%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT121+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 : n009.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 05:06:03 PM UTC 2026
% Result : Theorem 64.80s 38.62s
% Output : CNFRefutation 65.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 73 ( 26 unt; 0 def)
% Number of atoms : 191 ( 22 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 195 ( 77 ~; 77 |; 22 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 7 con; 0-4 aty)
% Number of variables : 164 ( 22 sgn 89 !; 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_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_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_r__into__trancl_H,axiom,
! [X6,X33,X5] :
( c_member(tc_prod(X5,X5),X33,X6)
=> c_member(tc_prod(X5,X5),X33,c_Transitive__Closure_Otrancl(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
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_3,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)) )
=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& 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(v_P)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(conj_1,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_1) ).
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(conj_2,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_2) ).
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_0,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_0) ).
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_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(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,
! [X2796,X2797,X2798,X2799] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2799,X2798,X2797),X2796))
| X2798 = X2796
| hBOOL(hAPP(X2797,X2796)) )
& ( X2798 != X2796
| hBOOL(hAPP(c_Set_Oinsert(X2799,X2798,X2797),X2796)) )
& ( ~ hBOOL(hAPP(X2797,X2796))
| hBOOL(hAPP(c_Set_Oinsert(X2799,X2798,X2797),X2796)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(c_0_16,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_17,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X2785,X2786,X2787] :
( ~ c_member(X2787,X2786,X2785)
| c_Set_Oinsert(X2787,X2786,X2785) = X2785 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_19,plain,
! [X2697,X2698,X2699,X2700,X2701] :
( ( ~ c_Wellfounded_Oacyclic(X2698,X2697)
| ~ c_member(tc_prod(X2698,X2698),c_Product__Type_OPair(X2698,X2698,X2699,X2699),c_Transitive__Closure_Otrancl(X2698,X2697)) )
& ( c_member(tc_prod(X2701,X2701),c_Product__Type_OPair(X2701,X2701,esk67_2(X2700,X2701),esk67_2(X2700,X2701)),c_Transitive__Closure_Otrancl(X2701,X2700))
| c_Wellfounded_Oacyclic(X2701,X2700) ) ),
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_16])])])])]) ).
fof(c_0_20,plain,
! [X2523,X2524,X2525] :
( ~ c_member(tc_prod(X2525,X2525),X2524,X2523)
| c_member(tc_prod(X2525,X2525),X2524,c_Transitive__Closure_Otrancl(X2525,X2523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).
fof(c_0_21,plain,
! [X1992,X1993,X1994] :
( ( ~ c_member(X1994,X1993,X1992)
| hBOOL(hAPP(X1992,X1993)) )
& ( ~ hBOOL(hAPP(X1992,X1993))
| c_member(X1994,X1993,X1992) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_22,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,hypothesis,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ 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,esk90_0)) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ 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,esk90_0)) )
& ( 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(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ 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,esk90_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])]) ).
fof(c_0_25,hypothesis,
! [X3877] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3877))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3877))
& 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,X3877)) ),
inference(variable_rename,[status(thm)],[conj_1]) ).
fof(c_0_26,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]) ).
cnf(c_0_27,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_19]) ).
cnf(c_0_28,plain,
( c_member(tc_prod(X1,X1),X2,c_Transitive__Closure_Otrancl(X1,X3))
| ~ c_member(tc_prod(X1,X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_member(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,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_2]) ).
fof(c_0_32,plain,
! [X2541,X2542] :
( ~ c_Relation_Otrans(X2542,X2541)
| c_Transitive__Closure_Otrancl(X2542,X2541) = X2541 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).
cnf(c_0_33,hypothesis,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ 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,esk90_0)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,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_25]) ).
fof(c_0_37,plain,
! [X1924,X1925,X1926,X1927,X1928] :
( ( ~ c_Relation_Oirrefl(X1925,X1924)
| ~ c_member(tc_prod(X1925,X1925),c_Product__Type_OPair(X1925,X1925,X1926,X1926),X1924) )
& ( c_member(tc_prod(X1928,X1928),c_Product__Type_OPair(X1928,X1928,esk2_2(X1927,X1928),esk2_2(X1927,X1928)),X1927)
| c_Relation_Oirrefl(X1928,X1927) ) ),
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_26])])])])]) ).
