,X1,X7,X2),X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X7)),c_Pair(X3,X4,X1,X7)),c_Relation_Orel__comp(X5,X6,X1,X2,X7))) ),
inference(rename_variables,[],[i_0_1408]) ).
cnf(i_0_2982,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X1),tc_bool)),X4,X3,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433]) ).
cnf(i_0_2983,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2984,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X4,X5,X1,X2),X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,X3,X1,X2))) ),
inference(rename_variables,[],[i_0_1433]) ).
cnf(i_0_2985,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_Arrow__Order__Mirabelle_Oalt),X1),c_Relation_OImage(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X2),X1),X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_1593,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434]) ).
cnf(i_0_2986,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2987,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X4,X5,X1,X2),X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),c_Relation_OImage(X5,X3,X1,X2))) ),
inference(rename_variables,[],[i_0_1434]) ).
cnf(i_0_2988,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_Orel__comp(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2),c_Transitive__Closure_Ortrancl(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_1593,i_0_2986,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447]) ).
cnf(i_0_2989,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2990,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X3,X4,X1),X4,X1,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X4,X1,X1)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1))) ),
inference(rename_variables,[],[i_0_1447]) ).
cnf(i_0_2991,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_Orel__comp(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1),c_Transitive__Closure_Ortrancl(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448]) ).
cnf(i_0_2992,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
inference(rename_variables,[],[i_0_1594]) ).
cnf(i_0_2993,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X3,X2,X4,X1),X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1))) ),
inference(rename_variables,[],[i_0_1448]) ).
cnf(i_0_2994,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),X3),c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X4,X1,X2))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466]) ).
cnf(i_0_2995,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2996,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X5)),X4),c_Product__Type_OSigma(X2,X3,X1,X5))) ),
inference(rename_variables,[],[i_0_1466]) ).
cnf(i_0_2997,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467]) ).
cnf(i_0_2998,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_2999,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Relation_OImage(X4,X2,X1,X5))) ),
inference(rename_variables,[],[i_0_1467]) ).
cnf(i_0_3000,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Relation_OImage(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5),X5,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468]) ).
cnf(i_0_3001,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XImageE__1__1(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Relation_OImage(X4,X2,X1,X5))) ),
inference(rename_variables,[],[i_0_1468]) ).
cnf(i_0_3002,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Oinv__image(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X5,X4,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489]) ).
cnf(i_0_3003,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3004,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(hAPP(X2,X3),hAPP(X2,X4),X1,X1)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(X3,X4,X6,X6)),c_Relation_Oinv__image(X5,X2,X1,X6))) ),
inference(rename_variables,[],[i_0_1489]) ).
cnf(i_0_3005,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Oinv__image(c_Relation_OId(X3),X4,X3,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490]) ).
cnf(i_0_3006,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_3007,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(hAPP(X2,X3),hAPP(X2,X4),X1,X1)),X5))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X6,X6)),c_Pair(X3,X4,X6,X6)),c_Relation_Oinv__image(X5,X2,X1,X6))) ),
inference(rename_variables,[],[i_0_1490]) ).
cnf(i_0_3008,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X1),tc_bool)),X3,X1),X1,X3))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_1593,i_0_2986,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491]) ).
cnf(i_0_3009,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3010,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ODomain(c_Relation_Oconverse(X4,X1,X2),X2,X1))) ),
inference(rename_variables,[],[i_0_1491]) ).
cnf(i_0_3011,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_Arrow__Order__Mirabelle_Oalt),X1),c_Relation_ODomain(c_Relation_Oconverse(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X2),X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492]) ).
cnf(i_0_3012,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_3013,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X3,X4,X2,X1),X3,X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Relation_ODomain(c_Relation_Oconverse(X4,X1,X2),X2,X1))) ),
inference(rename_variables,[],[i_0_1492]) ).
cnf(i_0_3014,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),X1,X3))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499]) ).
cnf(i_0_3015,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3016,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X3,X4,X1,X2),X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X4,X1,X2))) ),
inference(rename_variables,[],[i_0_1499]) ).
cnf(i_0_3017,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_Arrow__Order__Mirabelle_Oalt),X1),c_Relation_ODomain(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X2),X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500]) ).
cnf(i_0_3018,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
inference(rename_variables,[],[i_0_1594]) ).
cnf(i_0_3019,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X3,X4,X1,X2),X1,X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X4,X1,X2))) ),
inference(rename_variables,[],[i_0_1500]) ).
cnf(i_0_3020,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Oconverse(c_Relation_OId(X1),X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510]) ).
cnf(i_0_3021,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X1)),c_Pair(X4,X3,X2,X1)),c_Relation_Oconverse(X5,X1,X2))) ),
inference(rename_variables,[],[i_0_1510]) ).
cnf(i_0_3022,plain,
hAPP(c_Recdef_Ocut(X1,c_Relation_OId(X2),X3,X2,X4),X3) = hAPP(X1,X3),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512]) ).
cnf(i_0_3023,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hAPP(c_Recdef_Ocut(X5,X4,X3,X1,X6),X2) = hAPP(X5,X2) ),
inference(rename_variables,[],[i_0_1512]) ).
cnf(i_0_3024,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Orel__comp(c_Relation_OId(X1),c_Transitive__Closure_Ortrancl(c_Relation_OId(X1),X1),X1,X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521]) ).
cnf(i_0_3025,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1))) ),
inference(rename_variables,[],[i_0_1521]) ).
cnf(i_0_3026,plain,
~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)),X2),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_1645,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525]) ).
cnf(i_0_3027,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X4,tc_prod(X1,X1)),X1) ),
inference(rename_variables,[],[i_0_1525]) ).
cnf(i_0_3028,plain,
~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)),X2),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_1645,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526]) ).
cnf(i_0_3029,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X3,X2,X1,X1),X4,tc_prod(X1,X1)),X1) ),
inference(rename_variables,[],[i_0_1526]) ).
cnf(i_0_3030,plain,
c_Nitpick_Orefl_H(c_Relation_OId(X1),X1),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_1645,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561]) ).
cnf(i_0_3031,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_3032,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X1),X1,X1)),X2))
| c_Nitpick_Orefl_H(X2,X1) ),
inference(rename_variables,[],[i_0_1561]) ).
cnf(i_0_3033,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Wellfounded_Omeasure(X3,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578]) ).
cnf(i_0_3034,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(rename_variables,[],[i_0_2490]) ).
cnf(i_0_3035,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),c_Wellfounded_Omeasure(X1,X4))) ),
inference(rename_variables,[],[i_0_1578]) ).
cnf(i_0_3036,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(c_Relation_OId(X1),X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580]) ).
cnf(i_0_3037,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| hBOOL(hAPP(hAPP(c_in(X1),X3),c_Relation_ODomain(X5,X1,X2))) ),
inference(rename_variables,[],[i_0_1580]) ).
cnf(i_0_3038,plain,
~ c_Relation_Oirrefl(c_Relation_OId(X1),X1),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598]) ).
cnf(i_0_3039,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Relation_Oirrefl(X3,X1) ),
inference(rename_variables,[],[i_0_1598]) ).
cnf(i_0_3040,plain,
~ c_Wellfounded_Owf(c_Relation_OId(X1),X1),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599]) ).
cnf(i_0_3041,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Wellfounded_Owf(X3,X1) ),
inference(rename_variables,[],[i_0_1599]) ).
cnf(i_0_3042,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_1593,i_0_2986,i_0_2989,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604]) ).
cnf(i_0_3043,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3044,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X3,X1),X3,X1,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),c_Wellfounded_Oacc(X2,X1))) ),
inference(rename_variables,[],[i_0_1604]) ).
