%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW304+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 : n019.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 03:10:16 PM UTC 2026
% Result : ContradictoryAxioms 151.38s 22.10s
% Output : CNFRefutation 151.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 88 ( 68 unt; 0 def)
% Number of atoms : 110 ( 88 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 31 ~; 17 |; 1 &)
% ( 2 <=>; 2 =>; 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 : 146 ( 20 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_bot__apply,axiom,
! [X22,X17,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17,X5)),X22) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_Collect__empty__eq,axiom,
! [X23,X5] :
( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X314,X48,X5,X58] : hAPP(hAPP(c_COMBK(X58,X5),X48),X314) = X48,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_Collect__neg__eq,axiom,
! [X23,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X23)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_Zero__not__Suc,axiom,
! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X18,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)),X18)) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X23] :
( ~ hBOOL(X23)
| ~ hBOOL(hAPP(c_fNot,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__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_add__eq__self__zero,axiom,
! [X57,X72] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57) = X72
=> X57 = 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,
! [X31,X26,X23,X116,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X116),X23),X26),X31) = hAPP(X23,hAPP(X26,X31)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__Suc__right,axiom,
! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_converse__converse,axiom,
! [X171,X5,X17] : hAPP(c_Relation_Oconverse(X17,X5),hAPP(c_Relation_Oconverse(X5,X17),X171)) = X171,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X72,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X57] : X57 != hAPP(c_Nat_OSuc,X57),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_20,plain,
! [X11076] : c_Orderings_Obot__class_Obot(tc_fun(X11076,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11076),hAPP(c_COMBK(tc_HOL_Obool,X11076),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X11062,X11063] : hAPP(c_Set_OCollect(X11063),X11062) = X11062,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X363,X364,X365] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X364,X365)),X363) = c_Orderings_Obot__class_Obot(X365)
| ~ class_Orderings_Obot(X365) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])])]) ).
fof(c_0_23,plain,
! [X23,X5] :
( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_24,plain,
! [X17623,X17624,X17625,X17626] : hAPP(hAPP(c_COMBK(X17626,X17625),X17624),X17623) = X17624,
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]) ).
cnf(c_0_27,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
fof(c_0_29,plain,
! [X11041,X11042] : hAPP(c_Set_OCollect(X11042),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11042),c_fNot),X11041)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11042,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11042),X11041)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_30,plain,
! [X11064,X11065,X11066,X11067,X11069] :
( ( hAPP(c_Set_OCollect(X11069),X11067) = c_Orderings_Obot__class_Obot(tc_fun(X11069,tc_HOL_Obool))
| hBOOL(hAPP(X11067,esk287_1(X11067))) )
& ( ~ hBOOL(hAPP(X11064,X11066))
| hAPP(c_Set_OCollect(X11065),X11064) != c_Orderings_Obot__class_Obot(tc_fun(X11065,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_23])])])])])]) ).
cnf(c_0_31,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,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]) ).
cnf(c_0_33,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_34,plain,
! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_35,plain,
! [X2680,X2681] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2681,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2681,tc_HOL_Obool)),X2680)) = X2680,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_36,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_29]) ).
fof(c_0_37,plain,
! [X23] :
( ~ hBOOL(X23)
| ~ hBOOL(hAPP(c_fNot,X23)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_38,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk287_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
fof(c_0_40,plain,
! [X11058] : c_Orderings_Otop__class_Otop(tc_fun(X11058,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11058),hAPP(c_COMBK(tc_HOL_Obool,X11058),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_41,plain,
! [X862,X863] :
( X862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X863),X862) != X863 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_42,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_43,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_44,plain,
! [X532] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X532),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
fof(c_0_45,plain,
! [X17627,X17628,X17629,X17630,X17631,X17632] : hAPP(hAPP(hAPP(c_COMBB(X17632,X17631,X17630),X17629),X17628),X17627) = hAPP(X17629,hAPP(X17628,X17627)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_46,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_35]) ).
cnf(c_0_47,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_36,c_0_26]),c_0_26]) ).
fof(c_0_48,plain,
! [X17649] :
( ~ hBOOL(X17649)
| ~ hBOOL(hAPP(c_fNot,X17649)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
cnf(c_0_49,plain,
( hBOOL(hAPP(X1,esk287_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_50,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(rw,[status(thm)],[c_0_33,c_0_39]) ).
fof(c_0_51,plain,
! [X10085] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10085,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10085,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_52,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_40]) ).
cnf(c_0_53,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_41]) ).
