%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW371+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 : n016.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 0.19s 20.81s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 65 unt; 0 def)
% Number of atoms : 101 ( 84 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 : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 135 ( 16 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X17,X5] :
( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,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,
! [X17,X5] : hAPP(c_Set_OCollect(X5),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X17,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X323,X70,X15,X5] : hAPP(hAPP(c_COMBK(X5,X15),X70),X323) = X70,
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__neq__Suc,axiom,
! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X10,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)),X10)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X17] :
( ~ hBOOL(X17)
| ~ hBOOL(hAPP(c_fNot,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
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,
! [X99,X100] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X99) = X100
=> X99 = 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,
! [X33,X16,X17,X89,X5,X15] : hAPP(hAPP(hAPP(c_COMBB(X15,X5,X89),X17),X16),X33) = hAPP(X17,hAPP(X16,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X99,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),hAPP(c_Nat_OSuc,X99)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X99)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_converse__converse,axiom,
! [X171,X5,X15] : hAPP(c_Relation_Oconverse(X15,X5),hAPP(c_Relation_Oconverse(X5,X15),X171)) = X171,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X100,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X99] : X99 != hAPP(c_Nat_OSuc,X99),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X17,X5] :
( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X11186] : c_Orderings_Obot__class_Obot(tc_fun(X11186,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11186),hAPP(c_COMBK(tc_HOL_Obool,X11186),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X11164,X11165] : hAPP(c_Set_OCollect(X11165),X11164) = X11164,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X11166,X11167] : hAPP(c_Set_OCollect(X11167),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11167),c_fNot),X11166)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11167,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11167),X11166)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X11174,X11175,X11176,X11177,X11179] :
( ( hAPP(c_Set_OCollect(X11179),X11177) = c_Orderings_Obot__class_Obot(tc_fun(X11179,tc_HOL_Obool))
| hBOOL(hAPP(X11177,esk300_1(X11177))) )
& ( ~ hBOOL(hAPP(X11174,X11176))
| hAPP(c_Set_OCollect(X11175),X11174) != c_Orderings_Obot__class_Obot(tc_fun(X11175,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_18])])])])])]) ).
fof(c_0_23,plain,
! [X17589,X17590,X17591,X17592] : hAPP(hAPP(c_COMBK(X17592,X17591),X17590),X17589) = X17590,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X11190] : c_Orderings_Otop__class_Otop(tc_fun(X11190,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11190),hAPP(c_COMBK(tc_HOL_Obool,X11190),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_27,plain,
! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_28,plain,
! [X1604,X1605] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1605,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1605,tc_HOL_Obool)),X1604)) = X1604,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_29,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_21]) ).
fof(c_0_30,plain,
! [X17] :
( ~ hBOOL(X17)
| ~ hBOOL(hAPP(c_fNot,X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_31,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk300_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,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_24,c_0_25]) ).
fof(c_0_34,plain,
! [X6716] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6716,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6716,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6716,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_35,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_26]) ).
fof(c_0_36,plain,
! [X2711,X2712] :
( X2711 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2712),X2711) != X2712 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_37,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_38,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_39,plain,
! [X2696] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2696),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_40,plain,
! [X17593,X17594,X17595,X17596,X17597,X17598] : hAPP(hAPP(hAPP(c_COMBB(X17598,X17597,X17596),X17595),X17594),X17593) = hAPP(X17595,hAPP(X17594,X17593)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_41,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_28]) ).
cnf(c_0_42,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_29,c_0_25]),c_0_25]) ).
fof(c_0_43,plain,
! [X17615] :
( ~ hBOOL(X17615)
| ~ hBOOL(hAPP(c_fNot,X17615)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(X1,esk300_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_31,c_0_25]) ).
