%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW376+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 03:10:24 PM UTC 2026
% Result : ContradictoryAxioms 83.09s 13.90s
% Output : CNFRefutation 83.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 67 unt; 0 def)
% Number of atoms : 107 ( 84 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 56 ( 32 ~; 18 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 136 ( 16 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X19,X6] :
( hAPP(c_Set_OCollect(X6),X19) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X6] : c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X19,X6] : hAPP(c_Set_OCollect(X6),X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X19,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X326,X39,X7,X6] : hAPP(hAPP(c_COMBK(X6,X7),X39),X326) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_double__complement,axiom,
! [X4,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),X4)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_UNIV__def,axiom,
! [X6] : c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X127] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X127),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(help_c__fNot__1,axiom,
! [X19] :
( ~ hBOOL(X19)
| ~ hBOOL(hAPP(c_fNot,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__COMBB__1,axiom,
! [X67,X43,X19,X5,X6,X7] : hAPP(hAPP(hAPP(c_COMBB(X7,X6,X5),X19),X43),X67) = hAPP(X19,hAPP(X43,X67)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_converse__converse,axiom,
! [X119,X6,X7] : hAPP(c_Relation_Oconverse(X7,X6),hAPP(c_Relation_Oconverse(X6,X7),X119)) = X119,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_add__0__iff,axiom,
! [X13,X27,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( X27 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X27),X13)
<=> X13 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X136,X127] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X127),hAPP(c_Nat_OSuc,X136)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X127),X136)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X127] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X127),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X127,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X136] : X136 != hAPP(c_Nat_OSuc,X136),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X19,X6] :
( hAPP(c_Set_OCollect(X6),X19) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X8702] : c_Orderings_Obot__class_Obot(tc_fun(X8702,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8702),hAPP(c_COMBK(tc_HOL_Obool,X8702),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X8725,X8726] : hAPP(c_Set_OCollect(X8726),X8725) = X8725,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X8787,X8788] : hAPP(c_Set_OCollect(X8788),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8788),c_fNot),X8787)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8788,tc_HOL_Obool)),hAPP(c_Set_OCollect(X8788),X8787)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X8737,X8738,X8739,X8740,X8742] :
( ( hAPP(c_Set_OCollect(X8742),X8740) = c_Orderings_Obot__class_Obot(tc_fun(X8742,tc_HOL_Obool))
| hBOOL(hAPP(X8740,esk231_1(X8740))) )
& ( ~ hBOOL(hAPP(X8737,X8739))
| hAPP(c_Set_OCollect(X8738),X8737) != c_Orderings_Obot__class_Obot(tc_fun(X8738,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,
! [X17639,X17640,X17641,X17642] : hAPP(hAPP(c_COMBK(X17642,X17641),X17640),X17639) = X17640,
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,
! [X1788,X1789] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1789,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1789,tc_HOL_Obool)),X1788)) = X1788,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_28,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_29,plain,
! [X8783] : c_Orderings_Otop__class_Otop(tc_fun(X8783,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8783),hAPP(c_COMBK(tc_HOL_Obool,X8783),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_30,plain,
! [X127] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X127),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_31,plain,
! [X19] :
( ~ hBOOL(X19)
| ~ hBOOL(hAPP(c_fNot,X19)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_32,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk231_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,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_35,plain,
! [X17643,X17644,X17645,X17646,X17647,X17648] : hAPP(hAPP(hAPP(c_COMBB(X17648,X17647,X17646),X17645),X17644),X17643) = hAPP(X17645,hAPP(X17644,X17643)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_36,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_27]) ).
cnf(c_0_37,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_28,c_0_26]),c_0_26]) ).
fof(c_0_38,plain,
! [X2276] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2276,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2276,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2276,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_39,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_29]) ).
fof(c_0_40,plain,
! [X5463] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X5463),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_41,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_42,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_43,plain,
! [X17665] :
( ~ hBOOL(X17665)
| ~ hBOOL(hAPP(c_fNot,X17665)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(X1,esk231_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_45,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_46,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,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_36,c_0_37]),c_0_37]) ).
fof(c_0_48,plain,
! [X16839,X16840,X16841] : hAPP(c_Relation_Oconverse(X16841,X16840),hAPP(c_Relation_Oconverse(X16840,X16841),X16839)) = X16839,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
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_38]) ).
