%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT120+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:02 PM UTC 2026
% Result : Theorem 186.39s 141.44s
% Output : CNFRefutation 186.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 27 unt; 0 def)
% Number of atoms : 196 ( 22 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 200 ( 79 ~; 79 |; 23 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-5 aty)
% Number of functors : 24 ( 24 usr; 6 con; 0-4 aty)
% Number of variables : 177 ( 21 sgn 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_insert__code,axiom,
! [X4,X7,X17,X5] :
( hBOOL(hAPP(c_Set_Oinsert(X5,X17,X7),X4))
<=> ( X17 = X4
| hBOOL(hAPP(X7,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_insert__absorb,axiom,
! [X7,X13,X5] :
( c_member(X5,X13,X7)
=> c_Set_Oinsert(X5,X13,X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_irrefl__def,axiom,
! [X6,X5] :
( c_Relation_Oirrefl(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_mem__def,axiom,
! [X7,X4,X5] :
( c_member(X5,X4,X7)
<=> hBOOL(hAPP(X7,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(conj_0,hypothesis,
! [X3] :
( ! [X8] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3,X8))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3,X8))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X3,X8)) )
=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(conj_2,hypothesis,
! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(conj_3,hypothesis,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(fact_trancl__id,axiom,
! [X6,X5] :
( c_Relation_Otrans(X5,X6)
=> c_Transitive__Closure_Otrancl(X5,X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).
fof(fact_r__r__into__trancl,axiom,
! [X11,X19,X12,X13,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X12),X19)
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X12,X11),X19)
=> c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X11),c_Transitive__Closure_Otrancl(X5,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(conj_1,hypothesis,
! [X78] :
( ! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X78,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X78,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X78,X3)) )
=> ! [X38,X39] :
( X38 != X39
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X38,X39),hAPP(X78,v_i))
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X38,X39),v_F(X78)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_top1I,axiom,
! [X4,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_acyclic__def,axiom,
! [X6,X5] :
( c_Wellfounded_Oacyclic(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(fact_total__on__def,axiom,
! [X6,X7,X5] :
( c_Relation_Ototal__on(X5,X7,X6)
<=> ! [X3] :
( c_member(X5,X3,X7)
=> ! [X8] :
( c_member(X5,X8,X7)
=> ( X3 != X8
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X8),X6)
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X3),X6) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(fact_in__rel__def,axiom,
! [X17,X4,X19,X18,X5] :
( c_FunDef_Oin__rel(X5,X18,X19,X4,X17)
<=> c_member(tc_prod(X5,X18),c_Product__Type_OPair(X5,X18,X4,X17),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(conj_4,conjecture,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(c_0_15,plain,
! [X2797,X2798,X2799,X2800] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2800,X2799,X2798),X2797))
| X2799 = X2797
| hBOOL(hAPP(X2798,X2797)) )
& ( X2799 != X2797
| hBOOL(hAPP(c_Set_Oinsert(X2800,X2799,X2798),X2797)) )
& ( ~ hBOOL(hAPP(X2798,X2797))
| hBOOL(hAPP(c_Set_Oinsert(X2800,X2799,X2798),X2797)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
cnf(c_0_16,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X2786,X2787,X2788] :
( ~ c_member(X2788,X2787,X2786)
| c_Set_Oinsert(X2788,X2787,X2786) = X2786 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_18,plain,
! [X6,X5] :
( c_Relation_Oirrefl(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(c_0_19,plain,
! [X1993,X1994,X1995] :
( ( ~ c_member(X1995,X1994,X1993)
| hBOOL(hAPP(X1993,X1994)) )
& ( ~ hBOOL(hAPP(X1993,X1994))
| c_member(X1995,X1994,X1993) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_20,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,hypothesis,
! [X3872] :
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(X3872))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3872,esk87_1(X3872)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3872,esk88_1(X3872)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X3872,esk89_1(X3872))) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(X3872))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3872,esk87_1(X3872)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3872,esk88_1(X3872)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X3872,esk89_1(X3872))) )
& ( c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(X3872))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3872,esk87_1(X3872)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3872,esk88_1(X3872)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X3872,esk89_1(X3872))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])])]) ).
fof(c_0_23,hypothesis,
! [X3882] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3882))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3882))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3882)) ),
inference(variable_rename,[status(thm)],[conj_2]) ).
fof(c_0_24,plain,
! [X1925,X1926,X1927,X1928,X1929] :
( ( ~ c_Relation_Oirrefl(X1926,X1925)
| ~ c_member(tc_prod(X1926,X1926),c_Product__Type_OPair(X1926,X1926,X1927,X1927),X1925) )
& ( c_member(tc_prod(X1929,X1929),c_Product__Type_OPair(X1929,X1929,esk2_2(X1928,X1929),esk2_2(X1928,X1929)),X1928)
| c_Relation_Oirrefl(X1929,X1928) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
cnf(c_0_25,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_member(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(split_conjunct,[status(thm)],[conj_3]) ).
fof(c_0_28,plain,
! [X2542,X2543] :
( ~ c_Relation_Otrans(X2543,X2542)
| c_Transitive__Closure_Otrancl(X2543,X2542) = X2542 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).