cnf(i_0_3045,plain,
hBOOL(hAPP(hAPP(c_in(tc_Arrow__Order__Mirabelle_Oalt),X1),c_Wellfounded_Oacc(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X2),X1),tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605]) ).
cnf(i_0_3046,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X2))),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_3047,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X3,X1),X3,X1,X1)),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),c_Wellfounded_Oacc(X2,X1))) ),
inference(rename_variables,[],[i_0_1605]) ).
cnf(i_0_3048,plain,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617]) ).
cnf(i_0_3049,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3050,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X1),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X1),X1,X1)),X2))
| c_Relation_Oirrefl(X2,X1) ),
inference(rename_variables,[],[i_0_1617]) ).
cnf(i_0_3051,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(X1,X1),tc_prod(X1,X1))),c_Pair(c_Pair(X2,X2,X1,X1),c_Pair(X2,X2,X1,X1),tc_prod(X1,X1),tc_prod(X1,X1))),c_Relation_OId__on(c_Relation_OId(X1),tc_prod(X1,X1)))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629]) ).
cnf(i_0_3052,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId__on(X3,X1))) ),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_3053,plain,
~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647]) ).
cnf(i_0_3054,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3055,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ c_Nitpick_Orefl_H(X3,X1) ),
inference(rename_variables,[],[i_0_1647]) ).
cnf(i_0_3056,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668]) ).
cnf(i_0_3057,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3058,plain,
( hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
inference(rename_variables,[],[i_0_1668]) ).
cnf(i_0_3059,plain,
~ hBOOL(hAPP(c_Set_Ovimage(X1,hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X1,X2)),X3,X4),X2)),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681]) ).
cnf(i_0_3060,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(rename_variables,[],[i_0_2490]) ).
cnf(i_0_3061,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
inference(rename_variables,[],[i_0_1681]) ).
cnf(i_0_3062,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(hAPP(X3,X2),X4,X5),X1,X5))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701]) ).
cnf(i_0_3063,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3064,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),hAPP(X2,X3)),X4))
| hBOOL(hAPP(hAPP(c_in(X5),X3),c_Set_Ovimage(X2,X4,X5,X1))) ),
inference(rename_variables,[],[i_0_1701]) ).
cnf(i_0_3065,plain,
hBOOL(hAPP(c_Set_Ovimage(X1,c_Set_Oinsert(hAPP(X1,X2),X3,X4),X5,X6),X2)),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749]) ).
cnf(i_0_3066,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(rename_variables,[],[i_0_2306]) ).
cnf(i_0_3067,plain,
( ~ hBOOL(hAPP(X1,hAPP(X2,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
inference(rename_variables,[],[i_0_1749]) ).
cnf(i_0_3068,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756]) ).
cnf(i_0_3069,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3070,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X3),c_Relation_OId__on(X2,X1))) ),
inference(rename_variables,[],[i_0_1756]) ).
cnf(i_0_3071,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(c_Set_Oinsert(X2,X3,tc_prod(X1,X1)),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821]) ).
cnf(i_0_3072,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3073,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Transitive__Closure_Ortrancl(X3,X1))) ),
inference(rename_variables,[],[i_0_1821]) ).
cnf(i_0_3074,plain,
c_Pair(X1,X1,X2,X2) = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(c_Pair(X1,X1,X2,X2),X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(c_Pair(X1,X1,X2,X2),X2),X2,X2),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834]) ).
cnf(i_0_3075,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_OId(X1)))
| X2 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X2,X1),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X2,X1),X1,X1) ),
inference(rename_variables,[],[i_0_1834]) ).
cnf(i_0_3076,plain,
X1 = c_ATP__Linkup_Osko__Relation__XIdE__1__1(c_Pair(X1,X1,X2,X2),X2),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841]) ).
cnf(i_0_3077,plain,
( c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4)
| X1 = X5 ),
inference(rename_variables,[],[i_0_1841]) ).
cnf(i_0_3078,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Set_Oinsert(c_Pair(X1,X1,X2,X2),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_prod(X2,X2)),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942]) ).
cnf(i_0_3079,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)),X1) ),
inference(rename_variables,[],[i_0_1942]) ).
cnf(i_0_3080,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OId(X1),c_Set_Oinsert(c_Pair(X2,X2,X1,X1),X3,tc_prod(X1,X1)),tc_fun(tc_prod(X1,X1),tc_bool)) = c_Set_Oinsert(c_Pair(X2,X2,X1,X1),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OId(X1),X3,tc_fun(tc_prod(X1,X1),tc_bool)),tc_prod(X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943]) ).
cnf(i_0_3081,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X2,X4,X1),tc_fun(X1,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(X1,tc_bool)),X1) ),
inference(rename_variables,[],[i_0_1943]) ).
cnf(i_0_3082,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Set_Oinsert(X3,c_Relation_OId(X1),tc_prod(X1,X1)))),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984]) ).
cnf(i_0_3083,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X4,X3,X1))) ),
inference(rename_variables,[],[i_0_1984]) ).
cnf(i_0_3084,plain,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059]) ).
cnf(i_0_3085,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X2,X1)),c_Wellfounded_Oacc(X2,X1)))
| c_Wellfounded_Owf(X2,X1) ),
inference(rename_variables,[],[i_0_2059]) ).
cnf(i_0_3086,plain,
~ c_lessequals(c_Set_Oinsert(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X2,X3)),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156]) ).
cnf(i_0_3087,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1),tc_fun(X2,tc_bool)) ),
inference(rename_variables,[],[i_0_2156]) ).
cnf(i_0_3088,plain,
~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326]) ).
cnf(i_0_3089,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(rename_variables,[],[i_0_2326]) ).
cnf(i_0_3090,plain,
c_Set_Oinsert(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)) = c_Relation_OId(X2),
inference(scs_inference,[],[i_0_1404,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344]) ).
cnf(i_0_3091,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Set_Oinsert(X2,X3,X1) = X3 ),
inference(rename_variables,[],[i_0_2344]) ).
cnf(i_0_3092,plain,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743]) ).
cnf(i_0_3093,plain,
c_lessequals(c_Relation_OImage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X1,X2,X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4),X3,X2)),X2,X3),X4,tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2576,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577]) ).
cnf(i_0_3094,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(rename_variables,[],[i_0_2576]) ).
cnf(i_0_3095,plain,
( ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X3,X2,X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),X5),X4,X2)),tc_fun(X2,tc_bool))
| c_lessequals(c_Relation_OImage(X3,X1,X2,X4),X5,tc_fun(X4,tc_bool)) ),
inference(rename_variables,[],[i_0_1577]) ).
cnf(i_0_3096,plain,
c_lessequals(c_Set_Ovimage(X1,X2,X3,X4),c_Set_Ovimage(X1,c_Set_Oinsert(X5,X2,X4),X3,X4),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_2576,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745]) ).
cnf(i_0_3097,plain,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Ovimage(X4,X1,X5,X3),c_Set_Ovimage(X4,X2,X5,X3),tc_fun(X5,tc_bool)) ),
inference(rename_variables,[],[i_0_1745]) ).
cnf(i_0_3098,plain,
c_lessequals(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(c_Set_Oinsert(X4,X1,tc_prod(X2,X3)),X2,X3),tc_fun(X2,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_2576,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981]) ).
cnf(i_0_3099,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3100,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)) ),
inference(rename_variables,[],[i_0_1981]) ).
cnf(i_0_3101,plain,
c_lessequals(X1,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_2576,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037]) ).
cnf(i_0_3102,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3103,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(rename_variables,[],[i_0_2037]) ).