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_42,c_0_43]) ).
fof(c_0_55,plain,
! [X864,X865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X865),hAPP(c_Nat_OSuc,X864)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X865),X864)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_56,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,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_46,c_0_47]),c_0_47]) ).
fof(c_0_59,plain,
! [X15796,X15797,X15798] : hAPP(c_Relation_Oconverse(X15798,X15797),hAPP(c_Relation_Oconverse(X15797,X15798),X15796)) = X15796,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
cnf(c_0_60,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_49]),c_0_50]),c_0_31]) ).
cnf(c_0_62,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,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_52,c_0_26]) ).
cnf(c_0_64,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_53,c_0_54]) ).
cnf(c_0_65,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_55]) ).
cnf(c_0_66,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_56,c_0_54]) ).
fof(c_0_67,plain,
! [X859] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X859),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X859,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_68,plain,
! [X57] : X57 != hAPP(c_Nat_OSuc,X57),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_69,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_57]) ).
cnf(c_0_70,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_71,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_62,c_0_47]) ).
cnf(c_0_73,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_31,c_0_63]) ).
cnf(c_0_74,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_64,c_0_65]),c_0_66]) ).
cnf(c_0_75,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_67]) ).
fof(c_0_76,plain,
! [X488] : X488 != hAPP(c_Nat_OSuc,X488),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])]) ).
cnf(c_0_77,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_71,c_0_61]) ).
cnf(c_0_79,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_72]),c_0_73]),c_0_33]),c_0_39]) ).
cnf(c_0_80,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_74,c_0_65]) ).
cnf(c_0_81,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_75,c_0_54]) ).
cnf(c_0_82,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_86,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_83]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW304+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 09:46:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 151.38/22.10 % Version: 3.5.1
% 151.38/22.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 151.38/22.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.38/22.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 151.38/22.10 % Starting new_bool_3 with 300s (1) cores
% 151.38/22.10 % Starting new_bool_1 with 300s (1) cores
% 151.38/22.10 % Starting sh5l with 300s (1) cores
% 151.38/22.10 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2270154 completed with status 0
% 151.38/22.10 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 151.38/22.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 151.38/22.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.38/22.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 151.38/22.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 151.38/22.10 % No SInE strategy applied
% 151.38/22.10 % Search class: FGHSM-SMLM33-DFFFFFNN
% 151.38/22.10 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 151.38/22.10 % Starting SubtermCWHack with 135s (1) cores
% 151.38/22.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 151.38/22.10 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 151.38/22.10 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 151.38/22.10 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 151.38/22.10 % SAT001_CA_MinMin_p005000_rr with pid 2270164 completed with status 0
% 151.38/22.10 % Result found by SAT001_CA_MinMin_p005000_rr
% 151.38/22.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 151.38/22.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 151.38/22.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 151.38/22.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 151.38/22.10 % No SInE strategy applied
% 151.38/22.10 % Search class: FGHSM-SMLM33-DFFFFFNN
% 151.38/22.10 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 151.38/22.10 % Starting SubtermCWHack with 135s (1) cores
% 151.38/22.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 151.38/22.10 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 151.38/22.10 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 151.38/22.10 % Preprocessing time : 0.322 s
% 151.38/22.10 % Presaturation interreduction done
% 151.38/22.10
% 151.38/22.10 % Proof found!