cnf(c_0_29,hypothesis,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(X1))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk87_1(X1)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk88_1(X1)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X1,esk89_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
fof(c_0_35,plain,
! [X2546,X2547,X2548,X2549,X2550] :
( ~ c_member(tc_prod(X2550,X2550),c_Product__Type_OPair(X2550,X2550,X2549,X2548),X2547)
| ~ c_member(tc_prod(X2550,X2550),c_Product__Type_OPair(X2550,X2550,X2548,X2546),X2547)
| c_member(tc_prod(X2550,X2550),c_Product__Type_OPair(X2550,X2550,X2549,X2546),c_Transitive__Closure_Otrancl(X2550,X2547)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
cnf(c_0_36,hypothesis,
hBOOL(hAPP(v_F(v_P),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X2
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_39,plain,
~ c_Relation_Oirrefl(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X5),c_Transitive__Closure_Otrancl(X1,X4))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X4)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_42,hypothesis,
c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(X1))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk87_1(X1)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk88_1(X1)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X1,esk89_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_44,hypothesis,
! [X3876,X3880,X3881] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3876,esk90_1(X3876)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3876,esk91_1(X3876)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X3876,esk92_1(X3876)))
| X3880 = X3881
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3880,X3881),hAPP(X3876,v_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3880,X3881),v_F(X3876)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])])])]) ).
fof(c_0_45,plain,
! [X1956,X1957] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1957,tc_HOL_Obool)),X1956)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(c_0_46,plain,
! [X6,X5] :
( c_Wellfounded_Oacyclic(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
cnf(c_0_47,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_48,hypothesis,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_b),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_a),v_F(v_P)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_49,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_50,hypothesis,
( X2 = X3
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_F(X1))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk90_1(X1)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk91_1(X1)))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(X1,esk92_1(X1)))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),hAPP(X1,v_i)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_51,plain,
! [X1931,X1932,X1933,X1934,X1935,X1936,X1937,X1938] :
( ( ~ c_Relation_Ototal__on(X1933,X1932,X1931)
| ~ c_member(X1933,X1934,X1932)
| ~ c_member(X1933,X1935,X1932)
| X1934 = X1935
| c_member(tc_prod(X1933,X1933),c_Product__Type_OPair(X1933,X1933,X1934,X1935),X1931)
| c_member(tc_prod(X1933,X1933),c_Product__Type_OPair(X1933,X1933,X1935,X1934),X1931) )
& ( c_member(X1938,esk3_3(X1936,X1937,X1938),X1937)
| c_Relation_Ototal__on(X1938,X1937,X1936) )
& ( c_member(X1938,esk4_3(X1936,X1937,X1938),X1937)
| c_Relation_Ototal__on(X1938,X1937,X1936) )
& ( esk3_3(X1936,X1937,X1938) != esk4_3(X1936,X1937,X1938)
| c_Relation_Ototal__on(X1938,X1937,X1936) )
& ( ~ c_member(tc_prod(X1938,X1938),c_Product__Type_OPair(X1938,X1938,esk3_3(X1936,X1937,X1938),esk4_3(X1936,X1937,X1938)),X1936)
| c_Relation_Ototal__on(X1938,X1937,X1936) )
& ( ~ c_member(tc_prod(X1938,X1938),c_Product__Type_OPair(X1938,X1938,esk4_3(X1936,X1937,X1938),esk3_3(X1936,X1937,X1938)),X1936)
| c_Relation_Ototal__on(X1938,X1937,X1936) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__def])])])])])]) ).
cnf(c_0_52,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X2698,X2699,X2700,X2701,X2702] :
( ( ~ c_Wellfounded_Oacyclic(X2699,X2698)
| ~ c_member(tc_prod(X2699,X2699),c_Product__Type_OPair(X2699,X2699,X2700,X2700),c_Transitive__Closure_Otrancl(X2699,X2698)) )
& ( c_member(tc_prod(X2702,X2702),c_Product__Type_OPair(X2702,X2702,esk67_2(X2701,X2702),esk67_2(X2701,X2702)),c_Transitive__Closure_Otrancl(X2702,X2701))
| c_Wellfounded_Oacyclic(X2702,X2701) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])]) ).
fof(c_0_54,plain,
! [X1996,X1997,X1998,X1999,X2000] :
( ( ~ c_FunDef_Oin__rel(X2000,X1999,X1998,X1997,X1996)
| c_member(tc_prod(X2000,X1999),c_Product__Type_OPair(X2000,X1999,X1997,X1996),X1998) )
& ( ~ c_member(tc_prod(X2000,X1999),c_Product__Type_OPair(X2000,X1999,X1997,X1996),X1998)
| c_FunDef_Oin__rel(X2000,X1999,X1998,X1997,X1996) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(c_0_55,hypothesis,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_56,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_57,plain,
( X4 = X5
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X3)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_member(X1,X4,X2)
| ~ c_member(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
fof(c_0_59,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_4])]) ).
cnf(c_0_60,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk67_2(X2,X1),esk67_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
( c_FunDef_Oin__rel(X1,X2,X5,X3,X4)
| ~ c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,hypothesis,
( v_b = v_a
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_30]),c_0_58]),c_0_58])]) ).
cnf(c_0_64,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_67,hypothesis,
c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_b),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_68,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_69,hypothesis,
( ~ c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X1),v_F(v_P)) ),
inference(spm,[status(thm)],[c_0_65,c_0_42]) ).
cnf(c_0_70,hypothesis,
c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_42]),c_0_49])]) ).
cnf(c_0_71,plain,
( c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X4,X5),X3)
| ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_72,hypothesis,
c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_a),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,hypothesis,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X1),v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT120+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:57:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 186.39/141.44 % Version : CSE_E---1.7
% 186.39/141.44 % Problem : theBenchmark.p
% 186.39/141.44 % SZS status Theorem for theBenchmark.p
% 186.39/141.44 % SZS output start CNFRefutation
% See solution above
% 186.89/141.91 % Total time : 123.033s
%------------------------------------------------------------------------------