cnf(i_0_3104,plain,
c_lessequals(X1,c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_2576,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038]) ).
cnf(i_0_3105,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3106,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(rename_variables,[],[i_0_2038]) ).
cnf(i_0_3107,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_2576,i_0_2329,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039]) ).
cnf(i_0_3108,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2329]) ).
cnf(i_0_3109,plain,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
inference(rename_variables,[],[i_0_2039]) ).
cnf(i_0_3110,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_2576,i_0_2329,i_0_3108,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040]) ).
cnf(i_0_3111,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2329]) ).
cnf(i_0_3112,plain,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(rename_variables,[],[i_0_2040]) ).
cnf(i_0_3113,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_2576,i_0_2329,i_0_3108,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121]) ).
cnf(i_0_3114,plain,
( c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(rename_variables,[],[i_0_2121]) ).
cnf(i_0_3115,plain,
~ c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_2576,i_0_2329,i_0_3108,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134]) ).
cnf(i_0_3116,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X1,X3),X2,tc_fun(X3,tc_bool)) ),
inference(rename_variables,[],[i_0_2134]) ).
cnf(i_0_3117,plain,
c_lessequals(c_Wellfounded_Oacc(c_Set_Oinsert(X1,X2,tc_prod(X3,X3)),X3),c_Wellfounded_Oacc(X2,X3),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2329,i_0_3108,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187]) ).
cnf(i_0_3118,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3119,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X2,X3),c_Wellfounded_Oacc(X1,X3),tc_fun(X3,tc_bool)) ),
inference(rename_variables,[],[i_0_2187]) ).
cnf(i_0_3120,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2329,i_0_3108,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644]) ).
cnf(i_0_3121,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1) ),
inference(rename_variables,[],[i_0_2644]) ).
cnf(i_0_3122,plain,
c_lessequals(X1,X1,tc_bool),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2329,i_0_3108,i_0_2701,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645]) ).
cnf(i_0_3123,plain,
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,X2,X1) ),
inference(rename_variables,[],[i_0_2645]) ).
cnf(i_0_3124,plain,
c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X1,X2),X2),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680]) ).
cnf(i_0_3125,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(rename_variables,[],[i_0_2680]) ).
cnf(i_0_3126,plain,
c_Finite__Set_Ofinite(X1,tc_bool),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685]) ).
cnf(i_0_3127,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_2685]) ).
cnf(i_0_3128,plain,
hAPP(c_Set_Oinsert(X1,X2,X3),X1) != hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812]) ).
cnf(i_0_3129,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),c_Pair(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X6,X2,X1),X4,X1,X2),X7,tc_prod(X1,X2),tc_prod(X1,X2))),c_Relation_Orel__comp(c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X8,tc_prod(X1,X2),tc_prod(X1,X2)),c_Transitive__Closure_Ortrancl(c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X8,tc_prod(X1,X2),tc_prod(X1,X2)),tc_prod(X1,X2)),tc_prod(X1,X2),tc_prod(X1,X2),tc_prod(X1,X2)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443]) ).
cnf(i_0_3130,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X3,X4,X1),X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4)) ),
inference(rename_variables,[],[i_0_1443]) ).
cnf(i_0_3131,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),c_Pair(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X3,X4,X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X6,X2,X1),X4,X1,X2),X7,tc_prod(X1,X2),tc_prod(X1,X2))),c_Relation_Orel__comp(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),tc_prod(X1,X2)),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),tc_prod(X1,X2)),tc_prod(X1,X2)),tc_prod(X1,X2),tc_prod(X1,X2),tc_prod(X1,X2)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444]) ).
cnf(i_0_3132,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X3,X2,X4,X1),X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X4,X1,X1)),X3)) ),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_3133,plain,
~ c_Equiv__Relations_Oequiv(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585]) ).
cnf(i_0_3134,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_3135,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1) ),
inference(rename_variables,[],[i_0_1585]) ).
cnf(i_0_3136,plain,
~ c_Equiv__Relations_Oequiv(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Transitive__Closure_Ortrancl(X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586]) ).
cnf(i_0_3137,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3138,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1) ),
inference(rename_variables,[],[i_0_1586]) ).
cnf(i_0_3139,plain,
~ c_Relation_Orefl__on(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_1645,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587]) ).
cnf(i_0_3140,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_3141,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X5))
| ~ c_Relation_Orefl__on(X5,X4,X1) ),
inference(rename_variables,[],[i_0_1587]) ).
cnf(i_0_3142,plain,
~ c_Relation_Orefl__on(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Transitive__Closure_Ortrancl(X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_1645,i_0_3137,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588]) ).
cnf(i_0_3143,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3144,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_Relation_Orefl__on(X5,X4,X1) ),
inference(rename_variables,[],[i_0_1588]) ).
cnf(i_0_3145,plain,
~ c_lessequals(c_Relation_OId(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),tc_fun(tc_prod(X1,X1),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087]) ).
cnf(i_0_3146,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3147,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(rename_variables,[],[i_0_2087]) ).
cnf(i_0_3148,plain,
~ c_lessequals(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2),hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),tc_fun(X4,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397]) ).
cnf(i_0_3149,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(rename_variables,[],[i_0_2306]) ).
cnf(i_0_3150,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
inference(rename_variables,[],[i_0_2397]) ).
cnf(i_0_3151,plain,
~ c_Equiv__Relations_Oequiv(c_Relation_OId(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)),tc_bool)),tc_prod(X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924]) ).
cnf(i_0_3152,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3153,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Equiv__Relations_Oequiv(X4,X3,X1) ),
inference(rename_variables,[],[i_0_2924]) ).
cnf(i_0_3154,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X3,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X3,X1),X1),X1,X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457]) ).
cnf(i_0_3155,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X5,X1,X1)),X4)) ),
inference(rename_variables,[],[i_0_1457]) ).
cnf(i_0_3156,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Orel__comp(c_Relation_OId(X1),c_Relation_OId(X1),X1,X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458]) ).
cnf(i_0_3157,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X2,X6)),c_Pair(X4,X7,X2,X6)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X6)),c_Pair(X3,X7,X1,X6)),c_Relation_Orel__comp(X5,X8,X1,X2,X6))) ),
inference(rename_variables,[],[i_0_1458]) ).
cnf(i_0_3158,plain,
~ c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464]) ).
cnf(i_0_3159,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),X2),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X1),X1,X1,X1)))
| ~ c_lessequals(X3,X4,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(rename_variables,[],[i_0_1464]) ).
cnf(i_0_3160,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,X4,X2),X1,X1),X5,tc_prod(X1,X1)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,X4,X2),X1),c_Set_Oinsert(X3,X4,X2),X1,X1)),c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,X4,X2),X1,X1),X5,tc_prod(X1,X1)),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477]) ).
cnf(i_0_3161,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X2,X3,X1),X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| X2 = X3 ),
inference(rename_variables,[],[i_0_1477]) ).
cnf(i_0_3162,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_bool)),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483]) ).
cnf(i_0_3163,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2368]) ).
cnf(i_0_3164,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3165,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X5,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
inference(rename_variables,[],[i_0_1483]) ).
cnf(i_0_3166,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(c_Set_Ovimage(X4,c_Set_Oinsert(hAPP(X4,c_Pair(X2,X3,X1,X1)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),tc_prod(X1,X1),X5),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484]) ).
cnf(i_0_3167,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,c_Set_Oinsert(hAPP(X3,X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X1,X4))),
inference(rename_variables,[],[i_0_1656]) ).
cnf(i_0_3168,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3169,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X5,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1))) ),
inference(rename_variables,[],[i_0_1484]) ).
