%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW324+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 : n005.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 03:10:18 PM UTC 2026
% Result : ContradictoryAxioms 130.90s 20.75s
% Output : CNFRefutation 130.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 87 ( 66 unt; 0 def)
% Number of atoms : 110 ( 93 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 32 ~; 18 |; 1 &)
% ( 2 <=>; 2 =>; 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; 0-3 aty)
% Number of variables : 145 ( 19 sgn 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_empty__def,axiom,
! [X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X13,X10] : hAPP(c_Set_OCollect(X10),X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X13,X10] :
( hAPP(c_Set_OCollect(X10),X13) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X13,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X315,X314,X10,X66] : hAPP(hAPP(c_COMBK(X66,X10),X314),X315) = X314,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__neg__eq,axiom,
! [X13,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X13)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_Zero__neq__Suc,axiom,
! [X112] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X112),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X17,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X17)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X13] :
( ~ hBOOL(X13)
| ~ hBOOL(hAPP(c_fNot,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_UNIV__def,axiom,
! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X111,X112] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X112),X111) = X112
=> X111 = 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,
! [X43,X23,X13,X26,X10,X16] : hAPP(hAPP(hAPP(c_COMBB(X16,X10,X26),X13),X23),X43) = hAPP(X13,hAPP(X23,X43)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X111,X112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X112),hAPP(c_Nat_OSuc,X111)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X112),X111)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X235,X66] : hAPP(c_List_Orev(X66),hAPP(c_List_Orev(X66),X235)) = X235,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X112),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X111] : X111 != hAPP(c_Nat_OSuc,X111),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X979] : c_Orderings_Obot__class_Obot(tc_fun(X979,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X979),hAPP(c_COMBK(tc_HOL_Obool,X979),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X848,X849] : hAPP(c_Set_OCollect(X849),X848) = X848,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X13,X10] :
( hAPP(c_Set_OCollect(X10),X13) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X13,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X17698,X17699,X17700,X17701] : hAPP(hAPP(c_COMBK(X17701,X17700),X17699),X17698) = X17699,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_23,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_24,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X5180,X5181] : hAPP(c_Set_OCollect(X5181),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5181),c_fNot),X5180)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5181,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5181),X5180)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_26,plain,
! [X895,X896,X897,X898,X900] :
( ( hAPP(c_Set_OCollect(X900),X898) = c_Orderings_Obot__class_Obot(tc_fun(X900,tc_HOL_Obool))
| hBOOL(hAPP(X898,esk14_1(X898))) )
& ( ~ hBOOL(hAPP(X895,X897))
| hAPP(c_Set_OCollect(X896),X895) != c_Orderings_Obot__class_Obot(tc_fun(X896,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_21])])])])])]) ).
fof(c_0_27,plain,
! [X316,X317] :
( X317 = X316
| hAPP(X317,esk1_2(X316,X317)) != hAPP(X316,esk1_2(X316,X317)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_28,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,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_23,c_0_24]) ).
fof(c_0_30,plain,
! [X112] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X112),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_31,plain,
! [X5324,X5325] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5325,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5325,tc_HOL_Obool)),X5324)) = X5324,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_32,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_25]) ).
fof(c_0_33,plain,
! [X13] :
( ~ hBOOL(X13)
| ~ hBOOL(hAPP(c_fNot,X13)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_34,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk14_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X10335] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10335,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10335,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10335,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_36,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_38,plain,
! [X10250] : c_Orderings_Otop__class_Otop(tc_fun(X10250,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10250),hAPP(c_COMBK(tc_HOL_Obool,X10250),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_39,plain,
! [X3033,X3034] :
( X3033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3034),X3033) != X3034 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_40,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_41,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_42,plain,
! [X3022] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3022),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_43,plain,
! [X17702,X17703,X17704,X17705,X17706,X17707] : hAPP(hAPP(hAPP(c_COMBB(X17707,X17706,X17705),X17704),X17703),X17702) = hAPP(X17704,hAPP(X17703,X17702)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_44,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_31]) ).
cnf(c_0_45,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_32,c_0_24]),c_0_24]) ).
fof(c_0_46,plain,
! [X17724] :
( ~ hBOOL(X17724)
| ~ hBOOL(hAPP(c_fNot,X17724)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(X1,esk14_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_48,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_35]) ).
cnf(c_0_49,plain,
( hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_fFalse
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_50,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_38]) ).
