%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT076-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 05:05:57 PM UTC 2026
% Result : Unsatisfiable 0.73s 1.53s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_708)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_trancl__Int__subset_0,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__Int__subset_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/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
cnf(cls_trancl__trans_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
cnf(cls_trancl__converseI_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
cnf(cls_trancl__converseD_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
cnf(cls_converse__tranclE_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4))
| c_in(c_Pair(X2,X3,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
cnf(cls_tranclE_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X3,X4),X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4))
| c_in(c_Pair(X1,X2,X4,X4),X3,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclE_0) ).
cnf(cls_rtrancl__trancl__trancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
cnf(cls_trancl__rtrancl__trancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
cnf(cls_trancl__into__trancl2_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
cnf(cls_Transitive__Closure_Otrancl__into__trancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__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/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
cnf(cls_trancl_Ocases_0,axiom,
( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
cnf(cls_tranclE_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X3,X4),X2,X4,X4),X3,tc_prod(X4,X4))
| c_in(c_Pair(X1,X2,X4,X4),X3,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclE_1) ).
cnf(cls_converse__tranclE_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| c_in(c_Pair(X1,X3,X4,X4),X2,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Otrancl(X2,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
cnf(cls_trancl__mono_0,axiom,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
cnf(cls_tranclD_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_1) ).
cnf(cls_tranclD2_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X1,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Otrancl(X2,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_0) ).
cnf(cls_tranclD2_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X1,X2,X3,X4),X3,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_1) ).
cnf(cls_tranclD_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Otrancl(X2,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_0) ).
cnf(cls_trancl_Ocases_1,axiom,
( c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
cnf(cls_rtrancl__Int__subset_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_OId(X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
cnf(cls_rtrancl__empty_0,axiom,
c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__empty_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/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_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/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).
cnf(cls_fst__eq__Domain_0,axiom,
c_Set_Oimage(c_fst(X1,X2),X3,tc_prod(X1,X2),X1) = c_Relation_ODomain(X3,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fst__eq__Domain_0) ).
cnf(cls_rtrancl__eq__or__trancl_2,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
cnf(cls_trancl__into__rtrancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
cnf(cls_Range__Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X1,X2,X3),c_Relation_ORange(X4,X2,X3),tc_fun(X3,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
cnf(cls_Range__Int__subset_0,axiom,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
cnf(cls_irrefl__tranclI_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X3,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__tranclI_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/sandbox2/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
cnf(cls_rtrancl__into__trancl2_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
cnf(cls_rtrancl__into__trancl1_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
cnf(cls_trancl__subset__Sigma_0,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
cnf(cls_r__r__into__trancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
cnf(cls_acyclic__def_0,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Wellfounded_Oacyclic(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
cnf(cls_irrefl__trancl__rD_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
cnf(cls_rtranclD_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclD_0) ).
cnf(cls_rtrancl__eq__or__trancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
cnf(cls_trancl_Or__into__trancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
cnf(cls_Domain__Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
cnf(cls_Domain__Int__subset_0,axiom,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Int__subset_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/sandbox2/benchmark/theBenchmark.p',cls_Range__insert_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/sandbox2/benchmark/theBenchmark.p',cls_trancl__domain_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/sandbox2/benchmark/theBenchmark.p',cls_reflcl__trancl_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__unfold_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/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
cnf(cls_Range__iff_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
| ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_0) ).
cnf(cls_RangeE_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
| ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeE_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_comp__equivI_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/sandbox2/benchmark/theBenchmark.p',cls_wf__Un_0) ).
cnf(cls_r__into__trancl_H_0,axiom,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__trancl_H_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/sandbox2/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
cnf(cls_Domain__iff_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
cnf(cls_DomainE_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainE_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/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_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/sandbox2/benchmark/theBenchmark.p',cls_wf__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/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
cnf(cls_trans__trancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Otrancl(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__trancl_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/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
cnf(cls_trancl__empty_0,axiom,
c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__empty_0) ).
cnf(cls_RangeI_0,axiom,
( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
| ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).
cnf(cls_Range__iff_1,axiom,
( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
| ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).
cnf(cls_in__above_6,axiom,
( X1 = X2
| X1 = X3
| X1 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_6) ).
cnf(cls_in__below_6,axiom,
( X1 = X2
| X3 = X1
| X2 = X1
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_6) ).
cnf(cls_in__above_12,axiom,
( X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_12) ).
cnf(cls_in__below_12,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_12) ).
cnf(cls_in__above_7,axiom,
( X1 = X4
| X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_7) ).
cnf(cls_in__below_7,axiom,
( X2 = X4
| X4 = X2
| X4 = X1
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_7) ).
cnf(cls_in__below_11,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_11) ).
cnf(cls_in__above_11,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_11) ).
cnf(cls_total__on__diff__Id_0,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
cnf(cls_Not__Domain__rtrancl_0,axiom,
( X1 = X2
| c_in(X1,c_Relation_ODomain(X4,X3,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
cnf(cls_DomainI_0,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
| ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).
cnf(cls_Domain__iff_1,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
| ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_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/sandbox2/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
cnf(cls_pair__in__Id__conv_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
cnf(cls_trancl__id_0,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__id_0) ).
cnf(cls_Not__Domain__rtrancl_1,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X3),X3)
| c_in(c_Pair(X1,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
cnf(cls_quotient__eq__iff_0,axiom,
( c_in(c_Pair(X4,X1,X3,X3),X6,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X5,X6,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X5,X6,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
cnf(cls_total__on__diff__Id_1,axiom,
( c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
cnf(cls_trans__diff__Id_0,axiom,
( c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__diff__Id_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/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
cnf(cls_trans__reflclI_0,axiom,
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
cnf(cls_rtrancl__r__diff__Id_0,axiom,
c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_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)
| ~ c_in(X1,c_Relation_OId(X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdE_0) ).
cnf(cls_irrefl__diff__Id_0,axiom,
c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__diff__Id_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/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).
cnf(cls_IdI_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdI_0) ).
cnf(cls_pair__in__Id__conv_1,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
cnf(cls_in__above_5,axiom,
( X1 = X2
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_5) ).
cnf(cls_in__below_5,axiom,
( X1 = X2
| X2 = X1
| X2 = X1
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_5) ).
cnf(cls_Range__empty__iff_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
cnf(cls_Range__empty_0,axiom,
c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__empty_0) ).
cnf(cls_snd__eq__Range_0,axiom,
c_Set_Oimage(c_snd(X1,X2),X3,tc_prod(X1,X2),X2) = c_Relation_ORange(X3,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_snd__eq__Range_0) ).
cnf(cls_Domain__empty__iff_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).
cnf(cls_in__mktop_4,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
cnf(cls_in__mkbot_4,axiom,
( X1 = X2
| X2 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
cnf(cls_Image__Id_0,axiom,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).
cnf(cls_converse__Id_0,axiom,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
cnf(cls_Domain__empty_0,axiom,
c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
cnf(cls_Range__Id__on_0,axiom,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
cnf(cls_single__valued__Id_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
cnf(cls_antisym__Id_0,axiom,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
cnf(cls_trans__Id_0,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id_0) ).
cnf(cls_sym__Id_0,axiom,
c_Relation_Osym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).
cnf(cls_Domain__Id__on_0,axiom,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
cnf(cls_rel__compEpair_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X3,X4,X5,X6,X7),X2,X7,X6),X4,tc_prod(X7,X6))
| ~ c_in(c_Pair(X1,X2,X5,X6),c_Relation_Orel__comp(X3,X4,X5,X7,X6),tc_prod(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
cnf(cls_rel__compEpair_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X3,X4,X5,X6,X7),X5,X7),X3,tc_prod(X5,X7))
| ~ c_in(c_Pair(X1,X2,X5,X6),c_Relation_Orel__comp(X3,X4,X5,X7,X6),tc_prod(X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
cnf(cls_cuts__eq_1,axiom,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5),X3,X4,X4),X2,tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
cnf(cls_congruent2_Ocongruent2_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X4),X5)
| ~ c_in(c_Pair(X3,X5,X6,X6),X7,tc_prod(X6,X6))
| ~ c_in(c_Pair(X2,X4,X8,X8),X9,tc_prod(X8,X8))
| ~ c_Equiv__Relations_Ocongruent2(X9,X7,X1,X8,X6,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
cnf(cls_congruent2__implies__congruent_0,axiom,
( c_Equiv__Relations_Ocongruent(X1,hAPP(X2,X3),X4,X5)
| ~ c_in(X3,X6,X7)
| ~ c_Equiv__Relations_Ocongruent2(X8,X1,X2,X7,X4,X5)
| ~ c_Equiv__Relations_Oequiv(X6,X8,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_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/sandbox2/benchmark/theBenchmark.p',cls_O__assoc_0) ).
cnf(cls_splitD_H_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_split(X1,X5,X6,tc_fun(X7,tc_bool)),c_Pair(X2,X3,X5,X6)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splitD_H_0) ).
cnf(cls_equiv__class__nondisjoint_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X5,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Equiv__Relations_Oequiv(X6,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
cnf(cls_exI__realizer_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(c_snd(X2,X3),c_Pair(X4,X5,X2,X3))),hAPP(c_fst(X2,X3),c_Pair(X4,X5,X2,X3))))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exI__realizer_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
cnf(cls_rel__comp__subset__Sigma_0,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Product__Type_OSigma(X6,c_COMBK(X7,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
| ~ c_lessequals(X2,c_Product__Type_OSigma(X8,c_COMBK(X7,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(tc_prod(X4,X5),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X8,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
cnf(cls_Image__iff_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_1) ).
cnf(cls_ImageE_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_0) ).
cnf(cls_insert__times__insert_0,axiom,
c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6) = c_Set_Oinsert(c_Pair(X1,X4,X3,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X2,c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(X5,tc_fun(X6,tc_bool),X3),X3,X6),tc_fun(tc_prod(X3,X6),tc_bool)),tc_prod(X3,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
cnf(cls_union__comp__emptyL_0,axiom,
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X2,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X4,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).
cnf(cls_union__comp__emptyR_0,axiom,
( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
cnf(cls_rel__compI_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4))
| ~ c_in(c_Pair(X8,X2,X7,X4),X6,tc_prod(X7,X4))
| ~ c_in(c_Pair(X1,X8,X3,X7),X5,tc_prod(X3,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compI_0) ).
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)
| ~ c_in(c_Pair(X7,X3,X4,X4),X2,tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_wf__union__compatible_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
cnf(cls_subset__equiv__class_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X2,X5,X3)
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
cnf(cls_rtrancl__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X3,X4,X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X1,X3,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
cnf(cls_converse__rtrancl__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X1,X3,X4,X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X3,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
cnf(cls_in__below_14,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_14) ).
cnf(cls_in__above_14,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_14) ).
cnf(cls_SigmaE_0,axiom,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X1,X2,X3,X4,X5),X1,X4)
| ~ c_in(X3,c_Product__Type_OSigma(X1,X2,X4,X5),tc_prod(X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaE_0) ).
cnf(cls_cut__apply_0,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ c_in(c_Pair(X6,X3,X4,X4),X2,tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut__apply_0) ).
cnf(cls_tfl__cut__apply_0,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ c_in(c_Pair(X6,X3,X4,X4),X2,tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
cnf(cls_Image__iff_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_0) ).
cnf(cls_ImageE_1,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X1,X2,X3,X4,X5),X1,X4)
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_1) ).
cnf(cls_single__valued__confluent_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Relation_Osingle__valued(X4,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
cnf(cls_image__diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_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/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
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))
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
cnf(cls_Times__subset__cancel2_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
| ~ c_in(X6,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_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/sandbox2/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
cnf(cls_sym__trans__comp__subset_0,axiom,
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Osym(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
cnf(cls_acyclic__insert_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
cnf(cls_wf__insert_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_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/sandbox2/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
cnf(cls_in__below_10,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_10) ).
cnf(cls_in__above_8,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X5
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_8) ).
cnf(cls_in__below_8,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_8) ).
cnf(cls_in__above_10,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_10) ).
cnf(cls_in__above_13,axiom,
( X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_13) ).
cnf(cls_in__below_13,axiom,
( X4 = X2
| X4 = X1
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_13) ).
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))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/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))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
cnf(cls_converse__rtrancl__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X3,X4,X5),X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
cnf(cls_rtrancl__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X3,X4,X5),X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
cnf(cls_pair__imageI_0,axiom,
( c_in(hAPP(hAPP(X1,X2),X3),c_Set_Oimage(c_split(X1,X4,X5,X6),X7,tc_prod(X4,X5),X6),X6)
| ~ c_in(c_Pair(X2,X3,X4,X5),X7,tc_prod(X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__imageI_0) ).
cnf(cls_trans__O__subset_0,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
cnf(cls_converse__rtranclE_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
| X2 = X3
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
cnf(cls_rtranclE_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclE_0) ).
cnf(cls_rtranclE_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X3,X4),X2,X4,X4),X3,tc_prod(X4,X4))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclE_1) ).
cnf(cls_converse__rtranclE_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| X1 = X3
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
cnf(cls_rtrancl__trans_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_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/sandbox2/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
cnf(cls_trancl__subset__Sigma__aux_0,axiom,
( c_in(X1,X2,X3)
| X1 = X4
| ~ c_lessequals(X5,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X5,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
cnf(cls_converse__rtrancl__into__rtrancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
cnf(cls_rtrancl_Ortrancl__into__rtrancl_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
cnf(cls_transD_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transD_0) ).
cnf(cls_trans__def_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_0) ).
cnf(cls_in__inv__image_0,axiom,
( c_in(c_Pair(hAPP(X1,X2),hAPP(X1,X3),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X6,X6),c_Relation_Oinv__image(X5,X1,X4,X6),tc_prod(X6,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
cnf(cls_mem__splitI_0,axiom,
( c_in(X1,hAPP(c_split(X2,X3,X4,tc_fun(X5,tc_bool)),c_Pair(X6,X7,X3,X4)),X5)
| ~ c_in(X1,hAPP(hAPP(X2,X6),X7),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__splitI_0) ).
cnf(cls_Times__Un__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
cnf(cls_Times__Diff__distrib1_0,axiom,
c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).
cnf(cls_Times__Int__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
cnf(cls_eq__equiv__class__iff_0,axiom,
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| 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_in(X4,X5,X3)
| ~ c_in(X2,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
cnf(cls_equiv__class__eq__iff_3,axiom,
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| 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)
| ~ c_in(X4,X5,X3)
| ~ c_in(X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
cnf(cls_conjI__realizer_0,axiom,
( hBOOL(hAPP(X1,hAPP(c_fst(X2,X3),c_Pair(X4,X5,X2,X3))))
| ~ hBOOL(hAPP(X6,X5))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjI__realizer_0) ).
cnf(cls_conjI__realizer_1,axiom,
( hBOOL(hAPP(X1,hAPP(c_snd(X2,X3),c_Pair(X4,X5,X2,X3))))
| ~ hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjI__realizer_1) ).
cnf(cls_eq__equiv__class_0,axiom,
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| 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_in(X4,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
cnf(cls_in__inv__image_1,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oinv__image(X4,X5,X6,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(hAPP(X5,X1),hAPP(X5,X2),X6,X6),X4,tc_prod(X6,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
cnf(cls_Image__singleton__iff_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_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)
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_in(X4,X5,X3)
| ~ c_in(X2,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
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))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/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))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
cnf(cls_wf__no__loop_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
cnf(cls_Image__subset_0,axiom,
( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
cnf(cls_notin__Lin__iff_1,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).
cnf(cls_Lin__irrefl_0,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
cnf(cls_Times__subset__cancel2_1,axiom,
( c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),tc_fun(tc_prod(X4,X3),tc_bool))
| ~ c_lessequals(X1,X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
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)
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox2/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)
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
cnf(cls_single__valuedD_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X3,X2,X4,X5),X6,tc_prod(X4,X5))
| ~ c_in(c_Pair(X3,X1,X4,X5),X6,tc_prod(X4,X5))
| ~ c_Relation_Osingle__valued(X6,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
cnf(cls_rtrancl__converseD_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
cnf(cls_Image__singleton__iff_1,axiom,
( c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X5),X5)
| ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_0) ).