cnf(i_0_3170,plain,
~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X1,X2),X2),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498]) ).
cnf(i_0_3171,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Wellfounded_Owf(X4,X1) ),
inference(rename_variables,[],[i_0_1498]) ).
cnf(i_0_3172,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Wellfounded_Omlex__prod(X3,c_Relation_OId(X1),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507]) ).
cnf(i_0_3173,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3174,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Wellfounded_Omlex__prod(X5,X4,X1)))
| ~ c_lessequals(hAPP(X5,X2),hAPP(X5,X3),tc_nat) ),
inference(rename_variables,[],[i_0_1507]) ).
cnf(i_0_3175,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OImage(c_Transitive__Closure_Ortrancl(X3,tc_prod(X1,X1)),c_Relation_OId(X1),tc_prod(X1,X1),tc_prod(X1,X1)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549]) ).
cnf(i_0_3176,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3177,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X4)),c_Pair(X2,X5,X1,X4)),X6))
| hBOOL(hAPP(hAPP(c_in(X4),X5),c_Relation_OImage(X6,X3,X1,X4))) ),
inference(rename_variables,[],[i_0_1549]) ).
cnf(i_0_3178,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Relation_ODomain(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Set_Oinsert(X3,X4,X2),X1,X1),X5,tc_prod(X1,X1)),X1,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575]) ).
cnf(i_0_3179,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),c_Transitive__Closure_Ortrancl(X4,X1)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_ODomain(X4,X1,X1)))
| X2 = X3 ),
inference(rename_variables,[],[i_0_1575]) ).
cnf(i_0_3180,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2738,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607]) ).
cnf(i_0_3181,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3182,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X2,X3,X1,X4)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X4),c_HOL_Ozero__class_Ozero(X4)),c_Finite__Set_Osetprod(X3,X2,X1,X4)))
| ~ class_Ring__and__Field_Oordered__semidom(X4) ),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_3183,plain,
~ c_Relation_Orefl__on(c_Relation_OId(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)),tc_bool)),tc_prod(X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2738,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627]) ).
cnf(i_0_3184,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3185,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Relation_Orefl__on(X4,X3,X1) ),
inference(rename_variables,[],[i_0_1627]) ).
cnf(i_0_3186,plain,
c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2730,i_0_2738,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646]) ).
cnf(i_0_3187,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3188,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X2,X3,X1,X4)),X2))
| c_Finite__Set_Osetprod(X3,X2,X1,X4) = c_HOL_Oone__class_Oone(X4)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X4) ),
inference(rename_variables,[],[i_0_1646]) ).
cnf(i_0_3189,plain,
~ c_Equiv__Relations_Oequiv(c_Set_Oinsert(X1,X2,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X3),X1),tc_Arrow__Order__Mirabelle_Oalt),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2730,i_0_2738,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652]) ).
cnf(i_0_3190,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3191,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_Equiv__Relations_Oequiv(X4,X3,X1) ),
inference(rename_variables,[],[i_0_1652]) ).
cnf(i_0_3192,plain,
hAPP(hAPP(c_Finite__Set_Osetsum(X1,tc_nat),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653]) ).
cnf(i_0_3193,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3194,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X2,X3,X1,X4)),X2))
| hAPP(hAPP(c_Finite__Set_Osetsum(X1,X4),X3),X2) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(rename_variables,[],[i_0_1653]) ).
cnf(i_0_3195,plain,
~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Relation_OImage(c_Wellfounded_Omeasure(X4,X3),c_Set_Oinsert(X1,X2,X3),X3,X3),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793]) ).
cnf(i_0_3196,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2511]) ).
cnf(i_0_3197,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Relation_OImage(X3,X1,X2,X2),tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(rename_variables,[],[i_0_1793]) ).
cnf(i_0_3198,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877]) ).
cnf(i_0_3199,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X1)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(rename_variables,[],[i_0_1877]) ).
cnf(i_0_3200,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878]) ).
cnf(i_0_3201,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,X1)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(rename_variables,[],[i_0_1878]) ).
cnf(i_0_3202,plain,
~ class_OrderedGroup_Opordered__ab__group__add(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879]) ).
cnf(i_0_3203,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_3204,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_1879]) ).
cnf(i_0_3205,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905]) ).
cnf(i_0_3206,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(rename_variables,[],[i_0_1905]) ).
cnf(i_0_3207,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),X3,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945]) ).
cnf(i_0_3208,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),c_Power_Opower__class_Opower(X2,X3,X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(rename_variables,[],[i_0_1945]) ).
cnf(i_0_3209,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OId(X1),c_Relation_OId(X1),tc_fun(tc_prod(X1,X1),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976]) ).
cnf(i_0_3210,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_3211,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lattices_Oupper__semilattice__class_Osup(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),X3,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979]) ).
cnf(i_0_3212,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(rename_variables,[],[i_0_1979]) ).
cnf(i_0_3213,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lattices_Oupper__semilattice__class_Osup(X1,c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980]) ).
cnf(i_0_3214,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X1)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(rename_variables,[],[i_0_1980]) ).
cnf(i_0_3215,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982]) ).
cnf(i_0_3216,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(rename_variables,[],[i_0_1982]) ).
cnf(i_0_3217,plain,
c_Transitive__Closure_Ortrancl(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992]) ).
cnf(i_0_3218,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2329]) ).
cnf(i_0_3219,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(rename_variables,[],[i_0_2508]) ).
cnf(i_0_3220,plain,
( ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(tc_prod(X3,X3),tc_bool))
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ),
inference(rename_variables,[],[i_0_1992]) ).
cnf(i_0_3221,plain,
c_lessequals(c_Set_Oinsert(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000]) ).
cnf(i_0_3222,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(rename_variables,[],[i_0_2576]) ).
cnf(i_0_3223,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_lessequals(c_Set_Oinsert(X2,X4,X1),X3,tc_fun(X1,tc_bool))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
inference(rename_variables,[],[i_0_2000]) ).
cnf(i_0_3224,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036]) ).
cnf(i_0_3225,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_3226,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(rename_variables,[],[i_0_2036]) ).
cnf(i_0_3227,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115]) ).
cnf(i_0_3228,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)))
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(rename_variables,[],[i_0_2115]) ).
cnf(i_0_3229,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2700,i_0_2701,i_0_2702,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169]) ).
cnf(i_0_3230,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_2169]) ).
cnf(i_0_3231,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170]) ).
cnf(i_0_3232,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_2170]) ).
cnf(i_0_3233,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185]) ).
cnf(i_0_3234,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
inference(rename_variables,[],[i_0_2185]) ).
cnf(i_0_3235,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,tc_bool),tc_bool),tc_bool) = c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,tc_bool),tc_bool),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202]) ).
cnf(i_0_3236,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3237,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Ocard(c_Set_Oinsert(X2,X3,X1),X1) = c_Finite__Set_Ocard(X3,X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(rename_variables,[],[i_0_2202]) ).
cnf(i_0_3238,plain,
~ c_lessequals(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280]) ).
cnf(i_0_3239,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
inference(rename_variables,[],[i_0_2280]) ).
cnf(i_0_3240,plain,
~ c_lessequals(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283]) ).
cnf(i_0_3241,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_2283]) ).
cnf(i_0_3242,plain,
c_Set_Oinsert(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301]) ).
cnf(i_0_3243,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3244,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
inference(rename_variables,[],[i_0_2509]) ).
cnf(i_0_3245,plain,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| X2 = X1 ),
inference(rename_variables,[],[i_0_2301]) ).
cnf(i_0_3246,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333]) ).