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_39]) ).
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_40,c_0_41]) ).
fof(c_0_53,plain,
! [X2590,X2591] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2591),hAPP(c_Nat_OSuc,X2590)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2591),X2590)),
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_42]) ).
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_43]) ).
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_44,c_0_45]),c_0_45]) ).
fof(c_0_57,plain,
! [X15770,X15771] : hAPP(c_List_Orev(X15771),hAPP(c_List_Orev(X15771),X15770)) = X15770,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_58,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_37]),c_0_28]) ).
cnf(c_0_60,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_48,c_0_45]) ).
cnf(c_0_61,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_49,c_0_37]) ).
cnf(c_0_62,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_50,c_0_24]) ).
cnf(c_0_63,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_64,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_65,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_66,plain,
! [X3037] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3037),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3037,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_67,plain,
! [X111] : X111 != hAPP(c_Nat_OSuc,X111),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_68,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_69,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_73,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_63,c_0_64]),c_0_65]) ).
cnf(c_0_74,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_66]) ).
fof(c_0_75,plain,
! [X2240] : X2240 != hAPP(c_Nat_OSuc,X2240),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_67])]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_78,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_71]),c_0_72]),c_0_37]) ).
cnf(c_0_79,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_73,c_0_64]) ).
cnf(c_0_80,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_74,c_0_52]) ).
cnf(c_0_81,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_86,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_82]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW324+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:47:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 130.90/20.75 % Version: 3.5.1
% 130.90/20.75 % Preprocessing class: FMLMSMSMSSSNFFN.
% 130.90/20.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.90/20.75 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 130.90/20.75 % Starting new_bool_3 with 300s (1) cores
% 130.90/20.75 % Starting new_bool_1 with 300s (1) cores
% 130.90/20.75 % Starting sh5l with 300s (1) cores
% 130.90/20.75 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3152966 completed with status 0
% 130.90/20.75 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 130.90/20.75 % Preprocessing class: FMLMSMSMSSSNFFN.
% 130.90/20.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.90/20.75 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 130.90/20.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 130.90/20.75 % No SInE strategy applied
% 130.90/20.75 % Search class: FGHSM-SMLM33-DFFFFFNN
% 130.90/20.75 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 130.90/20.75 % Starting SubtermCWHack with 135s (1) cores
% 130.90/20.75 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 130.90/20.75 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 130.90/20.75 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 130.90/20.75 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 130.90/20.75 % SAT001_CA_MinMin_p005000_rr with pid 3152982 completed with status 0
% 130.90/20.75 % Result found by SAT001_CA_MinMin_p005000_rr
% 130.90/20.75 % Preprocessing class: FMLMSMSMSSSNFFN.
% 130.90/20.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 130.90/20.75 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 130.90/20.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 130.90/20.75 % No SInE strategy applied
% 130.90/20.75 % Search class: FGHSM-SMLM33-DFFFFFNN
% 130.90/20.75 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 130.90/20.75 % Starting SubtermCWHack with 135s (1) cores
% 130.90/20.75 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 130.90/20.75 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 130.90/20.75 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 130.90/20.75 % Preprocessing time : 0.308 s
% 130.90/20.75 % Presaturation interreduction done
% 130.90/20.75
% 130.90/20.75 % Proof found!
