%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT122+1 : TPTP v9.2.1. Released v5.2.0.
% 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 : n026.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 182.25s 143.40s
% Output : CNFRefutation 182.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 69 ( 26 unt; 0 def)
% Number of atoms : 184 ( 23 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 187 ( 72 ~; 76 |; 22 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-5 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 157 ( 24 sgn 80 !; 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
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)) )
=> ( 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/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(conj_0,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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,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/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_trancl__id,axiom,
! [X6,X5] :
( c_Relation_Otrans(X5,X6)
=> c_Transitive__Closure_Otrancl(X5,X6) = X6 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
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)) )
=> ! [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(v_P,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(v_P)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(fact_top1I,axiom,
! [X4,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(c_0_14,plain,
! [X2794,X2795,X2796,X2797] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2797,X2796,X2795),X2794))
| X2796 = X2794
| hBOOL(hAPP(X2795,X2794)) )
& ( X2796 != X2794
| hBOOL(hAPP(c_Set_Oinsert(X2797,X2796,X2795),X2794)) )
& ( ~ hBOOL(hAPP(X2795,X2794))
| hBOOL(hAPP(c_Set_Oinsert(X2797,X2796,X2795),X2794)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
cnf(c_0_15,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_16,plain,
! [X2783,X2784,X2785] :
( ~ c_member(X2785,X2784,X2783)
| c_Set_Oinsert(X2785,X2784,X2783) = X2783 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_17,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_18,plain,
! [X1990,X1991,X1992] :
( ( ~ c_member(X1992,X1991,X1990)
| hBOOL(hAPP(X1990,X1991)) )
& ( ~ hBOOL(hAPP(X1990,X1991))
| c_member(X1992,X1991,X1990) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_19,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,hypothesis,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_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,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_2])])])]) ).
fof(c_0_22,hypothesis,
! [X3869] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3869))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3869))
& 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,X3869)) ),
inference(variable_rename,[status(thm)],[conj_0]) ).
fof(c_0_23,plain,
! [X1922,X1923,X1924,X1925,X1926] :
( ( ~ c_Relation_Oirrefl(X1923,X1922)
| ~ c_member(tc_prod(X1923,X1923),c_Product__Type_OPair(X1923,X1923,X1924,X1924),X1922) )
& ( c_member(tc_prod(X1926,X1926),c_Product__Type_OPair(X1926,X1926,esk2_2(X1925,X1926),esk2_2(X1925,X1926)),X1925)
| c_Relation_Oirrefl(X1926,X1925) ) ),
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_17])])])])]) ).
cnf(c_0_24,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_member(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,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_1]) ).
fof(c_0_27,plain,
! [X2539,X2540] :
( ~ c_Relation_Otrans(X2540,X2539)
| c_Transitive__Closure_Otrancl(X2540,X2539) = X2539 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).
cnf(c_0_28,hypothesis,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,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_22]) ).
cnf(c_0_32,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_23]) ).
cnf(c_0_33,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
fof(c_0_34,plain,
! [X2543,X2544,X2545,X2546,X2547] :
( ~ c_member(tc_prod(X2547,X2547),c_Product__Type_OPair(X2547,X2547,X2546,X2545),X2544)
| ~ c_member(tc_prod(X2547,X2547),c_Product__Type_OPair(X2547,X2547,X2545,X2543),X2544)
| c_member(tc_prod(X2547,X2547),c_Product__Type_OPair(X2547,X2547,X2546,X2543),c_Transitive__Closure_Otrancl(X2547,X2544)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
cnf(c_0_35,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_25,c_0_26]) ).
cnf(c_0_36,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X2
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,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_28,c_0_29]),c_0_30]),c_0_31])]) ).
fof(c_0_38,hypothesis,
! [X3872,X3873] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_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,esk88_0))
| X3872 = X3873
| ~ 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,X3872,X3873),hAPP(v_P,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,X3872,X3873),v_F(v_P)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])]) ).