cnf(i_0_3247,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_2333]) ).
cnf(i_0_3248,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334]) ).
cnf(i_0_3249,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_2334]) ).
cnf(i_0_3250,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409]) ).
cnf(i_0_3251,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_3252,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_2409]) ).
cnf(i_0_3253,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428]) ).
cnf(i_0_3254,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3255,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ c_lessequals(X1,X2,tc_nat)
| X1 = X2 ),
inference(rename_variables,[],[i_0_2428]) ).
cnf(i_0_3256,plain,
c_lessequals(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448]) ).
cnf(i_0_3257,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_2448]) ).
cnf(i_0_3258,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,tc_bool),tc_bool) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577]) ).
cnf(i_0_3259,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2511]) ).
cnf(i_0_3260,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_2577]) ).
cnf(i_0_3261,plain,
c_Relation_OImage(c_Relation_OId(X1),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3,X3),X1,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X3),X2,X3,X3,X3),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2293,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744]) ).
cnf(i_0_3262,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3263,plain,
~ c_Equiv__Relations_Oequiv(c_Relation_Oconverse(c_Relation_OId(X1),X1,X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)),tc_bool)),tc_prod(X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2293,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820]) ).
cnf(i_0_3264,plain,
~ c_Equiv__Relations_Oequiv(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_Oconverse(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2293,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821]) ).
cnf(i_0_3265,plain,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
inference(rename_variables,[],[i_0_2636]) ).
cnf(i_0_3266,plain,
~ c_Equiv__Relations_Oequiv(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OImage(c_Relation_OId(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2293,i_0_3262,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822]) ).
cnf(i_0_3267,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3268,plain,
~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OImage(c_Relation_OId(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,X2)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2293,i_0_3262,i_0_3267,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827]) ).
cnf(i_0_3269,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3270,plain,
~ c_lessequals(c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X2,X3)),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838]) ).
cnf(i_0_3271,plain,
~ c_lessequals(c_Set_Oinsert(X1,X2,X3),c_Relation_OImage(c_Relation_OId(X4),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X2,X3)),X4,X4),tc_fun(X3,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839]) ).
cnf(i_0_3272,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3273,plain,
~ c_lessequals(c_Set_Oinsert(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_OImage(c_Relation_OId(X2),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),X2,X2)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840]) ).
cnf(i_0_3274,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3275,plain,
~ c_Nitpick_Orefl_H(c_Relation_OImage(c_Relation_OId(X1),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X1,X1),X2),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846]) ).
cnf(i_0_3276,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3277,plain,
~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2)),tc_bool)),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847]) ).
cnf(i_0_3278,plain,
~ c_Relation_Orefl__on(c_Relation_Oconverse(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_bool)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848]) ).
cnf(i_0_3279,plain,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
inference(rename_variables,[],[i_0_2636]) ).
cnf(i_0_3280,plain,
~ c_Relation_Orefl__on(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_Oconverse(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849]) ).
cnf(i_0_3281,plain,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
inference(rename_variables,[],[i_0_2636]) ).
cnf(i_0_3282,plain,
~ c_Relation_Orefl__on(v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OImage(c_Relation_OId(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850]) ).
cnf(i_0_3283,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3284,plain,
~ c_Relation_Oirrefl(c_Relation_Oconverse(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851]) ).
cnf(i_0_3285,plain,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
inference(rename_variables,[],[i_0_2636]) ).
cnf(i_0_3286,plain,
~ c_Relation_Oirrefl(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Relation_OImage(c_Relation_OId(X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852]) ).
cnf(i_0_3287,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3288,plain,
~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893]) ).
cnf(i_0_3289,plain,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
inference(rename_variables,[],[i_0_2636]) ).
cnf(i_0_3290,plain,
~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),c_Relation_OImage(c_Relation_OId(X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2,X2)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894]) ).
cnf(i_0_3291,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3292,plain,
c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(c_Set_Oinsert(X3,X1,tc_prod(X2,X2)),c_Set_Oinsert(X3,X1,tc_prod(X2,X2)),X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529]) ).
cnf(i_0_3293,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3294,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3295,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(tc_prod(X7,X3),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X5,X1,X7,X3,X4),c_Relation_Orel__comp(X6,X2,X7,X3,X4),tc_fun(tc_prod(X7,X4),tc_bool)) ),
inference(rename_variables,[],[i_0_1529]) ).
cnf(i_0_3296,plain,
c_lessequals(c_Relation_OImage(X1,X2,X3,X4),c_Relation_OImage(c_Set_Oinsert(X5,X1,tc_prod(X3,X4)),c_Set_Oinsert(X6,X2,X3),X3,X4),tc_fun(X4,tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705]) ).
cnf(i_0_3297,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3298,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X3,tc_bool))
| c_lessequals(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X6,X3,X4),tc_fun(X4,tc_bool)) ),
inference(rename_variables,[],[i_0_1705]) ).
cnf(i_0_3299,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154]) ).
cnf(i_0_3300,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X3,X2,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(rename_variables,[],[i_0_2154]) ).
cnf(i_0_3301,plain,
c_Relation_Osingle__valued(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1,X1),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167]) ).
cnf(i_0_3302,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2329]) ).
cnf(i_0_3303,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_Relation_Osingle__valued(X1,X3,X4)
| ~ c_Relation_Osingle__valued(X2,X3,X4) ),
inference(rename_variables,[],[i_0_2167]) ).
cnf(i_0_3304,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216]) ).
cnf(i_0_3305,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3306,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,X4,X3) ),
inference(rename_variables,[],[i_0_2216]) ).
cnf(i_0_3307,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218]) ).
cnf(i_0_3308,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3309,plain,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X2,X4,X3) ),
inference(rename_variables,[],[i_0_2218]) ).
cnf(i_0_3310,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),X1,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220]) ).
cnf(i_0_3311,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3312,plain,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X1,X2,X4) ),
inference(rename_variables,[],[i_0_2220]) ).
cnf(i_0_3313,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),X2,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222]) ).
cnf(i_0_3314,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3315,plain,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2222]) ).
cnf(i_0_3316,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235]) ).
cnf(i_0_3317,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1) ),
inference(rename_variables,[],[i_0_2235]) ).
cnf(i_0_3318,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236]) ).
cnf(i_0_3319,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X1) ),
inference(rename_variables,[],[i_0_2236]) ).
cnf(i_0_3320,plain,
c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265]) ).
cnf(i_0_3321,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3322,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(rename_variables,[],[i_0_2265]) ).
cnf(i_0_3323,plain,
c_Relation_Oantisym(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3293,i_0_2576,i_0_3094,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308]) ).
cnf(i_0_3324,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2329]) ).
cnf(i_0_3325,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Oantisym(X1,X3)
| ~ c_Relation_Oantisym(X2,X3) ),
inference(rename_variables,[],[i_0_2308]) ).
cnf(i_0_3326,plain,
~ c_Wellfounded_Oacyclic(c_Set_Oinsert(X1,c_Set_Oinsert(c_Pair(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X2,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3293,i_0_2576,i_0_3094,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309]) ).
cnf(i_0_3327,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3328,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Oacyclic(X2,X3)
| c_Wellfounded_Oacyclic(X1,X3) ),
inference(rename_variables,[],[i_0_2309]) ).
cnf(i_0_3329,plain,
~ c_Wellfounded_Owf(c_Set_Oinsert(X1,c_Set_Oinsert(c_Pair(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X2,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310]) ).
cnf(i_0_3330,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3331,plain,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X2,X3)
| c_Wellfounded_Owf(X1,X3) ),
inference(rename_variables,[],[i_0_2310]) ).
