%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW295+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:11:53 PM UTC 2026
% Result : ContradictoryAxioms 104.46s 17.36s
% Output : CNFRefutation 104.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 68 unt; 0 def)
% Number of atoms : 104 ( 87 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 29 ~; 15 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-5 aty)
% Number of variables : 147 ( 17 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X72,X31] :
( hAPP(c_Set_OCollect(X31),X72) = c_Orderings_Obot__class_Obot(tc_fun(X31,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X72,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X31] : c_Orderings_Obot__class_Obot(tc_fun(X31,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X31),hAPP(c_COMBK(tc_HOL_Obool,X31),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X72,X31] : hAPP(c_Set_OCollect(X31),X72) = X72,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X72,X31] : hAPP(c_Set_OCollect(X31),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31),c_fNot),X72)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X31,tc_HOL_Obool)),hAPP(c_Set_OCollect(X31),X72)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X318,X15,X31,X80] : hAPP(hAPP(c_COMBK(X80,X31),X15),X318) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_UNIV__def,axiom,
! [X31] : c_Orderings_Otop__class_Otop(tc_fun(X31,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X31),hAPP(c_COMBK(tc_HOL_Obool,X31),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X67] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X67),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X140,X31] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X31,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X31,tc_HOL_Obool)),X140)) = X140,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X72] :
( ~ hBOOL(X72)
| ~ hBOOL(hAPP(c_fNot,X72)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_sum__case__KK,axiom,
! [X75,X71,X107,X31,X90] : hAPP(c_Sum__Type_Osum_Osum__case(X90,X31,X107,hAPP(c_COMBK(X31,X90),X71),hAPP(c_COMBK(X31,X107),X71)),X75) = X71,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X31] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X31,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X31,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X31,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X5,X67] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),X5) = X67
=> X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X180,X183,X72,X107,X31,X90] : hAPP(hAPP(hAPP(c_COMBB(X90,X31,X107),X72),X183),X180) = hAPP(X72,hAPP(X183,X180)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X5,X67] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),hAPP(c_Nat_OSuc,X5)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X279,X80] : hAPP(c_List_Orev(X80),hAPP(c_List_Orev(X80),X279)) = X279,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X67] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X67,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X5] : X5 != hAPP(c_Nat_OSuc,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X72,X31] :
( hAPP(c_Set_OCollect(X31),X72) = c_Orderings_Obot__class_Obot(tc_fun(X31,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X72,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X12137] : c_Orderings_Obot__class_Obot(tc_fun(X12137,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X12137),hAPP(c_COMBK(tc_HOL_Obool,X12137),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X12132,X12133] : hAPP(c_Set_OCollect(X12133),X12132) = X12132,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X12168,X12169] : hAPP(c_Set_OCollect(X12169),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12169),c_fNot),X12168)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12169,tc_HOL_Obool)),hAPP(c_Set_OCollect(X12169),X12168)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X12144,X12145,X12146,X12147,X12149] :
( ( hAPP(c_Set_OCollect(X12149),X12147) = c_Orderings_Obot__class_Obot(tc_fun(X12149,tc_HOL_Obool))
| hBOOL(hAPP(X12147,esk303_1(X12147))) )
& ( ~ hBOOL(hAPP(X12144,X12146))
| hAPP(c_Set_OCollect(X12145),X12144) != c_Orderings_Obot__class_Obot(tc_fun(X12145,tc_HOL_Obool)) ) ),
inference(fof_nnf,[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)],[c_0_19])])])])])]) ).
fof(c_0_24,plain,
! [X17569,X17570,X17571,X17572] : hAPP(hAPP(c_COMBK(X17572,X17571),X17570),X17569) = X17570,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_25,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X12131] : c_Orderings_Otop__class_Otop(tc_fun(X12131,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X12131),hAPP(c_COMBK(tc_HOL_Obool,X12131),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_28,plain,
! [X67] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X67),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_29,plain,
! [X5472,X5473] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5473,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5473,tc_HOL_Obool)),X5472)) = X5472,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_30,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X72] :
( ~ hBOOL(X72)
| ~ hBOOL(hAPP(c_fNot,X72)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_32,plain,
! [X5869,X5870,X5871,X5872,X5873] : hAPP(c_Sum__Type_Osum_Osum__case(X5873,X5872,X5871,hAPP(c_COMBK(X5872,X5873),X5870),hAPP(c_COMBK(X5872,X5871),X5870)),X5869) = X5870,
inference(variable_rename,[status(thm)],[fact_sum__case__KK]) ).