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_39,c_0_26]) ).
fof(c_0_51,plain,
! [X5411,X5412,X5413] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5413)
| X5412 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5413),X5412),X5411)
| X5411 != c_Groups_Ozero__class_Ozero(X5413) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5413)
| X5411 = c_Groups_Ozero__class_Ozero(X5413)
| X5412 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5413),X5412),X5411) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
fof(c_0_52,plain,
! [X4252,X4253] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4253),hAPP(c_Nat_OSuc,X4252)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4253),X4252)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_53,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_55,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_45]),c_0_33]) ).
cnf(c_0_57,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_46]) ).
cnf(c_0_58,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,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_37]) ).
cnf(c_0_60,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_61,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,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_52]) ).
cnf(c_0_63,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_64,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_65,plain,
! [X5486] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5486),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5486,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_66,plain,
! [X136] : X136 != hAPP(c_Nat_OSuc,X136),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_67,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_59]),c_0_45]),c_0_60]) ).
cnf(c_0_70,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_54]),c_0_63])]),c_0_64]) ).
cnf(c_0_71,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_72,plain,
! [X4079] : X4079 != hAPP(c_Nat_OSuc,X4079),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_66])]) ).
cnf(c_0_73,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_67,c_0_56]) ).
cnf(c_0_74,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,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_70,c_0_62]) ).
cnf(c_0_76,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_71,c_0_54]) ).
cnf(c_0_77,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_73]),c_0_74]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_81,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_78]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW376+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n011.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 09:50:10 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.52 Running first-order theorem proving
% 0.25/0.52 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 83.09/13.90 % Version: 3.5.1
% 83.09/13.90 % Preprocessing class: FMLMSLSMSSSNFFN.
% 83.09/13.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.09/13.90 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 83.09/13.90 % Starting new_bool_3 with 300s (1) cores
% 83.09/13.90 % Starting new_bool_1 with 300s (1) cores
% 83.09/13.90 % Starting sh5l with 300s (1) cores
% 83.09/13.90 % SAT001_MinMin_p005000_rr_RG with pid 1601247 completed with status 0
% 83.09/13.90 % Result found by SAT001_MinMin_p005000_rr_RG
% 83.09/13.90 % Preprocessing class: FMLMSLSMSSSNFFN.
% 83.09/13.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.09/13.90 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 83.09/13.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 83.09/13.90 % No SInE strategy applied
% 83.09/13.90 % Search class: FGHSM-SMLM33-DFFFFFNN
% 83.09/13.90 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 83.09/13.90 % Starting SubtermCWHack with 135s (1) cores
% 83.09/13.90 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 83.09/13.90 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 83.09/13.90 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 83.09/13.90 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 83.09/13.90 % SAT001_CA_MinMin_p005000_rr with pid 1601257 completed with status 0
% 83.09/13.90 % Result found by SAT001_CA_MinMin_p005000_rr
% 83.09/13.90 % Preprocessing class: FMLMSLSMSSSNFFN.
% 83.09/13.90 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.09/13.90 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 83.09/13.90 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 83.09/13.90 % No SInE strategy applied
% 83.09/13.90 % Search class: FGHSM-SMLM33-DFFFFFNN
% 83.09/13.90 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 83.09/13.90 % Starting SubtermCWHack with 135s (1) cores
% 83.09/13.90 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 83.09/13.90 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 83.09/13.90 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 83.09/13.90 % Preprocessing time : 0.313 s
% 83.09/13.90 % Presaturation interreduction done
% 83.09/13.90
% 83.09/13.90 % Proof found!