cnf(i_0_3332,plain,
~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),X3,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355]) ).
cnf(i_0_3333,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,X3,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
inference(rename_variables,[],[i_0_2355]) ).
cnf(i_0_3334,plain,
c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),X1),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465]) ).
cnf(i_0_3335,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2329]) ).
cnf(i_0_3336,plain,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(rename_variables,[],[i_0_2465]) ).
cnf(i_0_3337,plain,
~ c_Equiv__Relations_Oequiv(c_Set_Oinsert(X1,X2,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1),tc_Arrow__Order__Mirabelle_Oalt),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523]) ).
cnf(i_0_3338,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
inference(rename_variables,[],[i_0_1594]) ).
cnf(i_0_3339,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3340,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(rename_variables,[],[i_0_2576]) ).
cnf(i_0_3341,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X5))
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1,X1),tc_fun(X1,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X1) ),
inference(rename_variables,[],[i_0_1523]) ).
cnf(i_0_3342,plain,
c_Finite__Set_Osetprod(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(X1,X2)),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767]) ).
cnf(i_0_3343,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3344,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetprod(X4,c_Set_Oinsert(X2,X3,X1),X1,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X2)),c_Finite__Set_Osetprod(X4,X3,X1,X5))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_3345,plain,
hAPP(hAPP(c_Finite__Set_Osetsum(X1,tc_nat),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(X2,X3)),hAPP(hAPP(c_Finite__Set_Osetsum(X1,tc_nat),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917]) ).
cnf(i_0_3346,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3347,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Finite__Set_Osetsum(X1,X4),X5),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X2)),hAPP(hAPP(c_Finite__Set_Osetsum(X1,X4),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(rename_variables,[],[i_0_1917]) ).
cnf(i_0_3348,plain,
~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),X4,X4),X5,tc_prod(X4,X4)),X4),X4,X4),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494]) ).
cnf(i_0_3349,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3350,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X4,X1,X2)),X5))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X2)),c_Pair(X3,X6,X1,X2)),X5))
| ~ c_Relation_Osingle__valued(X5,X1,X2)
| X4 = X6 ),
inference(rename_variables,[],[i_0_1494]) ).
cnf(i_0_3351,plain,
~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_bool)),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533]) ).
cnf(i_0_3352,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2368]) ).
cnf(i_0_3353,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_3354,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_OId(X1))),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_3355,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X3,X4,X1),X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ c_Wellfounded_Owf(X4,X1) ),
inference(rename_variables,[],[i_0_1533]) ).
cnf(i_0_3356,plain,
~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_prod(X1,X1),tc_prod(X1,X1)),tc_bool)),tc_prod(X1,X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534]) ).
cnf(i_0_3357,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2368]) ).
cnf(i_0_3358,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X3,X4,X1),X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ c_Wellfounded_Owf(X4,X1) ),
inference(rename_variables,[],[i_0_1534]) ).
cnf(i_0_3359,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_bool),tc_bool,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657]) ).
cnf(i_0_3360,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3361,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X4,X3,X1,tc_nat)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(X4,X2)))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(rename_variables,[],[i_0_1657]) ).
cnf(i_0_3362,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat)),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708]) ).
cnf(i_0_3363,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3364,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_Power_Opower__class_Opower(X2,X4,X1)),c_Power_Opower__class_Opower(X3,X4,X1)))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(rename_variables,[],[i_0_1708]) ).
cnf(i_0_3365,plain,
c_Ring__and__Field_Odvd__class_Odvd(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X1,c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_bool),tc_bool,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843]) ).
cnf(i_0_3366,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3367,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(X4,X2),c_Finite__Set_Osetprod(X4,X3,X1,X5),X5)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(rename_variables,[],[i_0_1843]) ).
cnf(i_0_3368,plain,
~ c_lessequals(c_Power_Opower__class_Opower(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),X3,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_2490,i_0_3034,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131]) ).
cnf(i_0_3369,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_3370,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X3,X4,X1) ),
inference(rename_variables,[],[i_0_2131]) ).
cnf(i_0_3371,plain,
~ c_lessequals(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132]) ).
cnf(i_0_3372,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(rename_variables,[],[i_0_2490]) ).
cnf(i_0_3373,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X4,X2,X1) ),
inference(rename_variables,[],[i_0_2132]) ).
cnf(i_0_3374,plain,
~ c_lessequals(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133]) ).
cnf(i_0_3375,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X4,X3,X1) ),
inference(rename_variables,[],[i_0_2133]) ).
cnf(i_0_3376,plain,
c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288]) ).
cnf(i_0_3377,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3378,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_2288]) ).
cnf(i_0_3379,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Osetprod(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_bool),tc_bool,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349]) ).
cnf(i_0_3380,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_3381,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1)
| X2 = X3 ),
inference(rename_variables,[],[i_0_2349]) ).
cnf(i_0_3382,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379]) ).
cnf(i_0_3383,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3384,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_2379]) ).
cnf(i_0_3385,plain,
~ c_lessequals(c_Finite__Set_Ocard(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_bool),tc_bool),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383]) ).
cnf(i_0_3386,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_3387,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_2383]) ).
cnf(i_0_3388,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421]) ).
cnf(i_0_3389,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3390,plain,
( ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(rename_variables,[],[i_0_2421]) ).
cnf(i_0_3391,plain,
c_lessequals(c_Power_Opower__class_Opower(c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Power_Opower__class_Opower(c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019]) ).
cnf(i_0_3392,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ c_lessequals(X3,X4,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(rename_variables,[],[i_0_2019]) ).
cnf(i_0_3393,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat),c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),c_Finite__Set_Osetprod(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5,tc_nat),tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034]) ).
cnf(i_0_3394,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X1,X4),c_Power_Opower__class_Opower(X5,X2,X4),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X4) ),
inference(rename_variables,[],[i_0_2034]) ).
cnf(i_0_3395,plain,
c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628]) ).
cnf(i_0_3396,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3397,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X2,X3,X1,X4)),X2))
| c_Finite__Set_Osetprod(X3,X2,X1,X4) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1628]) ).
cnf(i_0_3398,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),tc_nat)),c_Power_Opower__class_Opower(c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat),tc_nat))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744]) ).
cnf(i_0_3399,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3400,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_Power_Opower__class_Opower(X3,X1,X2)),c_Power_Opower__class_Opower(X4,X1,X2)))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(rename_variables,[],[i_0_1744]) ).
cnf(i_0_3401,plain,
~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),X3),X3,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918]) ).
cnf(i_0_3402,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(rename_variables,[],[i_0_2490]) ).
cnf(i_0_3403,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
inference(rename_variables,[],[i_0_1918]) ).
cnf(i_0_3404,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)),X1)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929]) ).
cnf(i_0_3405,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(rename_variables,[],[i_0_2490]) ).
cnf(i_0_3406,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3407,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1929]) ).
cnf(i_0_3408,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_Finite__Set_Osetprod(X1,X2,tc_bool,tc_nat),c_Finite__Set_Osetprod(X1,c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_bool),tc_bool,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743]) ).
cnf(i_0_3409,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(rename_variables,[],[i_0_2417]) ).
cnf(i_0_3410,plain,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Ring__and__Field_Odvd__class_Odvd(c_Finite__Set_Osetprod(X4,X1,X3,X5),c_Finite__Set_Osetprod(X4,X2,X3,X5),X5)
| ~ class_Ring__and__Field_Odvd(X5)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(rename_variables,[],[i_0_1743]) ).
cnf(i_0_3411,plain,
c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950]) ).