cnf(c_0_33,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk303_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_36,plain,
! [X7648] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7648,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7648,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7648,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_37,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_38,plain,
! [X842,X843] :
( X842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X843),X842) != X843 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_39,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_40,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_41,plain,
! [X594] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X594),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_42,plain,
! [X17573,X17574,X17575,X17576,X17577,X17578] : hAPP(hAPP(hAPP(c_COMBB(X17578,X17577,X17576),X17575),X17574),X17573) = hAPP(X17575,hAPP(X17574,X17573)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_43,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_44,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_26]),c_0_26]) ).
fof(c_0_45,plain,
! [X17595] :
( ~ hBOOL(X17595)
| ~ hBOOL(hAPP(c_fNot,X17595)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
cnf(c_0_46,plain,
hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4),hAPP(c_COMBK(X2,X3),X4)),X5) = X4,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(X1,esk303_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_48,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_49,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_51,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_52,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_53,plain,
! [X852,X853] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X853),hAPP(c_Nat_OSuc,X852)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X853),X852)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_54,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
fof(c_0_57,plain,
! [X17243,X17244] : hAPP(c_List_Orev(X17244),hAPP(c_List_Orev(X17244),X17243)) = X17243,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_58,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_59,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_46]) ).
cnf(c_0_60,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_61,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_62,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2
| X1 = hAPP(c_Int_Onat,c_Int_OPls) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_54,c_0_52]) ).
fof(c_0_65,plain,
! [X846] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X846),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X846,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_66,plain,
! [X5] : X5 != hAPP(c_Nat_OSuc,X5),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_67,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_55]) ).
cnf(c_0_68,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_60]),c_0_48]),c_0_61]) ).
cnf(c_0_71,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_72,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_73,plain,
! [X344] : X344 != hAPP(c_Nat_OSuc,X344),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_66])]) ).
cnf(c_0_74,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_69,c_0_59]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_61]),c_0_70]) ).
cnf(c_0_77,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_71,c_0_63]) ).
cnf(c_0_78,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
inference(rw,[status(thm)],[c_0_72,c_0_52]) ).
cnf(c_0_79,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_81,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_82,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_84,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW295+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 09:45:50 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.52 Running first-order theorem proving
% 0.26/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 104.46/17.36 % Version: 3.5.1
% 104.46/17.36 % Preprocessing class: FMLMSMSMSSSNFFN.
% 104.46/17.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.46/17.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.46/17.36 % Starting new_bool_3 with 300s (1) cores
% 104.46/17.36 % Starting new_bool_1 with 300s (1) cores
% 104.46/17.36 % Starting sh5l with 300s (1) cores
% 104.46/17.36 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2837149 completed with status 0
% 104.46/17.36 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 104.46/17.36 % Preprocessing class: FMLMSMSMSSSNFFN.
% 104.46/17.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.46/17.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.46/17.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 104.46/17.36 % No SInE strategy applied
% 104.46/17.36 % Search class: FGHSM-SMLM33-DFFFFFNN
% 104.46/17.36 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 104.46/17.36 % Starting SubtermCWHack with 135s (1) cores
% 104.46/17.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 104.46/17.36 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 104.46/17.36 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 104.46/17.36 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 104.46/17.36 % SAT001_CA_MinMin_p005000_rr with pid 2837159 completed with status 0
% 104.46/17.36 % Result found by SAT001_CA_MinMin_p005000_rr
% 104.46/17.36 % Preprocessing class: FMLMSMSMSSSNFFN.
% 104.46/17.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 104.46/17.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 104.46/17.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 104.46/17.36 % No SInE strategy applied
% 104.46/17.36 % Search class: FGHSM-SMLM33-DFFFFFNN
% 104.46/17.36 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 104.46/17.36 % Starting SubtermCWHack with 135s (1) cores
% 104.46/17.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 104.46/17.36 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 104.46/17.36 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 104.46/17.36 % Preprocessing time : 0.305 s
% 104.46/17.36 % Presaturation interreduction done
% 104.46/17.36
% 104.46/17.36 % Proof found!