cnf(cls_antisymD_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Oantisym(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisymD_0) ).
cnf(cls_antisym__def_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Oantisym(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__def_0) ).
cnf(cls_wf__asym_0,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__asym_0) ).
cnf(cls_in__above_2,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_2) ).
cnf(cls_in__below_2,axiom,
( X1 = X2
| X2 = X4
| c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_2) ).
cnf(cls_in__below_3,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X2 = X4
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_3) ).
cnf(cls_in__above_3,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| X5 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X5,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_3) ).
cnf(cls_in__above_1,axiom,
( X4 = X1
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_1) ).
cnf(cls_in__below_1,axiom,
( X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_1) ).
cnf(cls_acyclic__insert_2,axiom,
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Oacyclic(X4,X3) ),
file('/export/starexec/sandbox2/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)
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_2) ).
cnf(cls_SigmaD2_0,axiom,
( c_in(X1,hAPP(X2,X3),X4)
| ~ c_in(c_Pair(X3,X1,X5,X4),c_Product__Type_OSigma(X6,X2,X5,X4),tc_prod(X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
cnf(cls_rtrancl__converseI_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
cnf(cls_quotient__eqI_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(X4,X2,X5)
| ~ c_in(X3,X1,X5)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X7,X6,X5),tc_fun(X5,tc_bool))
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X7,X6,X5),tc_fun(X5,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X7,X6,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).
cnf(cls_in__below_4,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X2 = X4
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_4) ).
cnf(cls_in__above_4,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X1 = X5
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_4) ).
cnf(cls_in__below_9,axiom,
( X1 = X4
| X4 = X2
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_9) ).
cnf(cls_in__above_9,axiom,
( X4 = X2
| X1 = X4
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_9) ).
cnf(cls_SigmaD1_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X6,X3,X5),tc_prod(X3,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
cnf(cls_rtrancl_Ocases_0,axiom,
( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| X2 = X1
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ocases_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/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
cnf(cls_rtrancl_Ocases_1,axiom,
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| X2 = X1
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
cnf(cls_eq__equiv__class__iff2_1,axiom,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2)
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X4,X5,X2)
| ~ c_in(X1,X5,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
cnf(cls_eq__equiv__class__iff2_0,axiom,
( c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2)
| ~ c_in(X4,X5,X2)
| ~ c_in(X1,X5,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
cnf(cls_converseD_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
cnf(cls_converseI_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
cnf(cls_converse__iff_1,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Un__Image_0) ).
cnf(cls_Image__iff_2,axiom,
( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X6,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).
cnf(cls_rev__ImageI_0,axiom,
( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X6,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_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/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
cnf(cls_Sigma__Diff__distrib1_0,axiom,
c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_HOL_Ominus__class_Ominus(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/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
cnf(cls_Sigma__Int__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(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/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
cnf(cls_symD_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Osym(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symD_0) ).
cnf(cls_sym__def_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Osym(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__def_0) ).
cnf(cls_in__mkbot_2,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
cnf(cls_in__mktop_2,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).
cnf(cls_in__mktop_5,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).
cnf(cls_in__mkbot_5,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
cnf(cls_in__mktop_3,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).
cnf(cls_in__mkbot_3,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_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/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
cnf(cls_rel__comp__empty1_0,axiom,
c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
cnf(cls_rel__comp__empty2_0,axiom,
c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
cnf(cls_wfE__min_1,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X5,X2,X3)
| ~ c_Wellfounded_Owf(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_1) ).
cnf(cls_wf__eq__minimal_1,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X5,X2,X3)
| ~ c_Wellfounded_Owf(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
cnf(cls_acc__induct__rule_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
cnf(cls_acc__induct_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X5),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_1) ).
cnf(cls_in__rel__def_1,axiom,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5))
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
cnf(cls_total__on__def_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| X2 = X1
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| ~ c_Relation_Ototal__on(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_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/sandbox2/benchmark/theBenchmark.p',cls_equiv__comp__eq_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/sandbox2/benchmark/theBenchmark.p',cls_Image__mono_0) ).
cnf(cls_in__rel__def_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X5,X3,X4),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
cnf(cls_Times__eq__cancel2_0,axiom,
( X1 = X5
| c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3) != c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3)
| ~ c_in(X6,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
cnf(cls_subset__insert__iff_4,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
cnf(cls_wf__induct__rule_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
cnf(cls_wf__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__def_0) ).
cnf(cls_tfl__wf__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
cnf(cls_wf__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct_0) ).
cnf(cls_congruent_Ocongruent_0,axiom,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent(X5,X1,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
cnf(cls_notin__Lin__iff_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
cnf(cls_subset__insert__iff_3,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
cnf(cls_diff__single__insert_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
cnf(cls_SigmaI_0,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4))
| ~ c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(X1,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).
cnf(cls_mem__Sigma__iff_2,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4))
| ~ c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(X1,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
cnf(cls_in__below_0,axiom,
( X3 = X4
| ~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_0) ).
cnf(cls_in__above_0,axiom,
( X3 = X4
| ~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X2,X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_0) ).
cnf(cls_acc_Oinduct_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(X3,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
cnf(cls_acc_Oinducts_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(X3,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
cnf(cls_image__mono_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
cnf(cls_subset__image__iff_2,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
cnf(cls_quotientI_0,axiom,
( c_in(c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Equiv__Relations_Oquotient(X4,X1,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientI_0) ).
cnf(cls_acc__downwards_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
cnf(cls_acc__downwards__aux_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
cnf(cls_acc_Oinduct_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
cnf(cls_acc_Oinducts_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
cnf(cls_equiv__class__self_0,axiom,
( c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3)
| ~ c_in(X1,X4,X3)
| ~ c_Equiv__Relations_Oequiv(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
cnf(cls_acc_Ocases_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
cnf(cls_acc__downward_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).
cnf(cls_Nitpick_Orefl_H__def_1,axiom,
( c_Nitpick_Orefl_H(X1,X2)
| ~ c_in(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,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
cnf(cls_image__subset__iff_0,axiom,
( c_in(hAPP(X1,X2),X3,X4)
| ~ c_in(X2,X5,X6)
| ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
cnf(cls_equiv__class__eq__iff_1,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
cnf(cls_equiv__class__eq__iff_2,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
cnf(cls_refl__onD1_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
cnf(cls_refl__onD2_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
cnf(cls_split__case__cert_0,axiom,
hAPP(c_split(X1,X2,X3,X4),c_Pair(X5,X6,X2,X3)) = hAPP(hAPP(X1,X5),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
cnf(cls_Product__Type_Osplit_0,axiom,
hAPP(c_split(X1,X2,X3,X4),c_Pair(X5,X6,X2,X3)) = hAPP(hAPP(X1,X5),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
cnf(cls_subset__insert__iff_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
cnf(cls_equiv__type_0,axiom,
( c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__type_0) ).
cnf(cls_refl__on__def_0,axiom,
( c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
cnf(cls_Id__on__iff_1,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
cnf(cls_Id__on__subset__Times_0,axiom,
c_lessequals(c_Relation_OId__on(X1,X2),c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__subset__Times_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/sandbox2/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
cnf(cls_Id__on__iff_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
cnf(cls_irrefl__def_0,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Oirrefl(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_wf__irrefl_0,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
cnf(cls_in__mktop_1,axiom,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
cnf(cls_in__mkbot_1,axiom,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
cnf(cls_in__mktop_0,axiom,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
cnf(cls_in__mkbot_0,axiom,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
cnf(cls_insert__image_0,axiom,
( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
| ~ c_in(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
cnf(cls_acc_OaccI_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
cnf(cls_not__acc__down_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))
| c_in(X2,c_Wellfounded_Oacc(X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
cnf(cls_Diff__insert2_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
cnf(cls_in__rtrancl__UnI_0,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
cnf(cls_in__rtrancl__UnI_1,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
cnf(cls_split__beta_0,axiom,
hAPP(c_split(X1,X2,X3,X4),X5) = hAPP(hAPP(X1,hAPP(c_fst(X2,X3),X5)),hAPP(c_snd(X2,X3),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__beta_0) ).
cnf(cls_Pair__eq_0,axiom,
( X1 = X5
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
cnf(cls_quotient__disj_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__disj_0) ).
cnf(cls_refl__onD_0,axiom,
( c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X1,X4,X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).
cnf(cls_refl__on__def_1,axiom,
( c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X1,X4,X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
cnf(cls_insert__Diff_0,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
cnf(cls_irrefl__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| c_in(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,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
cnf(cls_Id__on__eqI_0,axiom,
( c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2))
| ~ c_in(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
cnf(cls_insert__Diff__single_0,axiom,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
cnf(cls_image__eqI_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
cnf(cls_imageI_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
cnf(cls_rev__image__eqI_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_image__iff_2,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_converse__Un_0) ).
cnf(cls_converse__Int_0,axiom,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Int_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_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/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
cnf(cls_refl__on__Int_0,axiom,
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Int_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)
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
cnf(cls_Diff__mono_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__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/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
cnf(cls_Diff__insert_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
cnf(cls_Diff__Int2_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
cnf(cls_Un__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_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/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
cnf(cls_Diff__Un_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
cnf(cls_Diff__Int_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_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/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
cnf(cls_Diff__Int__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(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/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
cnf(cls_rtrancl__eq__or__trancl_1,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
cnf(cls_rtrancl_Ortrancl__refl_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
cnf(cls_Nitpick_Orefl_H__def_0,axiom,
( c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
cnf(cls_Diff__subset__conv_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
cnf(cls_Diff__subset__conv_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
cnf(cls_complete__Lin_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
cnf(cls_Sigma__empty2_0,axiom,
c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_image__constant_0,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ c_in(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_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)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
file('/export/starexec/sandbox2/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)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_2) ).
cnf(cls_fst__conv_0,axiom,
hAPP(c_fst(X1,X2),c_Pair(X3,X4,X1,X2)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fst__conv_0) ).
cnf(cls_snd__conv_0,axiom,
hAPP(c_snd(X1,X2),c_Pair(X3,X4,X1,X2)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_snd__conv_0) ).
cnf(cls_fst__eqD_0,axiom,
X1 = hAPP(c_fst(X2,X3),c_Pair(X1,X4,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fst__eqD_0) ).
cnf(cls_snd__eqD_0,axiom,
X1 = hAPP(c_snd(X2,X3),c_Pair(X4,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_snd__eqD_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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
cnf(cls_trans__inv__image_0,axiom,
( c_Relation_Otrans(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
| ~ c_Relation_Otrans(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__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/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_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/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
cnf(cls_image__constant__conv_1,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_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/sandbox2/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
cnf(cls_sym__Int__converse_0,axiom,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int__converse_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)
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/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)
| ~ c_in(X2,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
cnf(cls_double__diff_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_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/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
cnf(cls_empty__is__image_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
cnf(cls_image__is__empty_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
| c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_insert__Diff__if_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_UnE_0,axiom,
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_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/sandbox2/benchmark/theBenchmark.p',cls_inf1I_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
cnf(cls_subset__insert_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X1,X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
cnf(cls_subset__insert__iff_1,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X1,X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
cnf(cls_singletonE_0,axiom,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
cnf(cls_DiffE_1,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(cls_below__Lin_0,axiom,
( c_in(c_Arrow__Order__Mirabelle_Obelow(X1,X2,X3),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__Lin_0) ).
cnf(cls_above__Lin_0,axiom,
( c_in(c_Arrow__Order__Mirabelle_Oabove(X1,X2,X3),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_above__Lin_0) ).
cnf(cls_pair__collapse_0,axiom,
c_Pair(hAPP(c_fst(X1,X2),X3),hAPP(c_snd(X1,X2),X3),X1,X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__collapse_0) ).
cnf(cls_surjective__pairing_0,axiom,
X1 = c_Pair(hAPP(c_fst(X2,X3),X1),hAPP(c_snd(X2,X3),X1),X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surjective__pairing_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))
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
cnf(cls_Un__Diff__Int_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_DiffE_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
cnf(cls_IntE_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
cnf(cls_IntE_1,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
cnf(cls_IntI_0,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
cnf(cls_Int__iff_2,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
cnf(cls_Sigma__empty1_0,axiom,
c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
cnf(cls_acc_OaccI_1,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
cnf(cls_not__acc__down_1,axiom,
( c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),c_Wellfounded_Oacc(X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
cnf(cls_subset__insert_1,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/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))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
cnf(cls_Diff__partition_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
cnf(cls_DiffI_0,axiom,
( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
cnf(cls_Diff__iff_2,axiom,
( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
cnf(cls_insert__Diff1_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
cnf(cls_acc__induct__rule_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X3,X4),c_Wellfounded_Oacc(X3,X4),X4)
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
cnf(cls_acc__induct_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X3,X4),c_Wellfounded_Oacc(X3,X4),X4)
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_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/sandbox2/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
cnf(cls_insert__subset_0,axiom,
( c_in(X1,X2,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_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/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_acc__subset_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_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/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_Id__onE_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X2,X3),X1,X3)
| ~ c_in(X2,c_Relation_OId__on(X1,X3),tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_0) ).
cnf(cls_image__empty_0,axiom,
c_Set_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/sandbox2/benchmark/theBenchmark.p',cls_image__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/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
cnf(cls_mktop__Lin_0,axiom,
( c_in(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
cnf(cls_mkbot__Lin_0,axiom,
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
cnf(cls_le__eqI_1,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/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)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
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))
| c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/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))
| c_in(X2,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
cnf(cls_trans__Int_0,axiom,
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Otrans(X2,X3)
| ~ c_Relation_Otrans(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Int_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/sandbox2/benchmark/theBenchmark.p',cls_sym__Un_0) ).
cnf(cls_sym__Int_0,axiom,
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X2,X3)
| ~ c_Relation_Osym(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
cnf(cls_insertE_0,axiom,
( c_in(X1,X2,X3)
| X1 = X4
| ~ c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
cnf(cls_Diff__idemp_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
cnf(cls_Un__Diff__cancel_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
cnf(cls_UnCI_1,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
cnf(cls_UnCI_0,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
cnf(cls_wf__Int1_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
cnf(cls_wf__Int2_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
cnf(cls_less__by__empty_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__by__empty_0) ).
cnf(cls_insert__ident_0,axiom,
( c_in(X1,X4,X3)
| c_in(X1,X2,X3)
| X2 = X4
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
cnf(cls_acc_Oinduct_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X3)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a) ),
file('/export/starexec/sandbox2/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)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
cnf(cls_wfE__min_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X1,X2,X3),X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_0) ).
cnf(cls_wf__eq__minimal_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X2,X3),X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
cnf(cls_singleton__iff_1,axiom,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_set__mp_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
cnf(cls_subsetD_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
cnf(cls_set__rev__mp_0,axiom,
( c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
cnf(cls_subset__iff_0,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_refl__on__empty_0,axiom,
c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
cnf(cls_Diff__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
cnf(cls_prod__eqI_0,axiom,
( X3 = X4
| hAPP(c_snd(X1,X2),X3) != hAPP(c_snd(X1,X2),X4)
| hAPP(c_fst(X1,X2),X3) != hAPP(c_fst(X1,X2),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prod__eqI_0) ).