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_32,c_0_33]) ).
cnf(c_0_46,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_34]) ).
cnf(c_0_47,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_35,c_0_25]) ).
cnf(c_0_48,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_36]) ).
cnf(c_0_49,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_50,plain,
! [X2253,X2254] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2254),hAPP(c_Nat_OSuc,X2253)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2254),X2253)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_51,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,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_41,c_0_42]),c_0_42]) ).
fof(c_0_54,plain,
! [X16672,X16673,X16674] : hAPP(c_Relation_Oconverse(X16674,X16673),hAPP(c_Relation_Oconverse(X16673,X16674),X16672)) = X16672,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
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_32,c_0_44]),c_0_45]),c_0_32]) ).
cnf(c_0_57,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_46,c_0_42]) ).
cnf(c_0_58,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_59,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_48,c_0_49]) ).
cnf(c_0_60,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_50]) ).
cnf(c_0_61,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_51,c_0_49]) ).
fof(c_0_62,plain,
! [X2708] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2708),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2708,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_63,plain,
! [X99] : X99 != hAPP(c_Nat_OSuc,X99),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_64,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).
cnf(c_0_65,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_57]),c_0_45]),c_0_58]) ).
cnf(c_0_68,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_59,c_0_60]),c_0_61]) ).
cnf(c_0_69,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_62]) ).
fof(c_0_70,plain,
! [X1870] : X1870 != hAPP(c_Nat_OSuc,X1870),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).
cnf(c_0_71,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_66,c_0_56]) ).
cnf(c_0_73,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_58]),c_0_67]) ).
cnf(c_0_74,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_68,c_0_60]) ).
cnf(c_0_75,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_69,c_0_49]) ).
cnf(c_0_76,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_80,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_77]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW371+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 21 09:54:23 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 0.19/20.81 % Version: 3.5.1
% 0.19/20.81 % Preprocessing class: FMLMSLSMSSSNFFN.
% 0.19/20.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/20.81 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 0.19/20.81 % Starting new_bool_3 with 300s (1) cores
% 0.19/20.81 % Starting new_bool_1 with 300s (1) cores
% 0.19/20.81 % Starting sh5l with 300s (1) cores
% 0.19/20.81 % SAT001_MinMin_p005000_rr_RG with pid 2158145 completed with status 0
% 0.19/20.81 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/20.81 % Preprocessing class: FMLMSLSMSSSNFFN.
% 0.19/20.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/20.81 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 0.19/20.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/20.81 % No SInE strategy applied
% 0.19/20.81 % Search class: FGHSM-SMLM33-DFFFFFNN
% 0.19/20.81 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 0.19/20.81 % Starting SubtermCWHack with 135s (1) cores
% 0.19/20.81 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 0.19/20.81 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 0.19/20.81 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 0.19/20.81 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 0.19/20.81 % SAT001_CA_MinMin_p005000_rr with pid 2158155 completed with status 0
% 0.19/20.81 % Result found by SAT001_CA_MinMin_p005000_rr
% 0.19/20.81 % Preprocessing class: FMLMSLSMSSSNFFN.
% 0.19/20.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/20.81 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 0.19/20.81 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/20.81 % No SInE strategy applied
% 0.19/20.81 % Search class: FGHSM-SMLM33-DFFFFFNN
% 0.19/20.81 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 0.19/20.81 % Starting SubtermCWHack with 135s (1) cores
% 0.19/20.81 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 0.19/20.81 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 0.19/20.81 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 0.19/20.81 % Preprocessing time : 0.330 s
% 0.19/20.81 % Presaturation interreduction done
% 0.19/20.81
% 0.19/20.81 % Proof found!