cnf(i_0_3412,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3413,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3414,plain,
( ~ c_lessequals(X1,c_HOL_Oone__class_Oone(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ c_lessequals(X3,X4,tc_nat)
| c_lessequals(c_Power_Opower__class_Opower(X1,X4,X2),c_Power_Opower__class_Opower(X1,X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(rename_variables,[],[i_0_1950]) ).
cnf(i_0_3415,plain,
~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ozero__class_Ozero(tc_nat))),X3,tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157]) ).
cnf(i_0_3416,plain,
c_lessequals(X1,X1,tc_nat),
inference(rename_variables,[],[i_0_2654]) ).
cnf(i_0_3417,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X4,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X1,X3,X2) ),
inference(rename_variables,[],[i_0_2157]) ).
cnf(i_0_3418,plain,
~ c_Wellfounded_Oacyclic(c_Relation_OId(X1),X1),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469]) ).
cnf(i_0_3419,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X1),X1,X1,X1)))
| ~ c_Wellfounded_Oacyclic(X3,X1) ),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_3420,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),X1,X1)),c_Wellfounded_Omlex__prod(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),X4,X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613]) ).
cnf(i_0_3421,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X1,X2)),hAPP(X1,X3)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),c_Wellfounded_Omlex__prod(X1,X5,X4))) ),
inference(rename_variables,[],[i_0_1613]) ).
cnf(i_0_3422,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),X1,X1)),c_Wellfounded_Omeasure(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),X1))),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616]) ).
cnf(i_0_3423,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X1,X2)),hAPP(X1,X3)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X4,X4)),c_Pair(X2,X3,X4,X4)),c_Wellfounded_Omeasure(X1,X4))) ),
inference(rename_variables,[],[i_0_1616]) ).
cnf(i_0_3424,plain,
~ c_lessequals(c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_bool)),c_Relation_OId(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_fun(tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_bool)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057]) ).
cnf(i_0_3425,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)) ),
inference(rename_variables,[],[i_0_2057]) ).
cnf(i_0_3426,plain,
c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389]) ).
cnf(i_0_3427,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| c_lessequals(X1,X2,tc_nat) ),
inference(rename_variables,[],[i_0_2389]) ).
cnf(i_0_3428,plain,
c_Finite__Set_Osetprod(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_bool),tc_bool,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530]) ).
cnf(i_0_3429,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rename_variables,[],[i_0_2530]) ).
cnf(i_0_3430,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561]) ).
cnf(i_0_3431,plain,
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rename_variables,[],[i_0_2561]) ).
cnf(i_0_3432,plain,
c_lessequals(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533]) ).
cnf(i_0_3433,plain,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
inference(rename_variables,[],[i_0_2533]) ).
cnf(i_0_3434,plain,
~ class_Orderings_Otop(tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622]) ).
cnf(i_0_3435,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(X2),X2)
| ~ class_Orderings_Otop(X2) ),
inference(rename_variables,[],[i_0_2622]) ).
cnf(i_0_3436,plain,
( ~ c_Relation_Osym(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X3,X3)),c_Pair(X2,X1,X3,X3)),c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)))) ),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516]) ).
cnf(i_0_3437,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3438,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Relation_Osym(X4,X1) ),
inference(rename_variables,[],[i_0_1516]) ).
cnf(i_0_3439,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441]) ).
cnf(i_0_3440,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3441,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X2,X1,tc_nat)
| X2 = X1 ),
inference(rename_variables,[],[i_0_2441]) ).
cnf(i_0_3442,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_bool),tc_bool),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531]) ).
cnf(i_0_3443,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
inference(rename_variables,[],[i_0_2531]) ).
cnf(i_0_3444,plain,
~ c_Relation_Osingle__valued(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),X4,X4),X5,tc_prod(X4,X4)),X4),c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),X4,X4),X5,tc_prod(X4,X4)),X4),X4,X4,X4),X4,X4),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823]) ).
cnf(i_0_3445,plain,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_3446,plain,
~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5)),X6,tc_prod(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5))),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5)),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X5),X5,X5,X5),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824]) ).
cnf(i_0_3447,plain,
~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5)),X6,tc_prod(c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5))),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5)),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X4,X5),X4,X5,X5,X5),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X5),X5,X5,X5)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825]) ).
cnf(i_0_3448,plain,
~ c_Wellfounded_Oacyclic(c_Set_Oinsert(X1,c_Set_Oinsert(X1,c_Set_Oinsert(c_Pair(c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X2,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826]) ).
cnf(i_0_3449,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(rename_variables,[],[i_0_2357]) ).
cnf(i_0_3450,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_Relation_OImage(c_Relation_OId(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1,X1),c_Finite__Set_Ocard(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_bool),tc_bool),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858]) ).
cnf(i_0_3451,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3452,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),c_Relation_OImage(c_Relation_OId(X1),c_Finite__Set_Ocard(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_bool),tc_bool),X1,X1),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859]) ).
cnf(i_0_3453,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3454,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_bool),tc_bool),c_Relation_OImage(c_Relation_OId(X2),tc_nat,X2,X2)),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860]) ).
cnf(i_0_3455,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(rename_variables,[],[i_0_2293]) ).
cnf(i_0_3456,plain,
tc_bool != tc_nat,
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920]) ).
cnf(i_0_3457,plain,
c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Otop__class_Otop(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Otop__class_Otop(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920,i_0_2518]) ).
cnf(i_0_3458,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3) ),
inference(rename_variables,[],[i_0_2518]) ).
cnf(i_0_3459,plain,
( ~ c_Relation_Oantisym(c_Set_Oinsert(c_Pair(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X4),X5,tc_prod(X4,X4)),X4)
| ~ c_Relation_Osym(c_Set_Oinsert(c_Pair(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X4),X5,tc_prod(X4,X4)),X4) ),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_3437,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920,i_0_2518,i_0_1497]) ).
cnf(i_0_3460,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X2,X3,X1))),
inference(rename_variables,[],[i_0_2211]) ).
cnf(i_0_3461,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(rename_variables,[],[i_0_2510]) ).
cnf(i_0_3462,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X3,X1,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X3,X2,X1,X1)),X4))
| ~ c_Relation_Oantisym(X4,X1)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1497]) ).
cnf(i_0_3463,plain,
( ~ c_Relation_Osym(c_Set_Oinsert(c_Pair(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X4),X5,tc_prod(X4,X4)),X4)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetprod(X6,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X7,tc_nat)),X8)),X8)) ),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_3437,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2694,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920,i_0_2518,i_0_1497,i_0_1779]) ).
cnf(i_0_3464,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_1779]) ).
cnf(i_0_3465,plain,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_Relation_Osym(c_Set_Oinsert(c_Pair(c_Set_Oinsert(X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6,X6),X7,tc_prod(X6,X6)),X6) ),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_3437,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_2694,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920,i_0_2518,i_0_1497,i_0_1779,i_0_2130]) ).
cnf(i_0_3466,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X4,X1) ),
inference(rename_variables,[],[i_0_2130]) ).
cnf(i_0_3467,plain,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetprod(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Otop__class_Otop(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_Relation_Osym(c_Set_Oinsert(c_Pair(c_Set_Oinsert(X3,X4,X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X6,X6),X7,tc_prod(X6,X6)),X6) ),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_3437,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_3440,i_0_2694,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920,i_0_2518,i_0_1497,i_0_1779,i_0_2130,i_0_2158]) ).
cnf(i_0_3468,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(rename_variables,[],[i_0_2651]) ).
cnf(i_0_3469,plain,
( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X1,X4,X2) ),
inference(rename_variables,[],[i_0_2158]) ).