cnf(cls_Pair__fst__snd__eq_0,axiom,
( X3 = X4
| hAPP(c_snd(X1,X2),X3) != hAPP(c_snd(X1,X2),X4)
| hAPP(c_fst(X1,X2),X3) != hAPP(c_fst(X1,X2),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__fst__snd__eq_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
cnf(cls_insertCI_0,axiom,
( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| ~ c_in(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
cnf(cls_insert__iff_2,axiom,
( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| ~ c_in(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_Diff__triv_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_r__into__rtrancl_0,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
cnf(cls_bex__empty_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
cnf(cls_trans__converse_0,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_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/sandbox2/benchmark/theBenchmark.p',cls_sym__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/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
cnf(cls_strict__linear__order__on__def_3,axiom,
( c_Order__Relation_Ostrict__linear__order__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Oirrefl(X2,X3)
| ~ c_Relation_Otrans(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
cnf(cls_acc__wfI_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
cnf(cls_wf__acc__iff_1,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_antisym__empty_0,axiom,
c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
cnf(cls_wf__empty_0,axiom,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__empty_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_emptyE_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
cnf(cls_empty__iff_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_converse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
cnf(cls_insertCI_1,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
cnf(cls_insertI1_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
cnf(cls_insert__iff_1,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
cnf(cls_empty__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(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/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_Id__on__empty_0,axiom,
c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
cnf(cls_complete__Lin_0,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
cnf(cls_wf__in__rel_0,axiom,
( c_Wellfounded_OwfP(c_FunDef_Oin__rel(X1,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__in__rel_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/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
cnf(cls_trans__converse_1,axiom,
( c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_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/sandbox2/benchmark/theBenchmark.p',cls_sym__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/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_strict__linear__order__on__def_2,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Order__Relation_Ostrict__linear__order__on(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
cnf(cls_equiv_Orefl__on_0,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_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/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_CHAINED_0,axiom,
c_in(v_Lba____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_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/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(cls_acc__wfD_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
cnf(cls_mem__def_1,axiom,
( c_in(X1,X2,X3)
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_sym__conv__converse__eq_1,axiom,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
cnf(cls_strict__linear__order__on__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
cnf(cls_strict__linear__order__on__def_0,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
cnf(cls_equiv_Otrans_0,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
cnf(cls_equiv_Osym_0,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_single__valued__Id__on_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(X1,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_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/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
cnf(cls_antisym__Id__on_0,axiom,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
cnf(cls_trans__Id__on_0,axiom,
c_Relation_Otrans(c_Relation_OId__on(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
cnf(cls_trans__rtrancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
cnf(cls_sym__Id__on_0,axiom,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(X1,X2))
| ~ class_HOL_Oord(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
cnf(cls_wf__acyclic_0,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(i_0_707,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_trancl__Int__subset_0 ).
cnf(i_0_708,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_709,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
cls_trancl__trans_0 ).
cnf(i_0_710,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3)) ),
cls_trancl__converseI_0 ).
cnf(i_0_711,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
cls_trancl__converseD_0 ).
cnf(i_0_712,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4))
| c_in(c_Pair(X2,X3,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4)) ),
cls_converse__tranclE_1 ).
cnf(i_0_713,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X3,X4),X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4))
| c_in(c_Pair(X1,X2,X4,X4),X3,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4)) ),
cls_tranclE_0 ).
cnf(i_0_714,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl__trancl__trancl_0 ).
cnf(i_0_715,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
cls_trancl__rtrancl__trancl_0 ).
cnf(i_0_716,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
cls_trancl__into__trancl2_0 ).
cnf(i_0_717,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
cls_Transitive__Closure_Otrancl__into__trancl_0 ).
cnf(i_0_718,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_719,axiom,
( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
cls_trancl_Ocases_0 ).
cnf(i_0_720,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X3,X4),X2,X4,X4),X3,tc_prod(X4,X4))
| c_in(c_Pair(X1,X2,X4,X4),X3,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Otrancl(X3,X4),tc_prod(X4,X4)) ),
cls_tranclE_1 ).
cnf(i_0_721,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| c_in(c_Pair(X1,X3,X4,X4),X2,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Otrancl(X2,X4),tc_prod(X4,X4)) ),
cls_converse__tranclE_0 ).
cnf(i_0_722,axiom,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
cls_trancl__mono_0 ).
cnf(i_0_723,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4)) ),
cls_tranclD_1 ).
cnf(i_0_724,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X1,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Otrancl(X2,X4),tc_prod(X4,X4)) ),
cls_tranclD2_0 ).
cnf(i_0_725,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X1,X2,X3,X4),X3,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Otrancl(X1,X4),tc_prod(X4,X4)) ),
cls_tranclD2_1 ).
cnf(i_0_726,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Otrancl(X2,X4),tc_prod(X4,X4)) ),
cls_tranclD_0 ).
cnf(i_0_727,axiom,
( c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
cls_trancl_Ocases_1 ).
cnf(i_0_728,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_OId(X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_rtrancl__Int__subset_0 ).
cnf(i_0_729,axiom,
c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
cls_rtrancl__empty_0 ).
cnf(i_0_730,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_731,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_732,axiom,
c_Set_Oimage(c_fst(X1,X2),X3,tc_prod(X1,X2),X1) = c_Relation_ODomain(X3,X1,X2),
cls_fst__eq__Domain_0 ).
cnf(i_0_733,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl__eq__or__trancl_2 ).
cnf(i_0_734,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
cls_trancl__into__rtrancl_0 ).
cnf(i_0_735,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X1,X2,X3),c_Relation_ORange(X4,X2,X3),tc_fun(X3,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X3,tc_bool)),
cls_Range__Diff__subset_0 ).
cnf(i_0_736,axiom,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Range__Int__subset_0 ).
cnf(i_0_737,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X3,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
cls_irrefl__tranclI_0 ).
cnf(i_0_738,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_739,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
cls_rtrancl__into__trancl2_0 ).
cnf(i_0_740,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl__into__trancl1_0 ).
cnf(i_0_741,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_trancl__subset__Sigma_0 ).
cnf(i_0_742,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
cls_r__r__into__trancl_0 ).
cnf(i_0_743,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_Wellfounded_Oacyclic(X3,X2) ),
cls_acyclic__def_0 ).
cnf(i_0_744,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_745,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_746,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X2),X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)) ),
cls_irrefl__trancl__rD_0 ).
cnf(i_0_747,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtranclD_0 ).
cnf(i_0_748,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl__eq__or__trancl_0 ).
cnf(i_0_749,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
cls_trancl_Or__into__trancl_0 ).
cnf(i_0_750,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X1,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X2,tc_bool)),
cls_Domain__Diff__subset_0 ).
cnf(i_0_751,axiom,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Domain__Int__subset_0 ).
cnf(i_0_752,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_753,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_754,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_755,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 ).
cnf(i_0_756,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_757,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
| ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
cls_Range__iff_0 ).
cnf(i_0_758,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
| ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
cls_RangeE_0 ).
cnf(i_0_759,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 ).
cnf(i_0_760,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_761,axiom,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
cls_r__into__trancl_H_0 ).
cnf(i_0_762,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_763,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
cls_Domain__iff_0 ).
cnf(i_0_764,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
cls_DomainE_0 ).
cnf(i_0_765,axiom,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__trancl_0 ).
cnf(i_0_766,axiom,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__trancl_0 ).
cnf(i_0_767,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_768,axiom,
c_Relation_Otrans(c_Transitive__Closure_Otrancl(X1,X2),X2),
cls_trans__trancl_0 ).
cnf(i_0_769,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_770,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 ).
cnf(i_0_771,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 ).
cnf(i_0_772,axiom,
c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
cls_trancl__empty_0 ).
cnf(i_0_773,axiom,
( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
| ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
cls_RangeI_0 ).
cnf(i_0_774,axiom,
( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
| ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
cls_Range__iff_1 ).
cnf(i_0_775,axiom,
( X1 = X2
| X1 = X3
| X1 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__above_6 ).
cnf(i_0_776,axiom,
( X1 = X2
| X3 = X1
| X2 = X1
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__below_6 ).
cnf(i_0_777,axiom,
( X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__above_12 ).
cnf(i_0_778,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__below_12 ).
cnf(i_0_779,plain,
( X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_in__above_7]) ).
cnf(i_0_780,axiom,
( X2 = X4
| X4 = X2
| X4 = X1
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_7 ).
cnf(i_0_781,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_in__below_11]) ).
cnf(i_0_782,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_in__above_11]) ).
cnf(i_0_783,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
cls_total__on__diff__Id_0 ).
cnf(i_0_784,axiom,
( X1 = X2
| c_in(X1,c_Relation_ODomain(X4,X3,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_Not__Domain__rtrancl_0 ).
cnf(i_0_785,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
| ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
cls_DomainI_0 ).
cnf(i_0_786,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
| ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
cls_Domain__iff_1 ).
cnf(i_0_787,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
cls_Id__O__R_0 ).
cnf(i_0_788,axiom,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
cls_R__O__Id_0 ).
cnf(i_0_789,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 ).
cnf(i_0_790,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 ).
cnf(i_0_791,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
cls_pair__in__Id__conv_0 ).
cnf(i_0_792,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_793,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
cls_trancl__id_0 ).
cnf(i_0_794,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X3),X3)
| c_in(c_Pair(X1,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
cls_Not__Domain__rtrancl_1 ).
cnf(i_0_795,axiom,
( c_in(c_Pair(X4,X1,X3,X3),X6,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X5,X6,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X5,X6,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X6,X3) ),
cls_quotient__eq__iff_0 ).
cnf(i_0_796,axiom,
( c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
cls_total__on__diff__Id_1 ).
cnf(i_0_797,axiom,
( c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Otrans(X1,X2) ),
cls_trans__diff__Id_0 ).
cnf(i_0_798,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 ).
cnf(i_0_799,axiom,
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2) ),
cls_trans__reflclI_0 ).
cnf(i_0_800,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 ).
cnf(i_0_801,axiom,
c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__r__diff__Id_0 ).
cnf(i_0_802,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)
| ~ c_in(X1,c_Relation_OId(X2),tc_prod(X2,X2)) ),
cls_IdE_0 ).
cnf(i_0_803,axiom,
c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
cls_irrefl__diff__Id_0 ).
cnf(i_0_804,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_805,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
cls_IdI_0 ).
cnf(i_0_806,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
cls_pair__in__Id__conv_1 ).
cnf(i_0_807,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[cls_in__above_5]) ).
cnf(i_0_808,axiom,
( X1 = X2
| X2 = X1
| X2 = X1
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_5 ).
cnf(i_0_809,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_Range__empty__iff_0 ).
cnf(i_0_810,axiom,
c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Range__empty_0 ).
cnf(i_0_811,axiom,
c_Set_Oimage(c_snd(X1,X2),X3,tc_prod(X1,X2),X2) = c_Relation_ORange(X3,X1,X2),
cls_snd__eq__Range_0 ).
cnf(i_0_812,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
cls_Domain__empty__iff_0 ).
cnf(i_0_813,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[cls_in__mktop_4]) ).
cnf(i_0_814,axiom,
( X1 = X2
| X2 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mkbot_4 ).
cnf(i_0_815,axiom,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
cls_Image__Id_0 ).
cnf(i_0_816,axiom,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
cls_converse__Id_0 ).
cnf(i_0_817,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 ).
cnf(i_0_818,axiom,
c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Domain__empty_0 ).
cnf(i_0_819,axiom,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
cls_Range__Id__on_0 ).
cnf(i_0_820,axiom,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
cls_single__valued__Id_0 ).
cnf(i_0_821,axiom,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
cls_antisym__Id_0 ).
cnf(i_0_822,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
cls_trans__Id_0 ).
cnf(i_0_823,axiom,
c_Relation_Osym(c_Relation_OId(X1),X1),
cls_sym__Id_0 ).
cnf(i_0_824,axiom,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
cls_Domain__Id__on_0 ).
cnf(i_0_825,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X3,X4,X5,X6,X7),X2,X7,X6),X4,tc_prod(X7,X6))
| ~ c_in(c_Pair(X1,X2,X5,X6),c_Relation_Orel__comp(X3,X4,X5,X7,X6),tc_prod(X5,X6)) ),
cls_rel__compEpair_1,
[final] ).
cnf(i_0_826,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X3,X4,X5,X6,X7),X5,X7),X3,tc_prod(X5,X7))
| ~ c_in(c_Pair(X1,X2,X5,X6),c_Relation_Orel__comp(X3,X4,X5,X7,X6),tc_prod(X5,X6)) ),
cls_rel__compEpair_0,
[final] ).
cnf(i_0_827,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_828,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_829,axiom,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5),X3,X4,X4),X2,tc_prod(X4,X4)) ),
cls_cuts__eq_1,
[final] ).
cnf(i_0_830,plain,
( c_lessequals(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_707,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_831,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_832,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_709,c_0_708]),c_0_708]),c_0_708]),
[final] ).
cnf(i_0_833,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(c_Relation_Oconverse(X4,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_710,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_834,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(c_Relation_Oconverse(X4,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_711,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_835,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X4),X5)
| ~ c_in(c_Pair(X3,X5,X6,X6),X7,tc_prod(X6,X6))
| ~ c_in(c_Pair(X2,X4,X8,X8),X9,tc_prod(X8,X8))
| ~ c_Equiv__Relations_Ocongruent2(X9,X7,X1,X8,X6,X10) ),
cls_congruent2_Ocongruent2_0,
[final] ).
cnf(i_0_836,axiom,
( c_Equiv__Relations_Ocongruent(X1,hAPP(X2,X3),X4,X5)
| ~ c_in(X3,X6,X7)
| ~ c_Equiv__Relations_Ocongruent2(X8,X1,X2,X7,X4,X5)
| ~ c_Equiv__Relations_Oequiv(X6,X8,X7) ),
cls_congruent2__implies__congruent_0,
[final] ).
cnf(i_0_837,plain,
( c_in(c_Pair(X2,X3,X4,X4),X1,tc_prod(X4,X4))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X1,X2,X3,X4),X3,X4,X4),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X4),X4,X4,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_712,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_838,plain,
( c_in(c_Pair(X1,X2,X4,X4),X3,tc_prod(X4,X4))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X3,X4),X4,X4),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X4),X4,X4,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_713,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_839,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_714,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_840,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_715,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_841,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_716,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_842,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_717,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_843,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_718,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_844,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(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),tc_prod(t_a,t_a))
| ~ c_in(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),tc_prod(t_a,t_a)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_719,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_845,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_846,plain,
( c_in(c_Pair(X1,X2,X4,X4),X3,tc_prod(X4,X4))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X3,X4),X2,X4,X4),X3,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[i_0_720,c_0_708]),
[final] ).
cnf(i_0_847,plain,
( c_in(c_Pair(X1,X3,X4,X4),X2,tc_prod(X4,X4))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[i_0_721,c_0_708]),
[final] ).
cnf(i_0_848,axiom,
( hBOOL(hAPP(hAPP(hAPP(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_split(X1,X5,X6,tc_fun(X7,tc_bool)),c_Pair(X2,X3,X5,X6)),X4)) ),
cls_splitD_H_0,
[final] ).
cnf(i_0_849,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X5,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Equiv__Relations_Oequiv(X6,X4,X3) ),
cls_equiv__class__nondisjoint_0,
[final] ).
cnf(i_0_850,plain,
( c_in(X1,c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(X1,c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_722,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_851,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(c_snd(X2,X3),c_Pair(X4,X5,X2,X3))),hAPP(c_fst(X2,X3),c_Pair(X4,X5,X2,X3))))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
cls_exI__realizer_0,
[final] ).
cnf(i_0_852,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_853,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_854,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[i_0_723,c_0_708]),
[final] ).
cnf(i_0_855,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X2,X1,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[i_0_724,c_0_708]),
[final] ).
cnf(i_0_856,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X1,X2,X3,X4),X3,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[i_0_725,c_0_708]),
[final] ).
cnf(i_0_857,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X4),X4,X4,X4),tc_prod(X4,X4)) ),
inference(rw,[status(thm)],[i_0_726,c_0_708]),
[final] ).
cnf(i_0_858,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X2,X3,X4,X5),c_Product__Type_OSigma(X6,c_COMBK(X7,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
| ~ c_lessequals(X2,c_Product__Type_OSigma(X8,c_COMBK(X7,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(tc_prod(X4,X5),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X8,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
cls_rel__comp__subset__Sigma_0,
[final] ).
