%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW353+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 : n020.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 03:10:22 PM UTC 2026
% Result : ContradictoryAxioms 108.94s 17.85s
% Output : CNFRefutation 108.94s
% 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 : 150 ( 17 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X324,X62,X10,X5] : hAPP(hAPP(c_COMBK(X5,X10),X62),X324) = X62,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_UNIV__def,axiom,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X138] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X138),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X13,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_sum__case__KK,axiom,
! [X12,X6,X81,X5,X10] : hAPP(c_Sum__Type_Osum_Osum__case(X10,X5,X81,hAPP(c_COMBK(X5,X10),X6),hAPP(c_COMBK(X5,X81),X6)),X12) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X137,X138] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X138),X137) = X138
=> X137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/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/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(help_c__COMBB__1,axiom,
! [X37,X17,X18,X81,X5,X10] : hAPP(hAPP(hAPP(c_COMBB(X10,X5,X81),X18),X17),X37) = hAPP(X18,hAPP(X17,X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X137,X138] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X138),hAPP(c_Nat_OSuc,X137)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X138),X137)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_converse__converse,axiom,
! [X112,X5,X10] : hAPP(c_Relation_Oconverse(X10,X5),hAPP(c_Relation_Oconverse(X5,X10),X112)) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X138] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X138,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X137] : X137 != hAPP(c_Nat_OSuc,X137),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X4356] : c_Orderings_Obot__class_Obot(tc_fun(X4356,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4356),hAPP(c_COMBK(tc_HOL_Obool,X4356),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X4238,X4239] : hAPP(c_Set_OCollect(X4239),X4238) = X4238,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X4374,X4375] : hAPP(c_Set_OCollect(X4375),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4375),c_fNot),X4374)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4375,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4375),X4374)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X4270,X4271,X4272,X4273,X4275] :
( ( hAPP(c_Set_OCollect(X4275),X4273) = c_Orderings_Obot__class_Obot(tc_fun(X4275,tc_HOL_Obool))
| hBOOL(hAPP(X4273,esk82_1(X4273))) )
& ( ~ hBOOL(hAPP(X4270,X4272))
| hAPP(c_Set_OCollect(X4271),X4270) != c_Orderings_Obot__class_Obot(tc_fun(X4271,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,
! [X17634,X17635,X17636,X17637] : hAPP(hAPP(c_COMBK(X17637,X17636),X17635),X17634) = X17635,
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,
! [X4367] : c_Orderings_Otop__class_Otop(tc_fun(X4367,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4367),hAPP(c_COMBK(tc_HOL_Obool,X4367),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_28,plain,
! [X138] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X138),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_29,plain,
! [X2321,X2322] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2322,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2322,tc_HOL_Obool)),X2321)) = X2321,
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,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_32,plain,
! [X3478,X3479,X3480,X3481,X3482] : hAPP(c_Sum__Type_Osum_Osum__case(X3482,X3481,X3480,hAPP(c_COMBK(X3481,X3482),X3479),hAPP(c_COMBK(X3481,X3480),X3479)),X3478) = X3479,
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,esk82_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,
! [X3275] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3275,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X3275,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3275,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,
! [X5192,X5193] :
( X5192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5193),X5192) != X5193 ),
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,
! [X5788] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X5788),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_42,plain,
! [X17638,X17639,X17640,X17641,X17642,X17643] : hAPP(hAPP(hAPP(c_COMBB(X17643,X17642,X17641),X17640),X17639),X17638) = hAPP(X17640,hAPP(X17639,X17638)),
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,
! [X17660] :
( ~ hBOOL(X17660)
| ~ hBOOL(hAPP(c_fNot,X17660)) ),
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,esk82_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,
! [X5817,X5818] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5818),hAPP(c_Nat_OSuc,X5817)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5818),X5817)),
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,
! [X16544,X16545,X16546] : hAPP(c_Relation_Oconverse(X16546,X16545),hAPP(c_Relation_Oconverse(X16545,X16546),X16544)) = X16544,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
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,
! [X5196] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5196),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5196,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_66,plain,
! [X137] : X137 != hAPP(c_Nat_OSuc,X137),
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_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
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,
! [X5787] : X5787 != hAPP(c_Nat_OSuc,X5787),
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
% 0.00/0.03 % Problem : SWW353+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 09:49:48 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 108.94/17.85 % Version: 3.5.1
% 108.94/17.85 % Preprocessing class: FMLMSLSMSSSNFFN.
% 108.94/17.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.94/17.85 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 108.94/17.85 % Starting new_bool_3 with 300s (1) cores
% 108.94/17.85 % Starting new_bool_1 with 300s (1) cores
% 108.94/17.85 % Starting sh5l with 300s (1) cores
% 108.94/17.85 % SAT001_MinMin_p005000_rr_RG with pid 2621986 completed with status 0
% 108.94/17.85 % Result found by SAT001_MinMin_p005000_rr_RG
% 108.94/17.85 % Preprocessing class: FMLMSLSMSSSNFFN.