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_32,c_0_33]) ).
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_34]) ).
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_24,c_0_35]) ).
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_36,c_0_37]) ).
cnf(c_0_43,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_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,esk87_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_44,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_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_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,esk88_0))
| ~ 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(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_45,plain,
! [X1953,X1954] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1954,tc_HOL_Obool)),X1953)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_46,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_20]) ).
cnf(c_0_47,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_48,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_43,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_49,plain,
( c_member(X1,X2,X3)
| ~ c_member(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_50,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(rw,[status(thm)],[c_0_44,c_0_29]),c_0_30]),c_0_31])]) ).
fof(c_0_51,plain,
! [X1928,X1929,X1930,X1931,X1932,X1933,X1934,X1935] :
( ( ~ c_Relation_Ototal__on(X1930,X1929,X1928)
| ~ c_member(X1930,X1931,X1929)
| ~ c_member(X1930,X1932,X1929)
| X1931 = X1932
| c_member(tc_prod(X1930,X1930),c_Product__Type_OPair(X1930,X1930,X1931,X1932),X1928)
| c_member(tc_prod(X1930,X1930),c_Product__Type_OPair(X1930,X1930,X1932,X1931),X1928) )
& ( c_member(X1935,esk3_3(X1933,X1934,X1935),X1934)
| c_Relation_Ototal__on(X1935,X1934,X1933) )
& ( c_member(X1935,esk4_3(X1933,X1934,X1935),X1934)
| c_Relation_Ototal__on(X1935,X1934,X1933) )
& ( esk3_3(X1933,X1934,X1935) != esk4_3(X1933,X1934,X1935)
| c_Relation_Ototal__on(X1935,X1934,X1933) )
& ( ~ c_member(tc_prod(X1935,X1935),c_Product__Type_OPair(X1935,X1935,esk3_3(X1933,X1934,X1935),esk4_3(X1933,X1934,X1935)),X1933)
| c_Relation_Ototal__on(X1935,X1934,X1933) )
& ( ~ c_member(tc_prod(X1935,X1935),c_Product__Type_OPair(X1935,X1935,esk4_3(X1933,X1934,X1935),esk3_3(X1933,X1934,X1935)),X1933)
| c_Relation_Ototal__on(X1935,X1934,X1933) ) ),
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,
! [X1993,X1994,X1995,X1996,X1997] :
( ( ~ c_FunDef_Oin__rel(X1997,X1996,X1995,X1994,X1993)
| c_member(tc_prod(X1997,X1996),c_Product__Type_OPair(X1997,X1996,X1994,X1993),X1995) )
& ( ~ c_member(tc_prod(X1997,X1996),c_Product__Type_OPair(X1997,X1996,X1994,X1993),X1995)
| c_FunDef_Oin__rel(X1997,X1996,X1995,X1994,X1993) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(c_0_54,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_46,c_0_47]),c_0_48])]) ).
cnf(c_0_55,hypothesis,
( X1 = X2
| c_member(X3,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(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,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_57,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_24,c_0_52]) ).
fof(c_0_58,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_59,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_53]) ).
cnf(c_0_60,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_54,c_0_55]) ).
cnf(c_0_61,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_56,c_0_31]),c_0_57]),c_0_57])]) ).
cnf(c_0_62,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_58]) ).
cnf(c_0_63,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_59,c_0_41]) ).
cnf(c_0_64,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_65,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_53]) ).
cnf(c_0_66,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_63,c_0_64]) ).
cnf(c_0_67,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_54,c_0_64]) ).
cnf(c_0_68,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT122+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n026.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 01:57:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 182.25/143.40 % Version : CSE_E---1.7
% 182.25/143.40 % Problem : theBenchmark.p
% 182.25/143.40 % SZS status Theorem for theBenchmark.p
% 182.25/143.40 % SZS output start CNFRefutation
% See solution above
% 182.65/143.85 % Total time : 125.894s
%------------------------------------------------------------------------------