cnf(i_0_859,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
cls_Image__iff_1,
[final] ).
cnf(i_0_860,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
cls_ImageE_0,
[final] ).
cnf(i_0_861,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(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),tc_prod(t_a,t_a)) ),
inference(rw,[status(thm)],[i_0_727,c_0_708]),
[final] ).
cnf(i_0_862,axiom,
c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6) = c_Set_Oinsert(c_Pair(X1,X4,X3,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X2,c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(X5,tc_fun(X6,tc_bool),X3),X3,X6),tc_fun(tc_prod(X3,X6),tc_bool)),tc_prod(X3,X6)),
cls_insert__times__insert_0,
[final] ).
cnf(i_0_863,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X3,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X1,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2),X3,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(rw,[status(thm)],[i_0_728,c_0_729]),
[final] ).
cnf(i_0_864,plain,
c_Set_Oimage(c_fst(X2,X2),c_Relation_Oconverse(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2,X2),tc_prod(X2,X2),X2) = c_Set_Oimage(c_fst(X2,X2),c_Relation_Oconverse(X1,X2,X2),tc_prod(X2,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_730,c_0_708]),c_0_731]),c_0_731]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_865,axiom,
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X2,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X4,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
cls_union__comp__emptyL_0,
[final] ).
cnf(i_0_866,axiom,
( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X2,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
cls_union__comp__emptyR_0,
[final] ).
cnf(i_0_867,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_733,c_0_708]),
[final] ).
cnf(i_0_868,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_734,c_0_708]),
[final] ).
cnf(i_0_869,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_870,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_fst(X3,X2),c_Relation_Oconverse(X1,X2,X3),tc_prod(X3,X2),X3),c_Set_Oimage(c_fst(X3,X2),c_Relation_Oconverse(X4,X2,X3),tc_prod(X3,X2),X3),tc_fun(X3,tc_bool)),c_Set_Oimage(c_fst(X3,X2),c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_prod(X3,X2),X3),tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_735,c_0_731]),c_0_731]),c_0_731]),c_0_732]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_871,plain,
c_lessequals(c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),tc_prod(X4,X3),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3),X4),c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3),X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_736,c_0_731]),c_0_731]),c_0_731]),c_0_732]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_872,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X3,X3,X2,X2),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),tc_prod(X2,X2)) ),
inference(rw,[status(thm)],[i_0_737,c_0_708]),
[final] ).
cnf(i_0_873,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_738,c_0_708]),
[final] ).
cnf(i_0_874,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_739,c_0_708]),
[final] ).
cnf(i_0_875,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_740,c_0_708]),
[final] ).
cnf(i_0_876,plain,
( c_lessequals(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(rw,[status(thm)],[i_0_741,c_0_708]),
[final] ).
cnf(i_0_877,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_742,c_0_708]),
[final] ).
cnf(i_0_878,plain,
( ~ c_Wellfounded_Oacyclic(X3,X2)
| ~ c_in(c_Pair(X1,X1,X2,X2),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X2),X2,X2,X2),tc_prod(X2,X2)) ),
inference(rw,[status(thm)],[i_0_743,c_0_708]),
[final] ).
cnf(i_0_879,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4))
| ~ c_in(c_Pair(X8,X2,X7,X4),X6,tc_prod(X7,X4))
| ~ c_in(c_Pair(X1,X8,X3,X7),X5,tc_prod(X3,X7)) ),
cls_rel__compI_0,
[final] ).
cnf(i_0_880,axiom,
( hAPP(X1,X7) = hAPP(X6,X7)
| c_Recdef_Ocut(X1,X2,X3,X4,X5) != c_Recdef_Ocut(X6,X2,X3,X4,X5)
| ~ c_in(c_Pair(X7,X3,X4,X4),X2,tc_prod(X4,X4)) ),
cls_cuts__eq_0,
[final] ).
cnf(i_0_881,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_882,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_744,c_0_708]),c_0_708]),
[final] ).
cnf(i_0_883,plain,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_745,c_0_708]),c_0_729]),c_0_729]),
[final] ).
cnf(i_0_884,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X3,X2),X2,X2),c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X2),X2,X2,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(rw,[status(thm)],[i_0_746,c_0_708]),
[final] ).
cnf(i_0_885,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_747,c_0_708]),
[final] ).
cnf(i_0_886,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_748,c_0_708]),
[final] ).
cnf(i_0_887,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Orel__comp(X4,c_Transitive__Closure_Ortrancl(X4,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_749,c_0_708]),
[final] ).
cnf(i_0_888,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_889,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_890,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X2,X5,X3)
| ~ c_lessequals(c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3) ),
cls_subset__equiv__class_0,
[final] ).
cnf(i_0_891,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_fst(X2,X3),X1,tc_prod(X2,X3),X2),c_Set_Oimage(c_fst(X2,X3),X4,tc_prod(X2,X3),X2),tc_fun(X2,tc_bool)),c_Set_Oimage(c_fst(X2,X3),c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)),tc_prod(X2,X3),X2),tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_750,c_0_732]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_892,plain,
c_lessequals(c_Set_Oimage(c_fst(X3,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),tc_prod(X3,X4),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(c_fst(X3,X4),X1,tc_prod(X3,X4),X3),c_Set_Oimage(c_fst(X3,X4),X2,tc_prod(X3,X4),X3),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_751,c_0_732]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_893,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X3,X4,X5),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X1,X3,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_rtrancl__induct_1,
[final] ).
cnf(i_0_894,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X1,X3,X4,X5),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X3,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_converse__rtrancl__induct_0,
[final] ).
cnf(i_0_895,plain,
c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4),tc_prod(X4,X3),X4) = c_Set_Oinsert(X2,c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3),X4),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_752,c_0_731]),c_0_731]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_896,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_14,
[final] ).
cnf(i_0_897,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_14,
[final] ).
cnf(i_0_898,axiom,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X1,X2,X3,X4,X5),X1,X4)
| ~ c_in(X3,c_Product__Type_OSigma(X1,X2,X4,X5),tc_prod(X4,X5)) ),
cls_SigmaE_0,
[final] ).
cnf(i_0_899,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ c_in(c_Pair(X6,X3,X4,X4),X2,tc_prod(X4,X4)) ),
cls_cut__apply_0,
[final] ).
cnf(i_0_900,axiom,
( hAPP(c_Recdef_Ocut(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| ~ c_in(c_Pair(X6,X3,X4,X4),X2,tc_prod(X4,X4)) ),
cls_tfl__cut__apply_0,
[final] ).
cnf(i_0_901,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X1,X2,X3,X4,X5),X1,X4)
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
cls_Image__iff_0,
[final] ).
cnf(i_0_902,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X1,X2,X3,X4,X5),X1,X4)
| ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
cls_ImageE_1,
[final] ).
cnf(i_0_903,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Relation_Osingle__valued(X4,X3,X3) ),
cls_single__valued__confluent_0,
[final] ).
cnf(i_0_904,plain,
c_Set_Oimage(c_fst(X2,X2),c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),tc_prod(X2,X2),X2) = c_Set_Oimage(c_fst(X2,X2),X1,tc_prod(X2,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_753,c_0_708]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_905,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)),c_Set_Oimage(X1,c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X3,tc_bool)),X3,X4),tc_fun(X4,tc_bool)),
cls_image__diff__subset_0,
[final] ).
cnf(i_0_906,axiom,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
cls_image__Int__subset_0,
[final] ).
cnf(i_0_907,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_908,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_754,c_0_708]),c_0_729]),
[final] ).
cnf(i_0_909,plain,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(rw,[status(thm)],[i_0_755,c_0_729]),
[final] ).
cnf(i_0_910,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_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_756,c_0_708]),c_0_729]),
[final] ).
cnf(i_0_911,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
| ~ c_in(X1,c_Set_Oimage(c_fst(X3,X4),c_Relation_Oconverse(X2,X4,X3),tc_prod(X3,X4),X3),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_757,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_912,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
| ~ c_in(X1,c_Set_Oimage(c_fst(X3,X4),c_Relation_Oconverse(X2,X4,X3),tc_prod(X3,X4),X3),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_758,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_913,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))
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_equiv__class__subset_0,
[final] ).
cnf(i_0_914,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool))
| ~ c_in(X6,X4,X5) ),
cls_Times__subset__cancel2_0,
[final] ).
cnf(i_0_915,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_916,axiom,
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__trans__comp__subset_0,
[final] ).
cnf(i_0_917,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
cls_acyclic__insert_1,
[final] ).
cnf(i_0_918,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
cls_wf__insert_1,
[final] ).
cnf(i_0_919,plain,
( c_Equiv__Relations_Oequiv(c_Set_Oimage(c_fst(X2,X2),X1,tc_prod(X2,X2),X2),X1,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1 ),
inference(rw,[status(thm)],[i_0_759,c_0_732]),
[final] ).
cnf(i_0_920,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_Set_Oimage(c_fst(X2,X2),X1,tc_prod(X2,X2),X2),c_Set_Oimage(c_fst(X2,X2),c_Relation_Oconverse(X3,X2,X2),tc_prod(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_760,c_0_731]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_921,plain,
( c_in(X1,c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X3),X3,X3,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_761,c_0_708]),
[final] ).
cnf(i_0_922,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_923,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_10,
[final] ).
cnf(i_0_924,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X5
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_8,
[final] ).
cnf(i_0_925,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X5,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_8,
[final] ).
cnf(i_0_926,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_10,
[final] ).
cnf(i_0_927,axiom,
( X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_13,
[final] ).
cnf(i_0_928,axiom,
( X4 = X2
| X4 = X1
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_13,
[final] ).
cnf(i_0_929,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))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_rtrancl__induct_3,
[final] ).
cnf(i_0_930,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))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_converse__rtrancl__induct_3,
[final] ).
cnf(i_0_931,plain,
c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),tc_prod(X4,X3),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3),X4),c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3),X4),tc_fun(X4,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_762,c_0_731]),c_0_731]),c_0_731]),c_0_732]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_932,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X1,X3,X4,X5),X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_converse__rtrancl__induct_1,
[final] ).
cnf(i_0_933,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X1,X3,X4,X5),X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5))
| ~ hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_rtrancl__induct_0,
[final] ).
cnf(i_0_934,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Set_Oimage(c_fst(X3,X4),X2,tc_prod(X3,X4),X3),X3) ),
inference(rw,[status(thm)],[i_0_763,c_0_732]),
[final] ).
cnf(i_0_935,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Set_Oimage(c_fst(X3,X4),X2,tc_prod(X3,X4),X3),X3) ),
inference(rw,[status(thm)],[i_0_764,c_0_732]),
[final] ).
cnf(i_0_936,axiom,
( c_in(hAPP(hAPP(X1,X2),X3),c_Set_Oimage(c_split(X1,X4,X5,X6),X7,tc_prod(X4,X5),X6),X6)
| ~ c_in(c_Pair(X2,X3,X4,X5),X7,tc_prod(X4,X5)) ),
cls_pair__imageI_0,
[final] ).
cnf(i_0_937,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2) ),
cls_trans__O__subset_0,
[final] ).
cnf(i_0_938,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X1,X2,X3,X4),X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4))
| X2 = X3
| ~ c_in(c_Pair(X2,X3,X4,X4),c_Transitive__Closure_Ortrancl(X1,X4),tc_prod(X4,X4)) ),
cls_converse__rtranclE_1,
[final] ).
cnf(i_0_939,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X3,X4),X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4)) ),
cls_rtranclE_0,
[final] ).
cnf(i_0_940,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X3,X4),X2,X4,X4),X3,tc_prod(X4,X4))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X4,X4),c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4)) ),
cls_rtranclE_1,
[final] ).
cnf(i_0_941,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X2,X1,X3,X4),X4,X4),X2,tc_prod(X4,X4))
| X1 = X3
| ~ c_in(c_Pair(X1,X3,X4,X4),c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4)) ),
cls_converse__rtranclE_0,
[final] ).
cnf(i_0_942,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_765,c_0_708]),
[final] ).
cnf(i_0_943,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_766,c_0_708]),
[final] ).
cnf(i_0_944,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_767,c_0_708]),
[final] ).
cnf(i_0_945,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl__trans_0,
[final] ).
cnf(i_0_946,plain,
c_Relation_Otrans(c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),X2),
inference(rw,[status(thm)],[i_0_768,c_0_708]),
[final] ).
cnf(i_0_947,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_769,c_0_708]),
[final] ).
cnf(i_0_948,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_949,axiom,
( c_in(X1,X2,X3)
| X1 = X4
| ~ c_lessequals(X5,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X5,X3),tc_prod(X3,X3)) ),
cls_trancl__subset__Sigma__aux_0,
[final] ).
cnf(i_0_950,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)) ),
cls_converse__rtrancl__into__rtrancl_0,
[final] ).
cnf(i_0_951,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl_Ortrancl__into__rtrancl_0,
[final] ).
cnf(i_0_952,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_953,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X4,X3) ),
cls_transD_0,
[final] ).
cnf(i_0_954,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X4,X3) ),
cls_trans__def_0,
[final] ).
cnf(i_0_955,axiom,
( c_in(c_Pair(hAPP(X1,X2),hAPP(X1,X3),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X2,X3,X6,X6),c_Relation_Oinv__image(X5,X1,X4,X6),tc_prod(X6,X6)) ),
cls_in__inv__image_0,
[final] ).
cnf(i_0_956,axiom,
( c_in(X1,hAPP(c_split(X2,X3,X4,tc_fun(X5,tc_bool)),c_Pair(X6,X7,X3,X4)),X5)
| ~ c_in(X1,hAPP(hAPP(X2,X6),X7),X5) ),
cls_mem__splitI_0,
[final] ).
cnf(i_0_957,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
cls_Times__Un__distrib1_0,
[final] ).
cnf(i_0_958,axiom,
c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
cls_Times__Diff__distrib1_0,
[final] ).
cnf(i_0_959,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
cls_Times__Int__distrib1_0,
[final] ).
cnf(i_0_960,axiom,
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| 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_in(X4,X5,X3)
| ~ c_in(X2,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_eq__equiv__class__iff_0,
[final] ).
cnf(i_0_961,axiom,
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| 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)
| ~ c_in(X4,X5,X3)
| ~ c_in(X2,X5,X3) ),
cls_equiv__class__eq__iff_3,
[final] ).
cnf(i_0_962,axiom,
( hBOOL(hAPP(X1,hAPP(c_fst(X2,X3),c_Pair(X4,X5,X2,X3))))
| ~ hBOOL(hAPP(X6,X5))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_conjI__realizer_0,
[final] ).
cnf(i_0_963,axiom,
( hBOOL(hAPP(X1,hAPP(c_snd(X2,X3),c_Pair(X4,X5,X2,X3))))
| ~ hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(X6,X4)) ),
cls_conjI__realizer_1,
[final] ).
cnf(i_0_964,axiom,
( c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| 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_in(X4,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_eq__equiv__class_0,
[final] ).
cnf(i_0_965,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oinv__image(X4,X5,X6,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(hAPP(X5,X1),hAPP(X5,X2),X6,X6),X4,tc_prod(X6,X6)) ),
cls_in__inv__image_1,
[final] ).
cnf(i_0_966,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
cls_Image__singleton__iff_0,
[final] ).
cnf(i_0_967,plain,
c_Set_Oimage(c_fst(X3,X4),c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),tc_prod(X3,X4),X3) = c_Set_Oinsert(X1,c_Set_Oimage(c_fst(X3,X4),X5,tc_prod(X3,X4),X3),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_770,c_0_732]),c_0_732]),
[final] ).
cnf(i_0_968,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)
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_in(X4,X5,X3)
| ~ c_in(X2,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_eq__equiv__class__iff_1,
[final] ).