% 108.94/17.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.94/17.85 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 108.94/17.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 108.94/17.85 % No SInE strategy applied
% 108.94/17.85 % Search class: FGHSM-SMLM33-DFFFFFNN
% 108.94/17.85 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 108.94/17.85 % Starting SubtermCWHack with 135s (1) cores
% 108.94/17.85 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 108.94/17.85 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 108.94/17.85 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 108.94/17.85 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 108.94/17.85 % SAT001_CA_MinMin_p005000_rr with pid 2621996 completed with status 0
% 108.94/17.85 % Result found by SAT001_CA_MinMin_p005000_rr
% 108.94/17.85 % Preprocessing class: FMLMSLSMSSSNFFN.
% 108.94/17.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 108.94/17.85 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 108.94/17.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 108.94/17.85 % No SInE strategy applied
% 108.94/17.85 % Search class: FGHSM-SMLM33-DFFFFFNN
% 108.94/17.85 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 108.94/17.85 % Starting SubtermCWHack with 135s (1) cores
% 108.94/17.85 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 108.94/17.85 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 108.94/17.85 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 108.94/17.85 % Preprocessing time : 0.330 s
% 108.94/17.85 % Presaturation interreduction done
% 108.94/17.85
% 108.94/17.85 % Proof found!
% 108.94/17.85 % SZS status ContradictoryAxioms
% 108.94/17.85 % SZS output start CNFRefutation
% See solution above
% 108.94/17.85 % Parsed axioms : 5245
% 108.94/17.85 % Removed by relevancy pruning/SinE : 0
% 108.94/17.85 % Initial clauses : 7569
% 108.94/17.85 % Removed in clause preprocessing : 234
% 108.94/17.85 % Initial clauses in saturation : 7335
% 108.94/17.85 % Processed clauses : 21618
% 108.94/17.85 % ...of these trivial : 446
% 108.94/17.85 % ...subsumed : 7792
% 108.94/17.85 % ...remaining for further processing : 13380
% 108.94/17.85 % Other redundant clauses eliminated : 1528
% 108.94/17.85 % Clauses deleted for lack of memory : 0
% 108.94/17.85 % Backward-subsumed : 244
% 108.94/17.85 % Backward-rewritten : 385
% 108.94/17.85 % Generated clauses : 197419
% 108.94/17.85 % ...of the previous two non-redundant : 186976
% 108.94/17.85 % ...aggressively subsumed : 0
% 108.94/17.85 % Contextual simplify-reflections : 49
% 108.94/17.85 % Paramodulations : 195899
% 108.94/17.85 % Factorizations : 2
% 108.94/17.85 % NegExts : 0
% 108.94/17.85 % Equation resolutions : 1584
% 108.94/17.85 % Disequality decompositions : 0
% 108.94/17.85 % Total rewrite steps : 63200
% 108.94/17.85 % ...of those cached : 44825
% 108.94/17.85 % Propositional unsat checks : 3
% 108.94/17.85 % Propositional check models : 2
% 108.94/17.85 % Propositional check unsatisfiable : 0
% 108.94/17.85 % Propositional clauses : 0
% 108.94/17.85 % Propositional clauses after purity: 0
% 108.94/17.85 % Propositional unsat core size : 0
% 108.94/17.85 % Propositional preprocessing time : 0.000
% 108.94/17.85 % Propositional encoding time : 0.230
% 108.94/17.85 % Propositional solver time : 0.124
% 108.94/17.85 % Success case prop preproc time : 0.000
% 108.94/17.85 % Success case prop encoding time : 0.000
% 108.94/17.85 % Success case prop solver time : 0.000
% 108.94/17.85 % Current number of processed clauses : 6350
% 108.94/17.85 % Positive orientable unit clauses : 1663
% 108.94/17.85 % Positive unorientable unit clauses: 127
% 108.94/17.85 % Negative unit clauses : 818
% 108.94/17.85 % Non-unit-clauses : 3742
% 108.94/17.85 % Current number of unprocessed clauses: 168456
% 108.94/17.85 % ...number of literals in the above : 332934
% 108.94/17.85 % Current number of archived formulas : 0
% 108.94/17.85 % Current number of archived clauses : 6580
% 108.94/17.85 % Clause-clause subsumption calls (NU) : 7024818
% 108.94/17.85 % Rec. Clause-clause subsumption calls : 3033261
% 108.94/17.85 % Non-unit clause-clause subsumptions : 6694
% 108.94/17.85 % Unit Clause-clause subsumption calls : 344899
% 108.94/17.85 % Rewrite failures with RHS unbound : 536
% 108.94/17.85 % BW rewrite match attempts : 39459
% 108.94/17.85 % BW rewrite match successes : 1155
% 108.94/17.85 % Condensation attempts : 219807
% 108.94/17.85 % Condensation successes : 1381
% 108.94/17.85 % Termbank termtop insertions : 6890103
% 108.94/17.85 % Search garbage collected termcells : 100314
% 108.94/17.85
% 108.94/17.85 % -------------------------------------------------
% 108.94/17.85 % User time : 16.043 s
% 108.94/17.85 % System time : 0.457 s
% 108.94/17.85 % Total time : 16.500 s
% 108.94/17.85 % Maximum resident set size: 42940 pages
% 108.94/17.85
% 108.94/17.85 % -------------------------------------------------
% 108.94/17.85 % User time : 73.724 s
% 108.94/17.85 % System time : 1.971 s
% 108.94/17.85 % Total time : 75.695 s
% 108.94/17.85 % Maximum resident set size: 12288 pages
% 108.94/17.85 % E exiting
%------------------------------------------------------------------------------