% 0.19/20.81 % SZS status ContradictoryAxioms
% 0.19/20.81 % SZS output start CNFRefutation
% See solution above
% 0.19/20.81 % Parsed axioms : 5249
% 0.19/20.81 % Removed by relevancy pruning/SinE : 0
% 0.19/20.81 % Initial clauses : 7536
% 0.19/20.81 % Removed in clause preprocessing : 228
% 0.19/20.81 % Initial clauses in saturation : 7308
% 0.19/20.81 % Processed clauses : 22377
% 0.19/20.81 % ...of these trivial : 439
% 0.19/20.81 % ...subsumed : 9406
% 0.19/20.81 % ...remaining for further processing : 12532
% 0.19/20.81 % Other redundant clauses eliminated : 1505
% 0.19/20.81 % Clauses deleted for lack of memory : 0
% 0.19/20.81 % Backward-subsumed : 202
% 0.19/20.81 % Backward-rewritten : 384
% 0.19/20.81 % Generated clauses : 197346
% 0.19/20.81 % ...of the previous two non-redundant : 186888
% 0.19/20.81 % ...aggressively subsumed : 0
% 0.19/20.81 % Contextual simplify-reflections : 35
% 0.19/20.81 % Paramodulations : 195853
% 0.19/20.81 % Factorizations : 2
% 0.19/20.81 % NegExts : 0
% 0.19/20.81 % Equation resolutions : 1558
% 0.19/20.81 % Disequality decompositions : 0
% 0.19/20.81 % Total rewrite steps : 65658
% 0.19/20.81 % ...of those cached : 46886
% 0.19/20.81 % Propositional unsat checks : 3
% 0.19/20.81 % Propositional check models : 2
% 0.19/20.81 % Propositional check unsatisfiable : 0
% 0.19/20.81 % Propositional clauses : 0
% 0.19/20.81 % Propositional clauses after purity: 0
% 0.19/20.81 % Propositional unsat core size : 0
% 0.19/20.81 % Propositional preprocessing time : 0.000
% 0.19/20.81 % Propositional encoding time : 0.321
% 0.19/20.81 % Propositional solver time : 0.189
% 0.19/20.81 % Success case prop preproc time : 0.000
% 0.19/20.81 % Success case prop encoding time : 0.000
% 0.19/20.81 % Success case prop solver time : 0.000
% 0.19/20.81 % Current number of processed clauses : 5551
% 0.19/20.81 % Positive orientable unit clauses : 1686
% 0.19/20.81 % Positive unorientable unit clauses: 129
% 0.19/20.81 % Negative unit clauses : 937
% 0.19/20.81 % Non-unit-clauses : 2799
% 0.19/20.81 % Current number of unprocessed clauses: 168849
% 0.19/20.81 % ...number of literals in the above : 321429
% 0.19/20.81 % Current number of archived formulas : 0
% 0.19/20.81 % Current number of archived clauses : 6529
% 0.19/20.81 % Clause-clause subsumption calls (NU) : 5437015
% 0.19/20.81 % Rec. Clause-clause subsumption calls : 2384167
% 0.19/20.81 % Non-unit clause-clause subsumptions : 7408
% 0.19/20.81 % Unit Clause-clause subsumption calls : 163605
% 0.19/20.81 % Rewrite failures with RHS unbound : 739
% 0.19/20.81 % BW rewrite match attempts : 39278
% 0.19/20.81 % BW rewrite match successes : 1271
% 0.19/20.81 % Condensation attempts : 220491
% 0.19/20.81 % Condensation successes : 1542
% 0.19/20.81 % Termbank termtop insertions : 6873933
% 0.19/20.81 % Search garbage collected termcells : 99255
% 0.19/20.81
% 0.19/20.81 % -------------------------------------------------
% 0.19/20.81 % User time : 18.655 s
% 0.19/20.81 % System time : 0.510 s
% 0.19/20.81 % Total time : 19.164 s
% 0.19/20.81 % Maximum resident set size: 41860 pages
% 0.19/20.81
% 0.19/20.81 % -------------------------------------------------
% 0.19/20.81 % User time : 85.511 s
% 0.19/20.81 % System time : 2.368 s
% 0.19/20.81 % Total time : 87.880 s
% 0.19/20.81 % Maximum resident set size: 12288 pages
% 0.19/20.81 % E exiting
%------------------------------------------------------------------------------