cnf(i_0_969,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))
| ~ c_in(c_Pair(X3,X2,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_rtrancl__induct_2,
[final] ).
cnf(i_0_970,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))
| ~ c_in(c_Pair(X2,X3,X5,X5),c_Transitive__Closure_Ortrancl(X4,X5),tc_prod(X5,X5)) ),
cls_converse__rtrancl__induct_2,
[final] ).
cnf(i_0_971,axiom,
( c_Wellfounded_Owf(X1,X2)
| c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
cls_wf__no__loop_0,
[final] ).
cnf(i_0_972,axiom,
( c_lessequals(c_Relation_OImage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X6,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),tc_fun(tc_prod(X3,X4),tc_bool)) ),
cls_Image__subset_0,
[final] ).
cnf(i_0_973,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_974,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_notin__Lin__iff_1,
[final] ).
cnf(i_0_975,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_Lin__irrefl_0,
[final] ).
cnf(i_0_976,axiom,
( c_lessequals(c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3),tc_fun(tc_prod(X4,X3),tc_bool))
| ~ c_lessequals(X1,X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
cls_Times__subset__cancel2_1,
[final] ).
cnf(i_0_977,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)
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_equiv__class__eq__iff_0,
[final] ).
cnf(i_0_978,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)
| ~ c_in(c_Pair(X2,X4,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X1,X3) ),
cls_equiv__class__eq_0,
[final] ).
cnf(i_0_979,axiom,
( X1 = X2
| ~ c_in(c_Pair(X3,X2,X4,X5),X6,tc_prod(X4,X5))
| ~ c_in(c_Pair(X3,X1,X4,X5),X6,tc_prod(X4,X5))
| ~ c_Relation_Osingle__valued(X6,X4,X5) ),
cls_single__valuedD_0,
[final] ).
cnf(i_0_980,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
cls_rtrancl__converseD_0,
[final] ).
cnf(i_0_981,axiom,
( c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X5),X5)
| ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
cls_Image__singleton__iff_1,
[final] ).
cnf(i_0_982,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_983,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_984,axiom,
( X1 = X2
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Oantisym(X4,X3) ),
cls_antisymD_0,
[final] ).
cnf(i_0_985,axiom,
( X1 = X2
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Oantisym(X4,X3) ),
cls_antisym__def_0,
[final] ).
cnf(i_0_986,plain,
c_Set_Oimage(c_fst(X3,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),tc_prod(X3,X4),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_fst(X3,X4),X1,tc_prod(X3,X4),X3),c_Set_Oimage(c_fst(X3,X4),X2,tc_prod(X3,X4),X3),tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_771,c_0_732]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_987,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X4,X3) ),
cls_wf__asym_0,
[final] ).
cnf(i_0_988,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_2,
[final] ).
cnf(i_0_989,axiom,
( X1 = X2
| X2 = X4
| c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_2,
[final] ).
cnf(i_0_990,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X2 = X4
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_3,
[final] ).
cnf(i_0_991,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| X5 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X5,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_3,
[final] ).
cnf(i_0_992,axiom,
( X4 = X1
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_1,
[final] ).
cnf(i_0_993,axiom,
( X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_1,
[final] ).
cnf(i_0_994,axiom,
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Oacyclic(X4,X3) ),
cls_acyclic__insert_2,
[final] ).
cnf(i_0_995,axiom,
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X4,X3) ),
cls_wf__insert_2,
[final] ).
cnf(i_0_996,plain,
c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(rw,[status(thm)],[i_0_772,c_0_708]),
[final] ).
cnf(i_0_997,plain,
( c_in(X1,c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3),X4),X4)
| ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_773,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_998,plain,
( c_in(X1,c_Set_Oimage(c_fst(X4,X3),c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3),X4),X4)
| ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_774,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_999,axiom,
( c_in(X1,hAPP(X2,X3),X4)
| ~ c_in(c_Pair(X3,X1,X5,X4),c_Product__Type_OSigma(X6,X2,X5,X4),tc_prod(X5,X4)) ),
cls_SigmaD2_0,
[final] ).
cnf(i_0_1000,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
cls_rtrancl__converseI_0,
[final] ).
cnf(i_0_1001,axiom,
( X1 = X2
| ~ c_in(c_Pair(X3,X4,X5,X5),X6,tc_prod(X5,X5))
| ~ c_in(X4,X2,X5)
| ~ c_in(X3,X1,X5)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X7,X6,X5),tc_fun(X5,tc_bool))
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X7,X6,X5),tc_fun(X5,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X7,X6,X5) ),
cls_quotient__eqI_0,
[final] ).
cnf(i_0_1002,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X2 = X4
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_4,
[final] ).
cnf(i_0_1003,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X5
| X1 = X5
| X1 = X2
| X4 = X5
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_4,
[final] ).
cnf(i_0_1004,axiom,
( X1 = X3
| X1 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1005,axiom,
( X1 = X3
| X1 = X2
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[i_0_776]),
[final] ).
cnf(i_0_1006,axiom,
( X1 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[i_0_777]),
[final] ).
cnf(i_0_1007,axiom,
( X2 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[i_0_778]),
[final] ).
cnf(i_0_1008,axiom,
( X1 = X4
| X4 = X2
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_9,
[final] ).
cnf(i_0_1009,plain,
( X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_779,
[final] ).
cnf(i_0_1010,axiom,
( X2 = X4
| X1 = X4
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1011,axiom,
( X4 = X2
| X1 = X4
| c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_9,
[final] ).
cnf(i_0_1012,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_781,
[final] ).
cnf(i_0_1013,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_782,
[final] ).
cnf(i_0_1014,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X6,X3,X5),tc_prod(X3,X5)) ),
cls_SigmaD1_0,
[final] ).
cnf(i_0_1015,axiom,
( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| X2 = X1
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
cls_rtrancl_Ocases_0,
[final] ).
cnf(i_0_1016,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_1017,axiom,
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| X2 = X1
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
cls_rtrancl_Ocases_1,
[final] ).
cnf(i_0_1018,axiom,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2)
| ~ c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X4,X5,X2)
| ~ c_in(X1,X5,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X3,X2) ),
cls_eq__equiv__class__iff2_1,
[final] ).
cnf(i_0_1019,axiom,
( c_in(c_Pair(X1,X4,X2,X2),X3,tc_prod(X2,X2))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3,X2)
| ~ c_in(X4,X5,X2)
| ~ c_in(X1,X5,X2)
| ~ c_Equiv__Relations_Oequiv(X5,X3,X2) ),
cls_eq__equiv__class__iff2_0,
[final] ).
cnf(i_0_1020,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
cls_converseD_0,
[final] ).
cnf(i_0_1021,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(rw,[status(thm)],[i_0_783,c_0_729]),
[final] ).
cnf(i_0_1022,plain,
( X1 = X2
| c_in(X1,c_Set_Oimage(c_fst(X3,X3),X4,tc_prod(X3,X3),X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_784,c_0_732]),
[final] ).
cnf(i_0_1023,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
cls_converseI_0,
[final] ).
cnf(i_0_1024,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
cls_converse__iff_1,
[final] ).
cnf(i_0_1025,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_1026,plain,
( c_in(X1,c_Set_Oimage(c_fst(X3,X4),X2,tc_prod(X3,X4),X3),X3)
| ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
inference(rw,[status(thm)],[i_0_785,c_0_732]),
[final] ).
cnf(i_0_1027,plain,
( c_in(X1,c_Set_Oimage(c_fst(X3,X4),X2,tc_prod(X3,X4),X3),X3)
| ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
inference(rw,[status(thm)],[i_0_786,c_0_732]),
[final] ).
cnf(i_0_1028,plain,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1,X3) = X2,
inference(rw,[status(thm)],[i_0_787,c_0_729]),
[final] ).
cnf(i_0_1029,plain,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X3,X2,X2) = X1,
inference(rw,[status(thm)],[i_0_788,c_0_729]),
[final] ).
cnf(i_0_1030,axiom,
( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X6,X3,X4) ),
cls_Image__iff_2,
[final] ).
cnf(i_0_1031,axiom,
( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X6,X3,X4) ),
cls_rev__ImageI_0,
[final] ).
cnf(i_0_1032,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_1033,axiom,
c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_HOL_Ominus__class_Ominus(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__Diff__distrib1_0,
[final] ).
cnf(i_0_1034,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(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__Int__distrib1_0,
[final] ).
cnf(i_0_1035,plain,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(rw,[status(thm)],[i_0_789,c_0_729]),
[final] ).
cnf(i_0_1036,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Osym(X4,X3) ),
cls_symD_0,
[final] ).
cnf(i_0_1037,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Relation_Osym(X4,X3) ),
cls_sym__def_0,
[final] ).
cnf(i_0_1038,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mkbot_2,
[final] ).
cnf(i_0_1039,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mktop_2,
[final] ).
cnf(i_0_1040,plain,
( c_lessequals(c_Set_Oimage(c_fst(X2,X3),X1,tc_prod(X2,X3),X2),c_Set_Oimage(c_fst(X2,X3),X4,tc_prod(X2,X3),X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_790,c_0_732]),c_0_732]),
[final] ).
cnf(i_0_1041,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mktop_5,
[final] ).
cnf(i_0_1042,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mkbot_5,
[final] ).
cnf(i_0_1043,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mktop_3,
[final] ).
cnf(i_0_1044,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
cls_in__mkbot_3,
[final] ).
cnf(i_0_1045,axiom,
c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X2,X4,X5),c_Set_Oimage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
cls_image__Un_0,
[final] ).
cnf(i_0_1046,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_1047,axiom,
c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
cls_rel__comp__empty1_0,
[final] ).
cnf(i_0_1048,axiom,
c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
cls_rel__comp__empty2_0,
[final] ).
cnf(i_0_1049,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_791,c_0_729]),
[final] ).
cnf(i_0_1050,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X5,X2,X3)
| ~ c_Wellfounded_Owf(X4,X3) ),
cls_wfE__min_1,
[final] ).
cnf(i_0_1051,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X5,X2,X3)
| ~ c_Wellfounded_Owf(X4,X3) ),
cls_wf__eq__minimal_1,
[final] ).
cnf(i_0_1052,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X5),X5) ),
cls_acc__induct__rule_1,
[final] ).
cnf(i_0_1053,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X5),X5) ),
cls_acc__induct_1,
[final] ).
cnf(i_0_1054,axiom,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X1,X2,X3),X4),X5))
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3)) ),
cls_in__rel__def_1,
[final] ).
cnf(i_0_1055,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3))
| X2 = X1
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| ~ c_Relation_Ototal__on(X5,X4,X3) ),
cls_total__on__def_0,
[final] ).
cnf(i_0_1056,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_1057,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_1058,axiom,
( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X5,X3,X4),X1),X2)) ),
cls_in__rel__def_0,
[final] ).
cnf(i_0_1059,axiom,
( X1 = X5
| c_Product__Type_OSigma(X1,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3) != c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X4),X4,X3)
| ~ c_in(X6,X2,X3) ),
cls_Times__eq__cancel2_0,
[final] ).
cnf(i_0_1060,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
cls_subset__insert__iff_4,
[final] ).
cnf(i_0_1061,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_792,c_0_708]),
[final] ).
cnf(i_0_1062,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
cls_wf__induct__rule_0,
[final] ).
cnf(i_0_1063,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
cls_wf__def_0,
[final] ).
cnf(i_0_1064,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
cls_tfl__wf__induct_0,
[final] ).
cnf(i_0_1065,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X1,X4,X5),X5,X5),X4,tc_prod(X5,X5))
| ~ c_Wellfounded_Owf(X4,X5) ),
cls_wf__induct_0,
[final] ).
cnf(i_0_1066,axiom,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_in(c_Pair(X2,X3,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent(X5,X1,X4,X6) ),
cls_congruent_Ocongruent_0,
[final] ).
cnf(i_0_1067,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_notin__Lin__iff_0,
[final] ).
cnf(i_0_1068,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
cls_subset__insert__iff_3,
[final] ).
cnf(i_0_1069,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| ~ c_in(X2,X1,X4)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
cls_diff__single__insert_0,
[final] ).
cnf(i_0_1070,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4))
| ~ c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(X1,X5,X3) ),
cls_SigmaI_0,
[final] ).
cnf(i_0_1071,axiom,
( c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4))
| ~ c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(X1,X5,X3) ),
cls_mem__Sigma__iff_2,
[final] ).
cnf(i_0_1072,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_1073,plain,
( c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
inference(rw,[status(thm)],[i_0_793,c_0_708]),
[final] ).
cnf(i_0_1074,plain,
( c_in(X1,c_Set_Oimage(c_fst(X3,X3),X2,tc_prod(X3,X3),X3),X3)
| c_in(c_Pair(X1,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(rw,[status(thm)],[i_0_794,c_0_732]),
[final] ).
cnf(i_0_1075,axiom,
( X3 = X4
| ~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__below_0,
[final] ).
cnf(i_0_1076,axiom,
( X3 = X4
| ~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X2,X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_in__above_0,
[final] ).
cnf(i_0_1077,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(X3,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
cls_acc_Oinduct_0,
[final] ).
cnf(i_0_1078,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(X3,c_Wellfounded_Oacc(X4,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
cls_acc_Oinducts_0,
[final] ).
cnf(i_0_1079,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
cls_image__mono_0,
[final] ).
cnf(i_0_1080,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_subset__image__iff_2,
[final] ).
cnf(i_0_1081,axiom,
( c_in(c_Relation_OImage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Equiv__Relations_Oquotient(X4,X1,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,X4,X3) ),
cls_quotientI_0,
[final] ).
cnf(i_0_1082,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
cls_acc__downwards_0,
[final] ).
cnf(i_0_1083,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
cls_acc__downwards__aux_0,
[final] ).
cnf(i_0_1084,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
cls_acc_Oinduct_1,
[final] ).
cnf(i_0_1085,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,X3))
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X4),t_a,t_a),X4,tc_prod(t_a,t_a))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,t_a),t_a) ),
cls_acc_Oinducts_1,
[final] ).
cnf(i_0_1086,axiom,
( c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3)
| ~ c_in(X1,X4,X3)
| ~ c_Equiv__Relations_Oequiv(X4,X2,X3) ),
cls_equiv__class__self_0,
[final] ).
cnf(i_0_1087,axiom,
( c_in(c_Pair(X4,X1,X3,X3),X6,tc_prod(X3,X3))
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X6,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X5,X6,X3),tc_fun(X3,tc_bool)) ),
inference(cn,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1088,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
cls_acc_Ocases_0,
[final] ).
cnf(i_0_1089,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
cls_acc__downward_0,
[final] ).
cnf(i_0_1090,axiom,
( c_Nitpick_Orefl_H(X1,X2)
| ~ c_in(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,tc_prod(X2,X2)) ),
cls_Nitpick_Orefl_H__def_1,
[final] ).
cnf(i_0_1091,plain,
( c_Relation_Ototal__on(X1,c_HOL_Ominus__class_Ominus(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(rw,[status(thm)],[i_0_796,c_0_729]),
[final] ).
cnf(i_0_1092,axiom,
( c_in(hAPP(X1,X2),X3,X4)
| ~ c_in(X2,X5,X6)
| ~ c_lessequals(c_Set_Oimage(X1,X5,X6,X4),X3,tc_fun(X4,tc_bool)) ),
cls_image__subset__iff_0,
[final] ).
cnf(i_0_1093,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3) ),
cls_equiv__class__eq__iff_1,
[final] ).
cnf(i_0_1094,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3) ),
cls_equiv__class__eq__iff_2,
[final] ).
cnf(i_0_1095,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X2,X5,X3) ),
cls_refl__onD1_0,
[final] ).
cnf(i_0_1096,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X2,X5,X3) ),
cls_refl__onD2_0,
[final] ).
cnf(i_0_1097,axiom,
hAPP(c_split(X1,X2,X3,X4),c_Pair(X5,X6,X2,X3)) = hAPP(hAPP(X1,X5),X6),
cls_split__case__cert_0,
[final] ).