% 104.46/17.36 % SZS status ContradictoryAxioms
% 104.46/17.36 % SZS output start CNFRefutation
% See solution above
% 104.46/17.36 % Parsed axioms : 5205
% 104.46/17.36 % Removed by relevancy pruning/SinE : 0
% 104.46/17.36 % Initial clauses : 7483
% 104.46/17.36 % Removed in clause preprocessing : 252
% 104.46/17.36 % Initial clauses in saturation : 7231
% 104.46/17.36 % Processed clauses : 21366
% 104.46/17.36 % ...of these trivial : 354
% 104.46/17.36 % ...subsumed : 9279
% 104.46/17.36 % ...remaining for further processing : 11733
% 104.46/17.36 % Other redundant clauses eliminated : 1131
% 104.46/17.36 % Clauses deleted for lack of memory : 0
% 104.46/17.36 % Backward-subsumed : 164
% 104.46/17.36 % Backward-rewritten : 319
% 104.46/17.36 % Generated clauses : 183102
% 104.46/17.36 % ...of the previous two non-redundant : 174448
% 104.46/17.36 % ...aggressively subsumed : 0
% 104.46/17.36 % Contextual simplify-reflections : 26
% 104.46/17.36 % Paramodulations : 181964
% 104.46/17.36 % Factorizations : 2
% 104.46/17.36 % NegExts : 0
% 104.46/17.36 % Equation resolutions : 1198
% 104.46/17.36 % Disequality decompositions : 0
% 104.46/17.36 % Total rewrite steps : 48982
% 104.46/17.36 % ...of those cached : 33183
% 104.46/17.36 % Propositional unsat checks : 3
% 104.46/17.36 % Propositional check models : 2
% 104.46/17.36 % Propositional check unsatisfiable : 0
% 104.46/17.36 % Propositional clauses : 0
% 104.46/17.36 % Propositional clauses after purity: 0
% 104.46/17.36 % Propositional unsat core size : 0
% 104.46/17.36 % Propositional preprocessing time : 0.000
% 104.46/17.36 % Propositional encoding time : 0.333
% 104.46/17.36 % Propositional solver time : 0.156
% 104.46/17.36 % Success case prop preproc time : 0.000
% 104.46/17.36 % Success case prop encoding time : 0.000
% 104.46/17.36 % Success case prop solver time : 0.000
% 104.46/17.36 % Current number of processed clauses : 4991
% 104.46/17.36 % Positive orientable unit clauses : 1506
% 104.46/17.36 % Positive unorientable unit clauses: 130
% 104.46/17.36 % Negative unit clauses : 942
% 104.46/17.36 % Non-unit-clauses : 2413
% 104.46/17.36 % Current number of unprocessed clauses: 157911
% 104.46/17.36 % ...number of literals in the above : 280903
% 104.46/17.36 % Current number of archived formulas : 0
% 104.46/17.36 % Current number of archived clauses : 6290
% 104.46/17.36 % Clause-clause subsumption calls (NU) : 3977438
% 104.46/17.36 % Rec. Clause-clause subsumption calls : 1896489
% 104.46/17.36 % Non-unit clause-clause subsumptions : 4416
% 104.46/17.36 % Unit Clause-clause subsumption calls : 205196
% 104.46/17.37 % Rewrite failures with RHS unbound : 520
% 104.46/17.37 % BW rewrite match attempts : 41601
% 104.46/17.37 % BW rewrite match successes : 1376
% 104.46/17.37 % Condensation attempts : 205110
% 104.46/17.37 % Condensation successes : 265
% 104.46/17.37 % Termbank termtop insertions : 7017005
% 104.46/17.37 % Search garbage collected termcells : 98618
% 104.46/17.37
% 104.46/17.37 % -------------------------------------------------
% 104.46/17.37 % User time : 15.238 s
% 104.46/17.37 % System time : 0.441 s
% 104.46/17.37 % Total time : 15.679 s
% 104.46/17.37 % Maximum resident set size: 42088 pages
% 104.46/17.37
% 104.46/17.37 % -------------------------------------------------
% 104.46/17.37 % User time : 69.271 s
% 104.46/17.37 % System time : 1.954 s
% 104.46/17.37 % Total time : 71.224 s
% 104.46/17.37 % Maximum resident set size: 12288 pages
% 104.46/17.37 % E exiting
%------------------------------------------------------------------------------