cnf(i_0_3470,plain,
( ~ c_Relation_Osym(c_Set_Oinsert(c_Pair(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),tc_prod(X4,X4)),X4)
| c_Pair(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X2,X3),X4,X4) = c_Pair(c_Set_Oinsert(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X4) ),
inference(scs_inference,[],[i_0_1404,i_0_1636,i_0_1731,i_0_2636,i_0_3265,i_0_3279,i_0_3281,i_0_3285,i_0_2357,i_0_2293,i_0_3262,i_0_3267,i_0_3269,i_0_3272,i_0_3274,i_0_3276,i_0_3283,i_0_3287,i_0_3291,i_0_3451,i_0_3453,i_0_1649,i_0_3006,i_0_3031,i_0_3134,i_0_3140,i_0_3354,i_0_1645,i_0_3137,i_0_3143,i_0_3164,i_0_3168,i_0_3176,i_0_2211,i_0_3063,i_0_3072,i_0_3190,i_0_3236,i_0_3339,i_0_3360,i_0_3366,i_0_3437,i_0_2306,i_0_3066,i_0_2467,i_0_3203,i_0_3225,i_0_3251,i_0_3369,i_0_3380,i_0_2490,i_0_3034,i_0_3060,i_0_3372,i_0_3402,i_0_2190,i_0_2957,i_0_2960,i_0_2977,i_0_2980,i_0_2983,i_0_2995,i_0_2998,i_0_3003,i_0_3009,i_0_3015,i_0_3043,i_0_3049,i_0_3054,i_0_3057,i_0_3069,i_0_3146,i_0_3152,i_0_3181,i_0_3184,i_0_3187,i_0_3193,i_0_3343,i_0_3346,i_0_2368,i_0_3163,i_0_3352,i_0_1593,i_0_2986,i_0_2989,i_0_3012,i_0_1594,i_0_2992,i_0_3018,i_0_1937,i_0_1656,i_0_2654,i_0_3173,i_0_3305,i_0_3308,i_0_3311,i_0_3314,i_0_3321,i_0_3363,i_0_3399,i_0_3406,i_0_3413,i_0_2648,i_0_2417,i_0_3099,i_0_3102,i_0_3105,i_0_3118,i_0_3243,i_0_3294,i_0_3297,i_0_3327,i_0_3330,i_0_3293,i_0_2576,i_0_3094,i_0_3222,i_0_2686,i_0_2662,i_0_2329,i_0_3108,i_0_3111,i_0_3218,i_0_3302,i_0_3324,i_0_2508,i_0_2509,i_0_2651,i_0_3254,i_0_3377,i_0_3383,i_0_3389,i_0_3412,i_0_3440,i_0_2694,i_0_2700,i_0_2701,i_0_2702,i_0_2705,i_0_2710,i_0_2715,i_0_2720,i_0_2724,i_0_2728,i_0_2730,i_0_2731,i_0_2737,i_0_2738,i_0_2740,i_0_2741,i_0_2635,i_0_2510,i_0_2511,i_0_3196,i_0_3259,i_0_1409,i_0_1508,i_0_1535,i_0_1589,i_0_2088,i_0_2128,i_0_2129,i_0_2399,i_0_2475,i_0_1407,i_0_1408,i_0_1433,i_0_1434,i_0_1447,i_0_1448,i_0_1466,i_0_1467,i_0_1468,i_0_1489,i_0_1490,i_0_1491,i_0_1492,i_0_1499,i_0_1500,i_0_1510,i_0_1512,i_0_1521,i_0_1525,i_0_1526,i_0_1561,i_0_1578,i_0_1580,i_0_1598,i_0_1599,i_0_1604,i_0_1605,i_0_1617,i_0_1629,i_0_1647,i_0_1668,i_0_1681,i_0_1701,i_0_1749,i_0_1756,i_0_1821,i_0_1834,i_0_1841,i_0_1942,i_0_1943,i_0_1984,i_0_2059,i_0_2156,i_0_2326,i_0_2344,i_0_2743,i_0_1577,i_0_1745,i_0_1981,i_0_2037,i_0_2038,i_0_2039,i_0_2040,i_0_2121,i_0_2134,i_0_2187,i_0_2644,i_0_2645,i_0_2680,i_0_2685,i_0_2812,i_0_1443,i_0_1444,i_0_1585,i_0_1586,i_0_1587,i_0_1588,i_0_2087,i_0_2397,i_0_2924,i_0_1457,i_0_1458,i_0_1464,i_0_1477,i_0_1483,i_0_1484,i_0_1498,i_0_1507,i_0_1549,i_0_1575,i_0_1607,i_0_1627,i_0_1646,i_0_1652,i_0_1653,i_0_1793,i_0_1877,i_0_1878,i_0_1879,i_0_1905,i_0_1945,i_0_1976,i_0_1979,i_0_1980,i_0_1982,i_0_1992,i_0_2000,i_0_2036,i_0_2115,i_0_2169,i_0_2170,i_0_2185,i_0_2202,i_0_2280,i_0_2283,i_0_2301,i_0_2333,i_0_2334,i_0_2409,i_0_2428,i_0_2448,i_0_2577,i_0_2744,i_0_2820,i_0_2821,i_0_2822,i_0_2827,i_0_2838,i_0_2839,i_0_2840,i_0_2846,i_0_2847,i_0_2848,i_0_2849,i_0_2850,i_0_2851,i_0_2852,i_0_2893,i_0_2894,i_0_1529,i_0_1705,i_0_2154,i_0_2167,i_0_2216,i_0_2218,i_0_2220,i_0_2222,i_0_2235,i_0_2236,i_0_2265,i_0_2308,i_0_2309,i_0_2310,i_0_2355,i_0_2465,i_0_1523,i_0_1767,i_0_1917,i_0_1494,i_0_1533,i_0_1534,i_0_1657,i_0_1708,i_0_1843,i_0_2131,i_0_2132,i_0_2133,i_0_2288,i_0_2349,i_0_2379,i_0_2383,i_0_2421,i_0_2019,i_0_2034,i_0_1628,i_0_1744,i_0_1918,i_0_1929,i_0_1743,i_0_1950,i_0_2157,i_0_1469,i_0_1613,i_0_1616,i_0_2057,i_0_2389,i_0_2530,i_0_2561,i_0_2533,i_0_2622,i_0_1516,i_0_2441,i_0_2531,i_0_2823,i_0_2824,i_0_2825,i_0_2826,i_0_2858,i_0_2859,i_0_2860,i_0_2920,i_0_2518,i_0_1497,i_0_1779,i_0_2130,i_0_2158,i_0_1830]) ).
cnf(i_0_3471,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)))
| X2 = X3 ),
inference(rename_variables,[],[i_0_1830]) ).
cnf(i_0_3472,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3473,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3474,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3475,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(rename_variables,[],[i_0_2190]) ).
cnf(i_0_3476,plain,
hBOOL(hAPP(hAPP(c_in(tc_prod(X1,X1)),c_Pair(X2,X2,X1,X1)),c_Transitive__Closure_Ortrancl(X3,X1))),
inference(rename_variables,[],[i_0_1645]) ).
cnf(i_0_3478,plain,
$false,
inference(scs_inference,[],[i_0_2955,i_0_2654,i_0_1406]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT097-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n031.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:58:23 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 2.96/3.72 % Version : CSE_E---1.7
% 2.96/3.72 % Problem : theBenchmark.p
% 2.96/3.72 % SZS status Unsatisfiable for theBenchmark.p
% 2.96/3.72 % SZS output start CNFRefutation
% See solution above
% 10.40/11.19 % Total time : 3.381s
%------------------------------------------------------------------------------