cnf(i_0_1098,axiom,
hAPP(c_split(X1,X2,X3,X4),c_Pair(X5,X6,X2,X3)) = hAPP(hAPP(X1,X5),X6),
cls_Product__Type_Osplit_0,
[final] ).
cnf(i_0_1099,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_1100,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_in(X2,X1,X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X4,X3),tc_fun(X3,tc_bool)) ),
cls_subset__insert__iff_0,
[final] ).
cnf(i_0_1101,axiom,
( c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X2,X1,X3) ),
cls_equiv__type_0,
[final] ).
cnf(i_0_1102,axiom,
( c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X2,X1,X3) ),
cls_refl__on__def_0,
[final] ).
cnf(i_0_1103,axiom,
( c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
cls_Id__on__iff_1,
[final] ).
cnf(i_0_1104,plain,
( c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Oantisym(X1,X2) ),
inference(rw,[status(thm)],[i_0_797,c_0_729]),
[final] ).
cnf(i_0_1105,plain,
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
inference(rw,[status(thm)],[i_0_798,c_0_729]),
[final] ).
cnf(i_0_1106,plain,
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(rw,[status(thm)],[i_0_799,c_0_729]),
[final] ).
cnf(i_0_1107,plain,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_800,c_0_729]),
[final] ).
cnf(i_0_1108,plain,
c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_801,c_0_729]),
[final] ).
cnf(i_0_1109,plain,
( 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)
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)) ),
inference(rw,[status(thm)],[i_0_802,c_0_729]),
[final] ).
cnf(i_0_1110,axiom,
c_lessequals(c_Relation_OId__on(X1,X2),c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
cls_Id__on__subset__Times_0,
[final] ).
cnf(i_0_1111,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_1112,plain,
c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X1,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(rw,[status(thm)],[i_0_803,c_0_729]),
[final] ).
cnf(i_0_1113,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
cls_Id__on__iff_0,
[final] ).
cnf(i_0_1114,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
cls_image__insert_0,
[final] ).
cnf(i_0_1115,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Relation_Oirrefl(X3,X2) ),
cls_irrefl__def_0,
[final] ).
cnf(i_0_1116,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X3,X2) ),
cls_wf__irrefl_0,
[final] ).
cnf(i_0_1117,axiom,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_in__mktop_1,
[final] ).
cnf(i_0_1118,axiom,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_in__mkbot_1,
[final] ).
cnf(i_0_1119,axiom,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_in__mktop_0,
[final] ).
cnf(i_0_1120,axiom,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_in__mkbot_0,
[final] ).
cnf(i_0_1121,plain,
c_Set_Oimage(c_fst(X2,X3),c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2),tc_prod(X2,X3),X2) = c_Set_Oimage(c_fst(X2,X3),X1,tc_prod(X2,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_804,c_0_731]),c_0_732]),c_0_732]),
[final] ).
cnf(i_0_1122,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_1123,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_1124,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)),
inference(rw,[status(thm)],[i_0_805,c_0_729]),
[final] ).
cnf(i_0_1125,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)),
inference(rw,[status(thm)],[i_0_806,c_0_729]),
[final] ).
cnf(i_0_1126,axiom,
( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
| ~ c_in(X2,X3,X4) ),
cls_insert__image_0,
[final] ).
cnf(i_0_1127,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_1128,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
cls_acc_OaccI_0,
[final] ).
cnf(i_0_1129,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))
| c_in(X2,c_Wellfounded_Oacc(X1,X3),X3) ),
cls_not__acc__down_0,
[final] ).
cnf(i_0_1130,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_807,
[final] ).
cnf(i_0_1131,axiom,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(cn,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1132,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_1133,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_1134,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_1135,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_1136,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
cls_Diff__insert2_0,
[final] ).
cnf(i_0_1137,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_1138,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X4),tc_prod(X4,X4)) ),
cls_in__rtrancl__UnI_0,
[final] ).
cnf(i_0_1139,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X3,X4),tc_prod(X4,X4)) ),
cls_in__rtrancl__UnI_1,
[final] ).
cnf(i_0_1140,axiom,
hAPP(c_split(X1,X2,X3,X4),X5) = hAPP(hAPP(X1,hAPP(c_fst(X2,X3),X5)),hAPP(c_snd(X2,X3),X5)),
cls_split__beta_0,
[final] ).
cnf(i_0_1141,axiom,
( X1 = X5
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
cls_Pair__eq_0,
[final] ).
cnf(i_0_1142,axiom,
( X2 = X6
| c_Pair(X1,X2,X3,X4) != c_Pair(X5,X6,X3,X4) ),
cls_Pair__eq_1,
[final] ).
cnf(i_0_1143,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X4,X5,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X4,X5,X3) ),
cls_quotient__disj_0,
[final] ).
cnf(i_0_1144,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Set_Oimage(c_fst(X3,X2),c_Relation_Oconverse(X1,X2,X3),tc_prod(X3,X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_809,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_1145,axiom,
( c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X1,X4,X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
cls_refl__onD_0,
[final] ).
cnf(i_0_1146,axiom,
( c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(X1,X4,X2)
| ~ c_Relation_Orefl__on(X4,X3,X2) ),
cls_refl__on__def_1,
[final] ).
cnf(i_0_1147,plain,
c_Set_Oimage(c_fst(X2,X1),c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2),tc_prod(X2,X1),X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_810,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_1148,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ c_in(X1,X2,X3) ),
cls_insert__Diff_0,
[final] ).
cnf(i_0_1149,plain,
c_Set_Oimage(c_snd(X1,X2),X3,tc_prod(X1,X2),X2) = c_Set_Oimage(c_fst(X2,X1),c_Relation_Oconverse(X3,X1,X2),tc_prod(X2,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_811,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_1150,axiom,
( c_Relation_Oirrefl(X1,X2)
| c_in(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,tc_prod(X2,X2)) ),
cls_irrefl__def_1,
[final] ).
cnf(i_0_1151,axiom,
( c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId__on(X3,X2),tc_prod(X2,X2))
| ~ c_in(X1,X3,X2) ),
cls_Id__on__eqI_0,
[final] ).
cnf(i_0_1152,axiom,
c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = c_Set_Oinsert(X1,X2,X3),
cls_insert__Diff__single_0,
[final] ).
cnf(i_0_1153,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
cls_image__eqI_0,
[final] ).
cnf(i_0_1154,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
cls_imageI_0,
[final] ).
cnf(i_0_1155,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
cls_rev__image__eqI_0,
[final] ).
cnf(i_0_1156,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
cls_image__iff_2,
[final] ).
cnf(i_0_1157,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_1158,axiom,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X1,X3,X4),c_Relation_Oconverse(X2,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
cls_converse__Int_0,
[final] ).
cnf(i_0_1159,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_1160,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_1161,axiom,
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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__Int_0,
[final] ).
cnf(i_0_1162,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)
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
cls_Id__onE_1,
[final] ).
cnf(i_0_1163,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_1164,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X5,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
cls_Diff__mono_0,
[final] ).
cnf(i_0_1165,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_1166,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)),
cls_Diff__insert_0,
[final] ).
cnf(i_0_1167,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
cls_Diff__Int2_0,
[final] ).
cnf(i_0_1168,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_1169,axiom,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Un__Diff_0,
[final] ).
cnf(i_0_1170,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_1171,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(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_Diff__Int__distrib2_0,
[final] ).
cnf(i_0_1172,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_1173,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Diff__Un_0,
[final] ).
cnf(i_0_1174,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
cls_Diff__Int_0,
[final] ).
cnf(i_0_1175,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_1176,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(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_Diff__Int__distrib_0,
[final] ).
cnf(i_0_1177,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
cls_rtrancl__eq__or__trancl_1,
[final] ).
cnf(i_0_1178,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
cls_rtrancl_Ortrancl__refl_0,
[final] ).
cnf(i_0_1179,axiom,
( c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X3,X2) ),
cls_Nitpick_Orefl_H__def_0,
[final] ).
cnf(i_0_1180,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Set_Oimage(c_fst(X2,X3),X1,tc_prod(X2,X3),X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(rw,[status(thm)],[i_0_812,c_0_732]),
[final] ).
cnf(i_0_1181,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
cls_Diff__subset__conv_1,
[final] ).
cnf(i_0_1182,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) ),
cls_Diff__subset__conv_0,
[final] ).
cnf(i_0_1183,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
cls_complete__Lin_1,
[final] ).
cnf(i_0_1184,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_813,
[final] ).
cnf(i_0_1185,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(cn,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1186,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_1187,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_1188,plain,
c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1) = X2,
inference(rw,[status(thm)],[i_0_815,c_0_729]),
[final] ).
cnf(i_0_1189,axiom,
c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
cls_Sigma__empty2_0,
[final] ).
cnf(i_0_1190,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_1191,plain,
c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_816,c_0_729]),c_0_729]),
[final] ).
cnf(i_0_1192,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_1193,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_1194,negated_conjecture,
c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_conjecture_0,
[final] ).
cnf(i_0_1195,axiom,
c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
cls_CHAINED_0_01,
[final] ).
cnf(i_0_1196,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ c_in(X5,X4,X3) ),
cls_image__constant_0,
[final] ).
cnf(i_0_1197,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X3,X4)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
cls_acc__induct__rule_2,
[final] ).
cnf(i_0_1198,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X3,X4)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
cls_acc__induct_2,
[final] ).
cnf(i_0_1199,axiom,
hAPP(c_fst(X1,X2),c_Pair(X3,X4,X1,X2)) = X3,
cls_fst__conv_0,
[final] ).
cnf(i_0_1200,axiom,
hAPP(c_snd(X1,X2),c_Pair(X3,X4,X1,X2)) = X4,
cls_snd__conv_0,
[final] ).
cnf(i_0_1201,axiom,
X1 = hAPP(c_fst(X2,X3),c_Pair(X1,X4,X2,X3)),
cls_fst__eqD_0,
[final] ).
cnf(i_0_1202,axiom,
X1 = hAPP(c_snd(X2,X3),c_Pair(X4,X1,X2,X3)),
cls_snd__eqD_0,
[final] ).
cnf(i_0_1203,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_1204,axiom,
( c_Relation_Otrans(c_Relation_Oinv__image(X1,X2,X3,X4),X4)
| ~ c_Relation_Otrans(X1,X3) ),
cls_trans__inv__image_0,
[final] ).
cnf(i_0_1205,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_1206,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_1207,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(rw,[status(thm)],[i_0_817,c_0_729]),
[final] ).
cnf(i_0_1208,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_1209,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_image__constant__conv_1,
[final] ).
cnf(i_0_1210,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_1211,axiom,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
cls_sym__Int__converse_0,
[final] ).
cnf(i_0_1212,plain,
c_Set_Oimage(c_fst(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),tc_prod(X1,X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[i_0_818,c_0_732]),
[final] ).
cnf(i_0_1213,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)
| ~ c_in(X1,X4,X3) ),
cls_Int__insert__left_0,
[final] ).
cnf(i_0_1214,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)
| ~ c_in(X2,X1,X4) ),
cls_Int__insert__right_0,
[final] ).
cnf(i_0_1215,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_1216,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
cls_double__diff_0,
[final] ).
cnf(i_0_1217,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_1218,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_1219,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_1220,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_1221,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_1222,axiom,
c_HOL_Ominus__class_Ominus(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_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
cls_Int__Diff_0,
[final] ).
cnf(i_0_1223,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_1224,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_1225,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_1226,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
cls_empty__is__image_0,
[final] ).
cnf(i_0_1227,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
cls_image__is__empty_0,
[final] ).
cnf(i_0_1228,plain,
c_Set_Oimage(c_fst(X2,X2),c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),tc_prod(X2,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_819,c_0_731]),c_0_732]),
[final] ).
cnf(i_0_1229,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) = X2
| c_in(X1,X2,X3) ),
cls_Diff__insert__absorb_0,
[final] ).
cnf(i_0_1230,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3) ),
cls_insert__Diff__if_1,
[final] ).
cnf(i_0_1231,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_1232,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_1233,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_1234,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_1235,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_1236,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_1237,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_1238,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_1239,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_1240,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_1241,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_1242,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_1243,axiom,
( c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3) ),
cls_UnE_0,
[final] ).
cnf(i_0_1244,axiom,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_image__constant__conv_0,
[final] ).
cnf(i_0_1245,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_1246,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_1247,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X1,X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
cls_subset__insert_0,
[final] ).
cnf(i_0_1248,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X1,X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
cls_subset__insert__iff_1,
[final] ).
cnf(i_0_1249,axiom,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_singletonE_0,
[final] ).
cnf(i_0_1250,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
cls_insert__code_0,
[final] ).
cnf(i_0_1251,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_1252,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X3,tc_bool)),X3) ),
cls_DiffE_1,
[final] ).
cnf(i_0_1253,axiom,
( c_in(c_Arrow__Order__Mirabelle_Obelow(X1,X2,X3),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_below__Lin_0,
[final] ).
cnf(i_0_1254,axiom,
( c_in(c_Arrow__Order__Mirabelle_Oabove(X1,X2,X3),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_above__Lin_0,
[final] ).
cnf(i_0_1255,axiom,
c_Pair(hAPP(c_fst(X1,X2),X3),hAPP(c_snd(X1,X2),X3),X1,X2) = X3,
cls_pair__collapse_0,
[final] ).
cnf(i_0_1256,axiom,
X1 = c_Pair(hAPP(c_fst(X2,X3),X1),hAPP(c_snd(X2,X3),X1),X2,X3),
cls_surjective__pairing_0,
[final] ).
cnf(i_0_1257,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
cls_insert__subset_2,
[final] ).
cnf(i_0_1258,plain,
c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1,X1),
inference(rw,[status(thm)],[i_0_820,c_0_729]),
[final] ).
cnf(i_0_1259,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_1260,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_1261,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_1262,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X1,
cls_Un__Diff__Int_0,
[final] ).
cnf(i_0_1263,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_1264,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_1265,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool)),X3) ),
cls_DiffE_0,
[final] ).
cnf(i_0_1266,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
cls_IntE_0,
[final] ).
cnf(i_0_1267,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
cls_IntE_1,
[final] ).
cnf(i_0_1268,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
cls_IntI_0,
[final] ).
cnf(i_0_1269,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
cls_Int__iff_2,
[final] ).
cnf(i_0_1270,axiom,
c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
cls_Sigma__empty1_0,
[final] ).
cnf(i_0_1271,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
cls_acc_OaccI_1,
[final] ).
cnf(i_0_1272,axiom,
( c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),c_Wellfounded_Oacc(X1,X3),X3) ),
cls_not__acc__down_1,
[final] ).
cnf(i_0_1273,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_1274,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
cls_subset__insert_1,
[final] ).
cnf(i_0_1275,axiom,
( c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
cls_subset__insert__iff_2,
[final] ).
cnf(i_0_1276,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
cls_Diff__partition_0,
[final] ).
cnf(i_0_1277,plain,
c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
inference(rw,[status(thm)],[i_0_821,c_0_729]),
[final] ).
cnf(i_0_1278,plain,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
inference(rw,[status(thm)],[i_0_822,c_0_729]),
[final] ).
cnf(i_0_1279,plain,
c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
inference(rw,[status(thm)],[i_0_823,c_0_729]),
[final] ).
cnf(i_0_1280,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_1281,axiom,
( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
cls_DiffI_0,
[final] ).
cnf(i_0_1282,axiom,
( c_in(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,X2,X4) ),
cls_Diff__iff_2,
[final] ).
cnf(i_0_1283,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X2,X4,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
cls_insert__Diff1_0,
[final] ).
cnf(i_0_1284,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X1,X3,X4),c_Wellfounded_Oacc(X3,X4),X4)
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
cls_acc__induct__rule_0,
[final] ).