% 151.38/22.10 % SZS status ContradictoryAxioms
% 151.38/22.10 % SZS output start CNFRefutation
% See solution above
% 151.38/22.10 % Parsed axioms : 5226
% 151.38/22.10 % Removed by relevancy pruning/SinE : 0
% 151.38/22.10 % Initial clauses : 7590
% 151.38/22.10 % Removed in clause preprocessing : 238
% 151.38/22.10 % Initial clauses in saturation : 7352
% 151.38/22.10 % Processed clauses : 21112
% 151.38/22.10 % ...of these trivial : 407
% 151.38/22.10 % ...subsumed : 7515
% 151.38/22.10 % ...remaining for further processing : 13190
% 151.38/22.10 % Other redundant clauses eliminated : 1517
% 151.38/22.10 % Clauses deleted for lack of memory : 0
% 151.38/22.10 % Backward-subsumed : 137
% 151.38/22.10 % Backward-rewritten : 414
% 151.38/22.10 % Generated clauses : 192375
% 151.38/22.10 % ...of the previous two non-redundant : 183097
% 151.38/22.10 % ...aggressively subsumed : 0
% 151.38/22.10 % Contextual simplify-reflections : 35
% 151.38/22.10 % Paramodulations : 190868
% 151.38/22.10 % Factorizations : 2
% 151.38/22.10 % NegExts : 0
% 151.38/22.10 % Equation resolutions : 1570
% 151.38/22.10 % Disequality decompositions : 0
% 151.38/22.10 % Total rewrite steps : 62425
% 151.38/22.10 % ...of those cached : 44844
% 151.38/22.10 % Propositional unsat checks : 3
% 151.38/22.10 % Propositional check models : 2
% 151.38/22.10 % Propositional check unsatisfiable : 0
% 151.38/22.10 % Propositional clauses : 0
% 151.38/22.10 % Propositional clauses after purity: 0
% 151.38/22.10 % Propositional unsat core size : 0
% 151.38/22.10 % Propositional preprocessing time : 0.000
% 151.38/22.10 % Propositional encoding time : 0.296
% 151.38/22.10 % Propositional solver time : 0.175
% 151.38/22.10 % Success case prop preproc time : 0.000
% 151.38/22.10 % Success case prop encoding time : 0.000
% 151.38/22.10 % Success case prop solver time : 0.000
% 151.38/22.10 % Current number of processed clauses : 6236
% 151.38/22.10 % Positive orientable unit clauses : 1568
% 151.38/22.10 % Positive unorientable unit clauses: 127
% 151.38/22.10 % Negative unit clauses : 870
% 151.38/22.10 % Non-unit-clauses : 3671
% 151.38/22.10 % Current number of unprocessed clauses: 167965
% 151.38/22.10 % ...number of literals in the above : 329565
% 151.38/22.10 % Current number of archived formulas : 0
% 151.38/22.10 % Current number of archived clauses : 6509
% 151.38/22.10 % Clause-clause subsumption calls (NU) : 3704846
% 151.38/22.10 % Rec. Clause-clause subsumption calls : 1794693
% 151.38/22.10 % Non-unit clause-clause subsumptions : 5944
% 151.38/22.10 % Unit Clause-clause subsumption calls : 187565
% 151.38/22.10 % Rewrite failures with RHS unbound : 558
% 151.38/22.10 % BW rewrite match attempts : 37302
% 151.38/22.10 % BW rewrite match successes : 1371
% 151.38/22.10 % Condensation attempts : 214317
% 151.38/22.10 % Condensation successes : 1273
% 151.38/22.10 % Termbank termtop insertions : 6976823
% 151.38/22.10 % Search garbage collected termcells : 101765
% 151.38/22.10
% 151.38/22.10 % -------------------------------------------------
% 151.38/22.10 % User time : 19.974 s
% 151.38/22.10 % System time : 0.532 s
% 151.38/22.10 % Total time : 20.506 s
% 151.38/22.10 % Maximum resident set size: 42592 pages
% 151.38/22.10
% 151.38/22.10 % -------------------------------------------------
% 151.38/22.10 % User time : 88.409 s
% 151.38/22.10 % System time : 2.284 s
% 151.38/22.10 % Total time : 90.693 s
% 151.38/22.10 % Maximum resident set size: 12544 pages
% 151.38/22.10 % E exiting
%------------------------------------------------------------------------------