% 130.90/20.75 % SZS status ContradictoryAxioms
% 130.90/20.75 % SZS output start CNFRefutation
% See solution above
% 130.90/20.75 % Parsed axioms : 5230
% 130.90/20.75 % Removed by relevancy pruning/SinE : 0
% 130.90/20.75 % Initial clauses : 7581
% 130.90/20.75 % Removed in clause preprocessing : 228
% 130.90/20.75 % Initial clauses in saturation : 7353
% 130.90/20.75 % Processed clauses : 21338
% 130.90/20.75 % ...of these trivial : 421
% 130.90/20.75 % ...subsumed : 7446
% 130.90/20.75 % ...remaining for further processing : 13471
% 130.90/20.75 % Other redundant clauses eliminated : 1392
% 130.90/20.75 % Clauses deleted for lack of memory : 0
% 130.90/20.75 % Backward-subsumed : 170
% 130.90/20.75 % Backward-rewritten : 412
% 130.90/20.75 % Generated clauses : 199132
% 130.90/20.75 % ...of the previous two non-redundant : 189572
% 130.90/20.75 % ...aggressively subsumed : 0
% 130.90/20.75 % Contextual simplify-reflections : 32
% 130.90/20.75 % Paramodulations : 197757
% 130.90/20.75 % Factorizations : 2
% 130.90/20.75 % NegExts : 0
% 130.90/20.75 % Equation resolutions : 1439
% 130.90/20.75 % Disequality decompositions : 0
% 130.90/20.75 % Total rewrite steps : 64703
% 130.90/20.75 % ...of those cached : 45610
% 130.90/20.75 % Propositional unsat checks : 3
% 130.90/20.75 % Propositional check models : 2
% 130.90/20.75 % Propositional check unsatisfiable : 0
% 130.90/20.75 % Propositional clauses : 0
% 130.90/20.75 % Propositional clauses after purity: 0
% 130.90/20.75 % Propositional unsat core size : 0
% 130.90/20.75 % Propositional preprocessing time : 0.000
% 130.90/20.75 % Propositional encoding time : 0.302
% 130.90/20.75 % Propositional solver time : 0.190
% 130.90/20.75 % Success case prop preproc time : 0.000
% 130.90/20.75 % Success case prop encoding time : 0.000
% 130.90/20.75 % Success case prop solver time : 0.000
% 130.90/20.75 % Current number of processed clauses : 6445
% 130.90/20.75 % Positive orientable unit clauses : 1599
% 130.90/20.75 % Positive unorientable unit clauses: 127
% 130.90/20.75 % Negative unit clauses : 1034
% 130.90/20.75 % Non-unit-clauses : 3685
% 130.90/20.75 % Current number of unprocessed clauses: 176574
% 130.90/20.75 % ...number of literals in the above : 338845
% 130.90/20.75 % Current number of archived formulas : 0
% 130.90/20.75 % Current number of archived clauses : 6573
% 130.90/20.75 % Clause-clause subsumption calls (NU) : 5589589
% 130.90/20.75 % Rec. Clause-clause subsumption calls : 2453946
% 130.90/20.75 % Non-unit clause-clause subsumptions : 5521
% 130.90/20.75 % Unit Clause-clause subsumption calls : 192906
% 130.90/20.75 % Rewrite failures with RHS unbound : 537
% 130.90/20.75 % BW rewrite match attempts : 38091
% 130.90/20.75 % BW rewrite match successes : 1354
% 130.90/20.75 % Condensation attempts : 221295
% 130.90/20.75 % Condensation successes : 970
% 130.90/20.75 % Termbank termtop insertions : 7156525
% 130.90/20.75 % Search garbage collected termcells : 102222
% 130.90/20.75
% 130.90/20.75 % -------------------------------------------------
% 130.90/20.75 % User time : 19.131 s
% 130.90/20.75 % System time : 0.502 s
% 130.90/20.75 % Total time : 19.633 s
% 130.90/20.75 % Maximum resident set size: 42620 pages
% 130.90/20.75
% 130.90/20.75 % -------------------------------------------------
% 130.90/20.75 % User time : 88.336 s
% 130.90/20.75 % System time : 2.266 s
% 130.90/20.75 % Total time : 90.602 s
% 130.90/20.75 % Maximum resident set size: 12544 pages
% 130.90/20.75 % E exiting
%------------------------------------------------------------------------------