cnf(i_0_1285,axiom,
( hBOOL(hAPP(X1,X2))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X1,X3,X4),c_Wellfounded_Oacc(X3,X4),X4)
| ~ c_in(X2,c_Wellfounded_Oacc(X3,X4),X4) ),
cls_acc__induct_0,
[final] ).
cnf(i_0_1286,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_1287,axiom,
( c_in(X1,X2,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
cls_insert__subset_0,
[final] ).
cnf(i_0_1288,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_1289,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_1290,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_1291,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_1292,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_1293,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_1294,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_1295,axiom,
( ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_disjoint__iff__not__equal_0,
[final] ).
cnf(i_0_1296,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_1297,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_1298,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_1299,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_1300,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_1301,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_1302,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_1303,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_1304,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_1305,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_1306,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X1,X2,X3),X1,X3)
| ~ c_in(X2,c_Relation_OId__on(X1,X3),tc_prod(X3,X3)) ),
cls_Id__onE_0,
[final] ).
cnf(i_0_1307,axiom,
c_Set_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_1308,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_1309,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
cls_empty__is__image_1,
[final] ).
cnf(i_0_1310,plain,
c_Set_Oimage(c_fst(X2,X2),c_Relation_OId__on(X1,X2),tc_prod(X2,X2),X2) = X1,
inference(rw,[status(thm)],[i_0_824,c_0_732]),
[final] ).
cnf(i_0_1311,axiom,
( c_in(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_mktop__Lin_0,
[final] ).
cnf(i_0_1312,axiom,
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
cls_mkbot__Lin_0,
[final] ).
cnf(i_0_1313,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_1314,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_1315,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_1316,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_1317,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))
| c_in(X1,X4,X3) ),
cls_Int__insert__left_1,
[final] ).
cnf(i_0_1318,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))
| c_in(X2,X1,X4) ),
cls_Int__insert__right_1,
[final] ).
cnf(i_0_1319,axiom,
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Otrans(X2,X3)
| ~ c_Relation_Otrans(X1,X3) ),
cls_trans__Int_0,
[final] ).
cnf(i_0_1320,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_1321,axiom,
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X2,X3)
| ~ c_Relation_Osym(X1,X3) ),
cls_sym__Int_0,
[final] ).
cnf(i_0_1322,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_1323,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_1324,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_1325,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_1326,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_1327,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_1328,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_1329,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_1330,axiom,
( c_in(X1,X2,X3)
| X1 = X4
| ~ c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
cls_insertE_0,
[final] ).
cnf(i_0_1331,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_1332,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_1333,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
cls_Un__Diff__cancel2_0,
[final] ).
cnf(i_0_1334,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),
cls_Diff__idemp_0,
[final] ).
cnf(i_0_1335,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_1336,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ominus__class_Ominus(X2,X1,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__Diff__cancel_0,
[final] ).
cnf(i_0_1337,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_1338,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_1339,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X2,X4) ),
cls_UnCI_1,
[final] ).
cnf(i_0_1340,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X1,X3,X4) ),
cls_UnCI_0,
[final] ).
cnf(i_0_1341,axiom,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X1,X3) ),
cls_wf__Int1_0,
[final] ).
cnf(i_0_1342,axiom,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
cls_wf__Int2_0,
[final] ).
cnf(i_0_1343,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_insert__code_2,
[final] ).
cnf(i_0_1344,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
cls_less__by__empty_0,
[final] ).
cnf(i_0_1345,axiom,
( c_in(X1,X4,X3)
| c_in(X1,X2,X3)
| X2 = X4
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
cls_insert__ident_0,
[final] ).
cnf(i_0_1346,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinduct__1(X1,X3)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a) ),
cls_acc_Oinduct_2,
[final] ).
cnf(i_0_1347,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,v_sko__Wellfounded__Xacc__Xinducts__1(X1,X3)))
| ~ c_in(X2,c_Wellfounded_Oacc(X3,t_a),t_a) ),
cls_acc_Oinducts_2,
[final] ).
cnf(i_0_1348,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X1,X2,X3),X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
cls_wfE__min_0,
[final] ).
cnf(i_0_1349,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X1,X2,X3),X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
cls_wf__eq__minimal_0,
[final] ).
cnf(i_0_1350,axiom,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
cls_singleton__iff_1,
[final] ).
cnf(i_0_1351,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
cls_set__mp_0,
[final] ).
cnf(i_0_1352,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
cls_subsetD_0,
[final] ).
cnf(i_0_1353,axiom,
( c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X4,X3) ),
cls_set__rev__mp_0,
[final] ).
cnf(i_0_1354,axiom,
( c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
cls_subset__iff_0,
[final] ).
cnf(i_0_1355,axiom,
c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
cls_refl__on__empty_0,
[final] ).
cnf(i_0_1356,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_Diff__disjoint_0,
[final] ).
cnf(i_0_1357,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_1358,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_1359,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_1360,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_1361,axiom,
( X3 = X4
| hAPP(c_snd(X1,X2),X3) != hAPP(c_snd(X1,X2),X4)
| hAPP(c_fst(X1,X2),X3) != hAPP(c_fst(X1,X2),X4) ),
cls_prod__eqI_0,
[final] ).
cnf(i_0_1362,axiom,
( X3 = X4
| hAPP(c_snd(X1,X2),X3) != hAPP(c_snd(X1,X2),X4)
| hAPP(c_fst(X1,X2),X3) != hAPP(c_fst(X1,X2),X4) ),
cls_Pair__fst__snd__eq_0,
[final] ).
cnf(i_0_1363,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_1364,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_1365,axiom,
( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| ~ c_in(X1,X3,X4) ),
cls_insertCI_0,
[final] ).
cnf(i_0_1366,axiom,
( c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| ~ c_in(X1,X3,X4) ),
cls_insert__iff_2,
[final] ).
cnf(i_0_1367,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_1368,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_1369,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1,
[final] ).
cnf(i_0_1370,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_Diff__triv_0,
[final] ).
cnf(i_0_1371,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_1372,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_1373,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_1374,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_1375,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_1376,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_1377,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
cls_r__into__rtrancl_0,
[final] ).
cnf(i_0_1378,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_1379,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
cls_Diff__subset_0,
[final] ).
cnf(i_0_1380,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_1381,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_1382,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_1383,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_1384,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_1385,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_1386,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_1387,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_1388,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_1389,axiom,
( ~ hBOOL(hAPP(X1,X2))
| ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
cls_bex__empty_0,
[final] ).
cnf(i_0_1390,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0,
[final] ).
cnf(i_0_1391,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_1392,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_antisym__converse_0,
[final] ).
cnf(i_0_1393,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_trans__converse_0,
[final] ).
cnf(i_0_1394,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_sym__converse_0,
[final] ).
cnf(i_0_1395,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
cls_acyclic__converse_0,
[final] ).
cnf(i_0_1396,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_1397,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_1398,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_1399,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_1400,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_1401,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_1402,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_1403,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_1404,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
cls_ball__empty_0,
[final] ).
cnf(i_0_1405,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_1406,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_1407,axiom,
( c_Order__Relation_Ostrict__linear__order__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Oirrefl(X2,X3)
| ~ c_Relation_Otrans(X2,X3) ),
cls_strict__linear__order__on__def_3,
[final] ).
cnf(i_0_1408,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
cls_subset__insertI_0,
[final] ).
cnf(i_0_1409,axiom,
( c_in(X1,X2,X3)
| 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_1410,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
cls_acc__wfI_0,
[final] ).
cnf(i_0_1411,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
cls_wf__acc__iff_1,
[final] ).
cnf(i_0_1412,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_1413,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_1414,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_1415,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_1416,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_1417,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_1418,axiom,
c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
cls_antisym__empty_0,
[final] ).
cnf(i_0_1419,axiom,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
cls_wf__empty_0,
[final] ).
cnf(i_0_1420,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_1421,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_1422,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_1423,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_1424,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_1425,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_1426,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_1427,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_1428,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_1429,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_1430,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
cls_emptyE_0,
[final] ).
cnf(i_0_1431,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
cls_empty__iff_0,
[final] ).
cnf(i_0_1432,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
cls_ex__in__conv_0,
[final] ).
cnf(i_0_1433,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(X1,X2,X3),X3,X2) = X1,
cls_converse__converse_0,
[final] ).
cnf(i_0_1434,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
cls_insertCI_1,
[final] ).
cnf(i_0_1435,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
cls_insertI1_0,
[final] ).
cnf(i_0_1436,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
cls_insert__iff_1,
[final] ).
cnf(i_0_1437,axiom,
c_HOL_Ominus__class_Ominus(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_empty__Diff_0,
[final] ).
cnf(i_0_1438,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_1439,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_1440,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_1441,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_1442,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_1443,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_1444,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_1445,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_1446,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_1447,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_1448,axiom,
c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
cls_Id__on__empty_0,
[final] ).
cnf(i_0_1449,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
cls_complete__Lin_0,
[final] ).
cnf(i_0_1450,axiom,
( c_Wellfounded_OwfP(c_FunDef_Oin__rel(X1,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__in__rel_0,
[final] ).
cnf(i_0_1451,axiom,
( c_Relation_Oantisym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
cls_antisym__converse_1,
[final] ).
cnf(i_0_1452,axiom,
( c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Otrans(X1,X2) ),
cls_trans__converse_1,
[final] ).
cnf(i_0_1453,axiom,
( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__converse_1,
[final] ).
cnf(i_0_1454,axiom,
( c_Wellfounded_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
cls_acyclic__converse_1,
[final] ).
cnf(i_0_1455,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
cls_insert__absorb_0,
[final] ).
cnf(i_0_1456,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Order__Relation_Ostrict__linear__order__on(X1,X2,X3) ),
cls_strict__linear__order__on__def_2,
[final] ).
cnf(i_0_1457,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
cls_equiv_Orefl__on_0,
[final] ).
cnf(i_0_1458,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_1459,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_1460,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Diff__empty_0,
[final] ).
cnf(i_0_1461,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_1462,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_1463,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_1464,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0,
[final] ).
cnf(i_0_1465,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_1466,axiom,
( hBOOL(hAPP(X1,X2))
| ~ c_in(X2,X1,X3) ),
cls_mem__def_0,
[final] ).
cnf(i_0_1467,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_1468,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_1469,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_1470,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_1471,axiom,
c_in(v_Lba____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
cls_CHAINED_0,
[final] ).
cnf(i_0_1472,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_1473,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_1474,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_1475,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__cancel_0,
[final] ).
cnf(i_0_1476,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_Wellfounded_Owf(X2,X3) ),
cls_acc__wfD_0,
[final] ).
cnf(i_0_1477,axiom,
( c_in(X1,X2,X3)
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1,
[final] ).
cnf(i_0_1478,axiom,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
cls_sym__conv__converse__eq_1,
[final] ).
cnf(i_0_1479,axiom,
( c_Relation_Oirrefl(X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X1,X2) ),
cls_strict__linear__order__on__def_1,
[final] ).
cnf(i_0_1480,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X1,X2) ),
cls_strict__linear__order__on__def_0,
[final] ).
cnf(i_0_1481,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
cls_equiv_Otrans_0,
[final] ).
cnf(i_0_1482,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Equiv__Relations_Oequiv(X3,X1,X2) ),
cls_equiv_Osym_0,
[final] ).
cnf(i_0_1483,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_1484,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_1485,axiom,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
cls_single__valued__Id__on_0,
[final] ).
cnf(i_0_1486,axiom,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
cls_refl__on__Id__on_0,
[final] ).
cnf(i_0_1487,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
cls_Un__absorb_0,
[final] ).
cnf(i_0_1488,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
cls_Int__absorb_0,
[final] ).
cnf(i_0_1489,axiom,
( c_Relation_Oconverse(X1,X2,X2) = X1
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__conv__converse__eq_0,
[final] ).
cnf(i_0_1490,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
cls_subset__refl_0,
[final] ).
cnf(i_0_1491,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
cls_equalityE_0,
[final] ).
cnf(i_0_1492,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_1493,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_1494,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_1495,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_1496,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0,
[final] ).
cnf(i_0_1497,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_1498,axiom,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
cls_sym__rtrancl_0,
[final] ).
cnf(i_0_1499,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,X1) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0,
[final] ).
cnf(i_0_1500,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,X1) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0,
[final] ).
cnf(i_0_1501,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_1502,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_1503,axiom,
c_fequal(X1,X1,X2),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_1504,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_1505,axiom,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
cls_antisym__Id__on_0,
[final] ).
cnf(i_0_1506,axiom,
c_Relation_Otrans(c_Relation_OId__on(X1,X2),X2),
cls_trans__Id__on_0,
[final] ).
cnf(i_0_1507,axiom,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X1,X2),X2),
cls_trans__rtrancl_0,
[final] ).
cnf(i_0_1508,axiom,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
cls_sym__Id__on_0,
[final] ).
cnf(i_0_1509,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
clsarity_fun__Orderings_Opreorder,
[final] ).
cnf(i_0_1510,axiom,
( class_HOL_Oord(tc_fun(X1,X2))
| ~ class_HOL_Oord(X2) ),
clsarity_fun__HOL_Oord,
[final] ).
cnf(i_0_1511,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder,
[final] ).
cnf(i_0_1512,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
clsarity_fun__Lattices_Obounded__lattice,
[final] ).
cnf(i_0_1513,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_1514,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olattice,
[final] ).
cnf(i_0_1515,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_1516,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Odistrib__lattice(X2) ),
clsarity_fun__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_1517,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
clsarity_fun__Orderings_Obot,
[final] ).
cnf(i_0_1518,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
cls_wf__acyclic_0,
[final] ).
cnf(i_0_1519,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder,
[final] ).
cnf(i_0_1520,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord,
[final] ).
cnf(i_0_1521,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder,
[final] ).
cnf(i_0_1522,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice,
[final] ).
cnf(i_0_1523,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_1524,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice,
[final] ).
cnf(i_0_1525,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_1526,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
clsarity_bool__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_1527,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot,
[final] ).
cnf(i_0_1528,axiom,
X1 = X1 ).
cnf(i_0_1529,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1530,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1531,axiom,
( X1 != X2
| c_Pair(X1,X3,X4,X5) = c_Pair(X2,X3,X4,X5) ) ).
cnf(i_0_1532,axiom,
( X1 != X2
| c_Pair(X3,X1,X4,X5) = c_Pair(X3,X2,X4,X5) ) ).
cnf(i_0_1533,axiom,
( X1 != X2
| c_Pair(X3,X4,X1,X5) = c_Pair(X3,X4,X2,X5) ) ).
cnf(i_0_1534,axiom,
( X1 != X2
| c_Pair(X3,X4,X5,X1) = c_Pair(X3,X4,X5,X2) ) ).
cnf(i_0_1535,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1536,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1537,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_1538,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_1539,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_1540,axiom,
( X1 != X2
| c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).
cnf(i_0_1541,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).
cnf(i_0_1542,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).
cnf(i_0_1543,axiom,
( X1 != X2
| c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).
cnf(i_0_1544,axiom,
( X1 != X2
| c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).
cnf(i_0_1545,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).
cnf(i_0_1546,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).
cnf(i_0_1547,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1548,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1549,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1550,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1551,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_1552,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_1553,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_1554,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_1555,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1556,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1557,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1558,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1559,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1560,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1561,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1562,axiom,
( X1 != X2
| c_Relation_Orel__comp(X1,X3,X4,X5,X6) = c_Relation_Orel__comp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1563,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X1,X4,X5,X6) = c_Relation_Orel__comp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1564,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X1,X5,X6) = c_Relation_Orel__comp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1565,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X1,X6) = c_Relation_Orel__comp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1566,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X6,X1) = c_Relation_Orel__comp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1567,axiom,
( X1 != X2
| c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).
cnf(i_0_1568,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).
cnf(i_0_1569,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).
cnf(i_0_1570,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).