cnf(c_0_38,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_39,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
fof(c_0_40,plain,
! [X2545,X2546,X2547,X2548,X2549] :
( ~ c_member(tc_prod(X2549,X2549),c_Product__Type_OPair(X2549,X2549,X2548,X2547),X2546)
| ~ c_member(tc_prod(X2549,X2549),c_Product__Type_OPair(X2549,X2549,X2547,X2545),X2546)
| c_member(tc_prod(X2549,X2549),c_Product__Type_OPair(X2549,X2549,X2548,X2545),c_Transitive__Closure_Otrancl(X2549,X2546)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
cnf(c_0_41,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_30,c_0_31]) ).
cnf(c_0_42,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X2
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,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(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36])]) ).
cnf(c_0_44,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_37]) ).
cnf(c_0_45,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_19]) ).
cnf(c_0_46,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ 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,esk90_0)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_47,plain,
~ c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,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_40]) ).
cnf(c_0_49,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_29,c_0_41]) ).
cnf(c_0_50,hypothesis,
c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,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(rw,[status(thm)],[c_0_46,c_0_34]),c_0_35]),c_0_36])]) ).
fof(c_0_53,hypothesis,
! [X3871,X3875,X3876] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3871,esk87_1(X3871)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X3871,esk88_1(X3871)))
| ~ 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(X3871,esk89_1(X3871)))
| X3875 = X3876
| ~ 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,X3875,X3876),hAPP(X3871,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,X3875,X3876),v_F(X3871)) ),
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_0])])])])]) ).
fof(c_0_54,plain,
! [X1955,X1956] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1956,tc_HOL_Obool)),X1955)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_55,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_23]) ).
cnf(c_0_56,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_48,c_0_49]),c_0_50]) ).
cnf(c_0_57,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_51,c_0_50]),c_0_52])]) ).
cnf(c_0_58,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,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)))
| ~ 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_53]) ).
fof(c_0_59,plain,
! [X1930,X1931,X1932,X1933,X1934,X1935,X1936,X1937] :
( ( ~ c_Relation_Ototal__on(X1932,X1931,X1930)
| ~ c_member(X1932,X1933,X1931)
| ~ c_member(X1932,X1934,X1931)
| X1933 = X1934
| c_member(tc_prod(X1932,X1932),c_Product__Type_OPair(X1932,X1932,X1933,X1934),X1930)
| c_member(tc_prod(X1932,X1932),c_Product__Type_OPair(X1932,X1932,X1934,X1933),X1930) )
& ( c_member(X1937,esk3_3(X1935,X1936,X1937),X1936)
| c_Relation_Ototal__on(X1937,X1936,X1935) )
& ( c_member(X1937,esk4_3(X1935,X1936,X1937),X1936)
| c_Relation_Ototal__on(X1937,X1936,X1935) )
& ( esk3_3(X1935,X1936,X1937) != esk4_3(X1935,X1936,X1937)
| c_Relation_Ototal__on(X1937,X1936,X1935) )
& ( ~ c_member(tc_prod(X1937,X1937),c_Product__Type_OPair(X1937,X1937,esk3_3(X1935,X1936,X1937),esk4_3(X1935,X1936,X1937)),X1935)
| c_Relation_Ototal__on(X1937,X1936,X1935) )
& ( ~ c_member(tc_prod(X1937,X1937),c_Product__Type_OPair(X1937,X1937,esk4_3(X1935,X1936,X1937),esk3_3(X1935,X1936,X1937)),X1935)
| c_Relation_Ototal__on(X1937,X1936,X1935) ) ),
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_60,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,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_55,c_0_56]),c_0_57])]) ).
cnf(c_0_62,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_58,c_0_36]),c_0_35]),c_0_34])]) ).
cnf(c_0_63,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_59]) ).
cnf(c_0_64,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_29,c_0_60]) ).
fof(c_0_65,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_66,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_61,c_0_62]) ).
cnf(c_0_67,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_63,c_0_36]),c_0_64]),c_0_64])]) ).
cnf(c_0_68,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_65]) ).
cnf(c_0_69,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_70,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_a),v_F(v_P)),
inference(rw,[status(thm)],[c_0_61,c_0_69]) ).
cnf(c_0_71,hypothesis,
c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_a),v_F(v_P)),
inference(rw,[status(thm)],[c_0_49,c_0_69]) ).
cnf(c_0_72,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT121+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 : n009.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 01:57:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 64.80/38.62 % Version : CSE_E---1.7
% 64.80/38.62 % Problem : theBenchmark.p
% 64.80/38.62 % SZS status Theorem for theBenchmark.p
% 64.80/38.62 % SZS output start CNFRefutation
% See solution above
% 65.00/38.89 % Total time : 27.592s
%------------------------------------------------------------------------------