% 83.09/13.90 % SZS status ContradictoryAxioms
% 83.09/13.90 % SZS output start CNFRefutation
% See solution above
% 83.09/13.91 % Parsed axioms : 5243
% 83.09/13.91 % Removed by relevancy pruning/SinE : 0
% 83.09/13.91 % Initial clauses : 7564
% 83.09/13.91 % Removed in clause preprocessing : 233
% 83.09/13.91 % Initial clauses in saturation : 7331
% 83.09/13.91 % Processed clauses : 21040
% 83.09/13.91 % ...of these trivial : 394
% 83.09/13.91 % ...subsumed : 7190
% 83.09/13.91 % ...remaining for further processing : 13456
% 83.09/13.91 % Other redundant clauses eliminated : 2047
% 83.09/13.91 % Clauses deleted for lack of memory : 0
% 83.09/13.91 % Backward-subsumed : 344
% 83.09/13.91 % Backward-rewritten : 389
% 83.09/13.91 % Generated clauses : 189125
% 83.09/13.91 % ...of the previous two non-redundant : 179676
% 83.09/13.91 % ...aggressively subsumed : 0
% 83.09/13.91 % Contextual simplify-reflections : 41
% 83.09/13.91 % Paramodulations : 187069
% 83.09/13.91 % Factorizations : 2
% 83.09/13.91 % NegExts : 0
% 83.09/13.91 % Equation resolutions : 2120
% 83.09/13.91 % Disequality decompositions : 0
% 83.09/13.91 % Total rewrite steps : 58303
% 83.09/13.91 % ...of those cached : 42575
% 83.09/13.91 % Propositional unsat checks : 3
% 83.09/13.91 % Propositional check models : 2
% 83.09/13.91 % Propositional check unsatisfiable : 0
% 83.09/13.91 % Propositional clauses : 0
% 83.09/13.91 % Propositional clauses after purity: 0
% 83.09/13.91 % Propositional unsat core size : 0
% 83.09/13.91 % Propositional preprocessing time : 0.000
% 83.09/13.91 % Propositional encoding time : 0.192
% 83.09/13.91 % Propositional solver time : 0.104
% 83.09/13.91 % Success case prop preproc time : 0.000
% 83.09/13.91 % Success case prop encoding time : 0.000
% 83.09/13.91 % Success case prop solver time : 0.000
% 83.09/13.91 % Current number of processed clauses : 6339
% 83.09/13.91 % Positive orientable unit clauses : 1610
% 83.09/13.91 % Positive unorientable unit clauses: 131
% 83.09/13.91 % Negative unit clauses : 943
% 83.09/13.91 % Non-unit-clauses : 3655
% 83.09/13.91 % Current number of unprocessed clauses: 159951
% 83.09/13.91 % ...number of literals in the above : 306696
% 83.09/13.91 % Current number of archived formulas : 0
% 83.09/13.91 % Current number of archived clauses : 6671
% 83.09/13.91 % Clause-clause subsumption calls (NU) : 6534901
% 83.09/13.91 % Rec. Clause-clause subsumption calls : 2813910
% 83.09/13.91 % Non-unit clause-clause subsumptions : 5748
% 83.09/13.91 % Unit Clause-clause subsumption calls : 271207
% 83.09/13.91 % Rewrite failures with RHS unbound : 493
% 83.09/13.91 % BW rewrite match attempts : 41024
% 83.09/13.91 % BW rewrite match successes : 1192
% 83.09/13.91 % Condensation attempts : 210946
% 83.09/13.91 % Condensation successes : 1564
% 83.09/13.91 % Termbank termtop insertions : 6762328
% 83.09/13.91 % Search garbage collected termcells : 100228
% 83.09/13.91
% 83.09/13.91 % -------------------------------------------------
% 83.09/13.91 % User time : 12.276 s
% 83.09/13.91 % System time : 0.351 s
% 83.09/13.91 % Total time : 12.627 s
% 83.09/13.91 % Maximum resident set size: 42924 pages
% 83.09/13.91
% 83.09/13.91 % -------------------------------------------------
% 83.09/13.91 % User time : 55.660 s
% 83.09/13.91 % System time : 1.548 s
% 83.09/13.91 % Total time : 57.208 s
% 83.09/13.91 % Maximum resident set size: 12288 pages
% 83.09/13.91 % E exiting
%------------------------------------------------------------------------------