cnf(i_0_1571,axiom,
( X1 != X2
| c_Equiv__Relations_Oquotient(X1,X3,X4) = c_Equiv__Relations_Oquotient(X2,X3,X4) ) ).
cnf(i_0_1572,axiom,
( X1 != X2
| c_Equiv__Relations_Oquotient(X3,X1,X4) = c_Equiv__Relations_Oquotient(X3,X2,X4) ) ).
cnf(i_0_1573,axiom,
( X1 != X2
| c_Equiv__Relations_Oquotient(X3,X4,X1) = c_Equiv__Relations_Oquotient(X3,X4,X2) ) ).
cnf(i_0_1574,axiom,
( X1 != X2
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1575,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X1,X4,X5,X6) = c_Recdef_Ocut(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1576,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X1,X5,X6) = c_Recdef_Ocut(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1577,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X1,X6) = c_Recdef_Ocut(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1578,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X6,X1) = c_Recdef_Ocut(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1579,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1580,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1581,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1582,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1583,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).
cnf(i_0_1584,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).
cnf(i_0_1585,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).
cnf(i_0_1586,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_1587,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_1588,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_1589,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_1590,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_1591,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_1592,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X1,X3)
| c_Relation_Otrans(X2,X3) ) ).
cnf(i_0_1593,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X3,X1)
| c_Relation_Otrans(X3,X2) ) ).
cnf(i_0_1594,axiom,
( X1 != X2
| ~ c_Relation_Osym(X1,X3)
| c_Relation_Osym(X2,X3) ) ).
cnf(i_0_1595,axiom,
( X1 != X2
| ~ c_Relation_Osym(X3,X1)
| c_Relation_Osym(X3,X2) ) ).
cnf(i_0_1596,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X1,X3)
| c_Relation_Oantisym(X2,X3) ) ).
cnf(i_0_1597,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X3,X1)
| c_Relation_Oantisym(X3,X2) ) ).
cnf(i_0_1598,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_1599,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_1600,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_1601,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1602,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1603,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_1604,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_1605,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_1606,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_1607,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_1608,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_1609,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_1610,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_1611,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1612,axiom,
( X1 != X2
| ~ class_HOL_Oord(X1)
| class_HOL_Oord(X2) ) ).
cnf(i_0_1613,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1614,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1615,axiom,
( X1 != X2
| ~ c_Order__Relation_Ostrict__linear__order__on(X1,X3,X4)
| c_Order__Relation_Ostrict__linear__order__on(X2,X3,X4) ) ).
cnf(i_0_1616,axiom,
( X1 != X2
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X1,X4)
| c_Order__Relation_Ostrict__linear__order__on(X3,X2,X4) ) ).
cnf(i_0_1617,axiom,
( X1 != X2
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X4,X1)
| c_Order__Relation_Ostrict__linear__order__on(X3,X4,X2) ) ).
cnf(i_0_1618,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1619,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_1620,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_1621,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1622,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_1623,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1624,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1625,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1626,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1627,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1628,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1629,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1630,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_1631,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_1632,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_1633,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_1634,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_1635,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_1636,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_1637,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_1638,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_1639,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_1640,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_1641,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_1642,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_1643,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1644,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_1645,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_1646,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_1647,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_1648,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_1528_001,axiom,
X1 = X1 ).
cnf(i_0_1529_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1530_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1531_004,axiom,
( X1 != X2
| c_Pair(X1,X3,X4,X5) = c_Pair(X2,X3,X4,X5) ) ).
cnf(i_0_1532_005,axiom,
( X1 != X2
| c_Pair(X3,X1,X4,X5) = c_Pair(X3,X2,X4,X5) ) ).
cnf(i_0_1533_006,axiom,
( X1 != X2
| c_Pair(X3,X4,X1,X5) = c_Pair(X3,X4,X2,X5) ) ).
cnf(i_0_1534_007,axiom,
( X1 != X2
| c_Pair(X3,X4,X5,X1) = c_Pair(X3,X4,X5,X2) ) ).
cnf(i_0_1535_008,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).
cnf(i_0_1536_009,axiom,
( X1 != X2
| c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).
cnf(i_0_1537_010,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4) ) ).
cnf(i_0_1538_011,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,X4) ) ).
cnf(i_0_1539_012,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X1) = c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X2) ) ).
cnf(i_0_1540_013,axiom,
( X1 != X2
| c_Relation_Oconverse(X1,X3,X4) = c_Relation_Oconverse(X2,X3,X4) ) ).
cnf(i_0_1541_014,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X1,X4) = c_Relation_Oconverse(X3,X2,X4) ) ).
cnf(i_0_1542_015,axiom,
( X1 != X2
| c_Relation_Oconverse(X3,X4,X1) = c_Relation_Oconverse(X3,X4,X2) ) ).
cnf(i_0_1543_016,axiom,
( X1 != X2
| c_Relation_OImage(X1,X3,X4,X5) = c_Relation_OImage(X2,X3,X4,X5) ) ).
cnf(i_0_1544_017,axiom,
( X1 != X2
| c_Relation_OImage(X3,X1,X4,X5) = c_Relation_OImage(X3,X2,X4,X5) ) ).
cnf(i_0_1545_018,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X1,X5) = c_Relation_OImage(X3,X4,X2,X5) ) ).
cnf(i_0_1546_019,axiom,
( X1 != X2
| c_Relation_OImage(X3,X4,X5,X1) = c_Relation_OImage(X3,X4,X5,X2) ) ).
cnf(i_0_1547_020,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1548_021,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1549_022,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1550_023,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1551_024,axiom,
( X1 != X2
| c_Product__Type_OSigma(X1,X3,X4,X5) = c_Product__Type_OSigma(X2,X3,X4,X5) ) ).
cnf(i_0_1552_025,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X1,X4,X5) = c_Product__Type_OSigma(X3,X2,X4,X5) ) ).
cnf(i_0_1553_026,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X1,X5) = c_Product__Type_OSigma(X3,X4,X2,X5) ) ).
cnf(i_0_1554_027,axiom,
( X1 != X2
| c_Product__Type_OSigma(X3,X4,X5,X1) = c_Product__Type_OSigma(X3,X4,X5,X2) ) ).
cnf(i_0_1555_028,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1556_029,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1557_030,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1558_031,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1559_032,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1560_033,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1561_034,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1562_035,axiom,
( X1 != X2
| c_Relation_Orel__comp(X1,X3,X4,X5,X6) = c_Relation_Orel__comp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1563_036,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X1,X4,X5,X6) = c_Relation_Orel__comp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1564_037,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X1,X5,X6) = c_Relation_Orel__comp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1565_038,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X1,X6) = c_Relation_Orel__comp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1566_039,axiom,
( X1 != X2
| c_Relation_Orel__comp(X3,X4,X5,X6,X1) = c_Relation_Orel__comp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1567_040,axiom,
( X1 != X2
| c_Relation_Oinv__image(X1,X3,X4,X5) = c_Relation_Oinv__image(X2,X3,X4,X5) ) ).
cnf(i_0_1568_041,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X1,X4,X5) = c_Relation_Oinv__image(X3,X2,X4,X5) ) ).
cnf(i_0_1569_042,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X1,X5) = c_Relation_Oinv__image(X3,X4,X2,X5) ) ).
cnf(i_0_1570_043,axiom,
( X1 != X2
| c_Relation_Oinv__image(X3,X4,X5,X1) = c_Relation_Oinv__image(X3,X4,X5,X2) ) ).
cnf(i_0_1571_044,axiom,
( X1 != X2
| c_Equiv__Relations_Oquotient(X1,X3,X4) = c_Equiv__Relations_Oquotient(X2,X3,X4) ) ).
cnf(i_0_1572_045,axiom,
( X1 != X2
| c_Equiv__Relations_Oquotient(X3,X1,X4) = c_Equiv__Relations_Oquotient(X3,X2,X4) ) ).
cnf(i_0_1573_046,axiom,
( X1 != X2
| c_Equiv__Relations_Oquotient(X3,X4,X1) = c_Equiv__Relations_Oquotient(X3,X4,X2) ) ).
cnf(i_0_1574_047,axiom,
( X1 != X2
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1575_048,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X1,X4,X5,X6) = c_Recdef_Ocut(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1576_049,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X1,X5,X6) = c_Recdef_Ocut(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1577_050,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X1,X6) = c_Recdef_Ocut(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1578_051,axiom,
( X1 != X2
| c_Recdef_Ocut(X3,X4,X5,X6,X1) = c_Recdef_Ocut(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1579_052,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1580_053,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1581_054,axiom,
( X1 != X2
| c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).
cnf(i_0_1582_055,axiom,
( X1 != X2
| c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).
cnf(i_0_1583_056,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4) ) ).
cnf(i_0_1584_057,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X4) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) ) ).
cnf(i_0_1585_058,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X1) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X2) ) ).
cnf(i_0_1586_059,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_1587_060,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_1588_061,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_1589_062,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X1,X3,X4)
| c_Relation_Orefl__on(X2,X3,X4) ) ).
cnf(i_0_1590_063,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X1,X4)
| c_Relation_Orefl__on(X3,X2,X4) ) ).
cnf(i_0_1591_064,axiom,
( X1 != X2
| ~ c_Relation_Orefl__on(X3,X4,X1)
| c_Relation_Orefl__on(X3,X4,X2) ) ).
cnf(i_0_1592_065,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X1,X3)
| c_Relation_Otrans(X2,X3) ) ).
cnf(i_0_1593_066,axiom,
( X1 != X2
| ~ c_Relation_Otrans(X3,X1)
| c_Relation_Otrans(X3,X2) ) ).
cnf(i_0_1594_067,axiom,
( X1 != X2
| ~ c_Relation_Osym(X1,X3)
| c_Relation_Osym(X2,X3) ) ).
cnf(i_0_1595_068,axiom,
( X1 != X2
| ~ c_Relation_Osym(X3,X1)
| c_Relation_Osym(X3,X2) ) ).
cnf(i_0_1596_069,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X1,X3)
| c_Relation_Oantisym(X2,X3) ) ).
cnf(i_0_1597_070,axiom,
( X1 != X2
| ~ c_Relation_Oantisym(X3,X1)
| c_Relation_Oantisym(X3,X2) ) ).
cnf(i_0_1598_071,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X1,X3,X4)
| c_Relation_Ototal__on(X2,X3,X4) ) ).
cnf(i_0_1599_072,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X1,X4)
| c_Relation_Ototal__on(X3,X2,X4) ) ).
cnf(i_0_1600_073,axiom,
( X1 != X2
| ~ c_Relation_Ototal__on(X3,X4,X1)
| c_Relation_Ototal__on(X3,X4,X2) ) ).
cnf(i_0_1601_074,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1602_075,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1603_076,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X1,X3)
| c_Relation_Oirrefl(X2,X3) ) ).
cnf(i_0_1604_077,axiom,
( X1 != X2
| ~ c_Relation_Oirrefl(X3,X1)
| c_Relation_Oirrefl(X3,X2) ) ).
cnf(i_0_1605_078,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_1606_079,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_1607_080,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_1608_081,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(X2,X3) ) ).
cnf(i_0_1609_082,axiom,
( X1 != X2
| ~ c_Wellfounded_Owf(X3,X1)
| c_Wellfounded_Owf(X3,X2) ) ).
cnf(i_0_1610_083,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_1611_084,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1612_085,axiom,
( X1 != X2
| ~ class_HOL_Oord(X1)
| class_HOL_Oord(X2) ) ).
cnf(i_0_1613_086,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1614_087,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1615_088,axiom,
( X1 != X2
| ~ c_Order__Relation_Ostrict__linear__order__on(X1,X3,X4)
| c_Order__Relation_Ostrict__linear__order__on(X2,X3,X4) ) ).
cnf(i_0_1616_089,axiom,
( X1 != X2
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X1,X4)
| c_Order__Relation_Ostrict__linear__order__on(X3,X2,X4) ) ).
cnf(i_0_1617_090,axiom,
( X1 != X2
| ~ c_Order__Relation_Ostrict__linear__order__on(X3,X4,X1)
| c_Order__Relation_Ostrict__linear__order__on(X3,X4,X2) ) ).
cnf(i_0_1618_091,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1619_092,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X1,X3)
| c_Wellfounded_OwfP(X2,X3) ) ).
cnf(i_0_1620_093,axiom,
( X1 != X2
| ~ c_Wellfounded_OwfP(X3,X1)
| c_Wellfounded_OwfP(X3,X2) ) ).
cnf(i_0_1621_094,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1622_095,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_1623_096,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1624_097,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1625_098,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1626_099,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1627_100,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1628_101,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1629_102,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1630_103,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_1631_104,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_1632_105,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_1633_106,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_1634_107,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_1635_108,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_1636_109,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
| c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).
cnf(i_0_1637_110,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
| c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).
cnf(i_0_1638_111,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
| c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).
cnf(i_0_1639_112,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
| c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).
cnf(i_0_1640_113,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
| c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).
cnf(i_0_1641_114,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
| c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).
cnf(i_0_1642_115,axiom,
( X1 != X2
| ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
| c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).
cnf(i_0_1643_116,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1644_117,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X1,X3)
| c_Wellfounded_Oacyclic(X2,X3) ) ).
cnf(i_0_1645_118,axiom,
( X1 != X2
| ~ c_Wellfounded_Oacyclic(X3,X1)
| c_Wellfounded_Oacyclic(X3,X2) ) ).
cnf(i_0_1646_119,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X1,X3,X4)
| c_Relation_Osingle__valued(X2,X3,X4) ) ).
cnf(i_0_1647_120,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X1,X4)
| c_Relation_Osingle__valued(X3,X2,X4) ) ).
cnf(i_0_1648_121,axiom,
( X1 != X2
| ~ c_Relation_Osingle__valued(X3,X4,X1)
| c_Relation_Osingle__valued(X3,X4,X2) ) ).
cnf(i_0_1649,plain,
c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X1,X2,X3,X4,X5),
inference(equality_inference,[],[827]) ).
cnf(i_0_1650,plain,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| hAPP(X5,X1) = hAPP(X5,X1) ),
inference(equality_inference,[],[880]) ).
cnf(i_0_1651,plain,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3)) ),
inference(equality_inference,[],[964]) ).
cnf(i_0_1652,plain,
( ~ c_in(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X2,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X1,X3,X3),X4,tc_prod(X3,X3)) ),
inference(equality_inference,[],[1019]) ).
cnf(i_0_1653,plain,
( X1 = X1
| ~ c_in(X2,X3,X4) ),
inference(equality_inference,[],[1059]) ).
cnf(i_0_1654,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1132]) ).
cnf(i_0_1655,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1133]) ).
cnf(i_0_1656,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1134]) ).
cnf(i_0_1657,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1135]) ).
cnf(i_0_1658,plain,
X1 = X1,
inference(equality_inference,[],[1141]) ).
cnf(i_0_1659,plain,
X1 = X1,
inference(equality_inference,[],[1142]) ).
cnf(i_0_1660,plain,
X1 = X1,
inference(equality_inference,[],[1296]) ).
cnf(i_0_1661,plain,
( X1 = X1
| c_in(X2,X1,X3)
| c_in(X2,X1,X3) ),
inference(equality_inference,[],[1345]) ).
cnf(i_0_1662,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[1416]) ).
cnf(i_0_1663,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[1417]) ).
cnf(i_0_1664,plain,
$false,
inference(scs_inference,[],[i_0_1194,i_0_1195,i_0_1471,i_0_975]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SCT076-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.26 % Computer : n012.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 5 01:54:46 EDT 2026
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % start to proof: theBenchmark
% 0.73/1.53 % Version : CSE_E---1.7
% 0.73/1.53 % Problem : theBenchmark.p
% 0.73/1.53 % SZS status Unsatisfiable for theBenchmark.p
% 0.73/1.53 % SZS output start CNFRefutation
% See solution above
% 0.73/1.56 % Total time : 1.264s
%------------------------------------------------------------------------------