%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 03:10:20 PM UTC 2026
% Result : ContradictoryAxioms 139.55s 22.91s
% Output : CNFRefutation 139.55s
% 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 : 132 ( 16 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X27,X28] :
( hAPP(c_Set_OCollect(X28),X27) = c_Orderings_Obot__class_Obot(tc_fun(X28,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X27,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X28] : c_Orderings_Obot__class_Obot(tc_fun(X28,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X28),hAPP(c_COMBK(tc_HOL_Obool,X28),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X27,X28] : hAPP(c_Set_OCollect(X28),X27) = X27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X27,X28] : hAPP(c_Set_OCollect(X28),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28),c_fNot),X27)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28,tc_HOL_Obool)),hAPP(c_Set_OCollect(X28),X27)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X325,X30,X28,X6] : hAPP(hAPP(c_COMBK(X6,X28),X30),X325) = X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_UNIV__def,axiom,
! [X28] : c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X28),hAPP(c_COMBK(tc_HOL_Obool,X28),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X60] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X139,X28] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28,tc_HOL_Obool)),X139)) = X139,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X27] :
( ~ hBOOL(X27)
| ~ hBOOL(hAPP(c_fNot,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X28] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X5,X60] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X5) = X60
=> X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X187,X26,X27,X182,X28,X52] : hAPP(hAPP(hAPP(c_COMBB(X52,X28,X182),X27),X26),X187) = hAPP(X27,hAPP(X26,X187)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X5,X60] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),hAPP(c_Nat_OSuc,X5)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X287,X6] : hAPP(c_List_Orev(X6),hAPP(c_List_Orev(X6),X287)) = X287,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X60] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X60,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X5] : X5 != hAPP(c_Nat_OSuc,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X27,X28] :
( hAPP(c_Set_OCollect(X28),X27) = c_Orderings_Obot__class_Obot(tc_fun(X28,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X27,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X11702] : c_Orderings_Obot__class_Obot(tc_fun(X11702,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11702),hAPP(c_COMBK(tc_HOL_Obool,X11702),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X11700,X11701] : hAPP(c_Set_OCollect(X11701),X11700) = X11700,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X11670,X11671] : hAPP(c_Set_OCollect(X11671),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11671),c_fNot),X11670)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11671,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11671),X11670)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X11709,X11710,X11711,X11712,X11714] :
( ( hAPP(c_Set_OCollect(X11714),X11712) = c_Orderings_Obot__class_Obot(tc_fun(X11714,tc_HOL_Obool))
| hBOOL(hAPP(X11712,esk306_1(X11712))) )
& ( ~ hBOOL(hAPP(X11709,X11711))
| hAPP(c_Set_OCollect(X11710),X11709) != c_Orderings_Obot__class_Obot(tc_fun(X11710,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,
! [X17518,X17519,X17520,X17521] : hAPP(hAPP(c_COMBK(X17521,X17520),X17519),X17518) = X17519,
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,
! [X11690] : c_Orderings_Otop__class_Otop(tc_fun(X11690,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11690),hAPP(c_COMBK(tc_HOL_Obool,X11690),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_27,plain,
! [X60] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X60),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_28,plain,
! [X5054,X5055] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5055,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5055,tc_HOL_Obool)),X5054)) = X5054,
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,
! [X27] :
( ~ hBOOL(X27)
| ~ hBOOL(hAPP(c_fNot,X27)) ),
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,esk306_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,
! [X10815] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10815,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10815,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10815,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,
! [X876,X877] :
( X876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X877),X876) != X877 ),
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,
! [X607] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X607),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_40,plain,
! [X17522,X17523,X17524,X17525,X17526,X17527] : hAPP(hAPP(hAPP(c_COMBB(X17527,X17526,X17525),X17524),X17523),X17522) = hAPP(X17524,hAPP(X17523,X17522)),
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,
! [X17544] :
( ~ hBOOL(X17544)
| ~ hBOOL(hAPP(c_fNot,X17544)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(X1,esk306_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,
! [X882,X883] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X883),hAPP(c_Nat_OSuc,X882)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X883),X882)),
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,
! [X17238,X17239] : hAPP(c_List_Orev(X17239),hAPP(c_List_Orev(X17239),X17238)) = X17238,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
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,
! [X873] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X873),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X873,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_63,plain,
! [X5] : X5 != hAPP(c_Nat_OSuc,X5),
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_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
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,
! [X586] : X586 != hAPP(c_Nat_OSuc,X586),
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
% 0.00/0.02 % Problem : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.51 % Computer : n002.cluster.edu
% 0.10/0.51 % Model : x86_64 x86_64
% 0.10/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.51 % Memory : 8046.5625MB
% 0.10/0.51 % OS : Linux 6.8.0-71-generic
% 0.10/0.51 % CPULimit : 300
% 0.10/0.51 % WCLimit : 300
% 0.10/0.51 % DateTime : Mon Sep 21 09:51:02 UTC 2026
% 0.10/0.51 % CPUTime :
% 0.10/0.51 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.56 Running first-order theorem proving
% 0.10/0.56 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 139.55/22.91 % Version: 3.5.1
% 139.55/22.91 % Preprocessing class: FMLMSMSMSSSNFFN.
% 139.55/22.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 139.55/22.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 139.55/22.91 % Starting new_bool_3 with 300s (1) cores
% 139.55/22.91 % Starting new_bool_1 with 300s (1) cores
% 139.55/22.91 % Starting sh5l with 300s (1) cores
% 139.55/22.91 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3004009 completed with status 0
% 139.55/22.91 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 139.55/22.91 % Preprocessing class: FMLMSMSMSSSNFFN.
% 139.55/22.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 139.55/22.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 139.55/22.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 139.55/22.91 % No SInE strategy applied
% 139.55/22.91 % Search class: FGHSM-SMLM33-DFFFFFNN
% 139.55/22.91 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 139.55/22.91 % Starting SubtermCWHack with 135s (1) cores
% 139.55/22.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 139.55/22.91 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 139.55/22.91 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 139.55/22.91 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 139.55/22.91 % SAT001_CA_MinMin_p005000_rr with pid 3004050 completed with status 0
% 139.55/22.91 % Result found by SAT001_CA_MinMin_p005000_rr
% 139.55/22.91 % Preprocessing class: FMLMSMSMSSSNFFN.
% 139.55/22.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 139.55/22.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 139.55/22.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 139.55/22.91 % No SInE strategy applied
% 139.55/22.91 % Search class: FGHSM-SMLM33-DFFFFFNN
% 139.55/22.91 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 139.55/22.91 % Starting SubtermCWHack with 135s (1) cores
% 139.55/22.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 139.55/22.91 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 139.55/22.91 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 139.55/22.91 % Preprocessing time : 0.325 s
% 139.55/22.91 % Presaturation interreduction done
% 139.55/22.91
% 139.55/22.91 % Proof found!
% 139.55/22.91 % SZS status ContradictoryAxioms
% 139.55/22.91 % SZS output start CNFRefutation
% See solution above
% 139.55/22.91 % Parsed axioms : 5209
% 139.55/22.91 % Removed by relevancy pruning/SinE : 0
% 139.55/22.91 % Initial clauses : 7489
% 139.55/22.91 % Removed in clause preprocessing : 250
% 139.55/22.91 % Initial clauses in saturation : 7239
% 139.55/22.91 % Processed clauses : 21122
% 139.55/22.91 % ...of these trivial : 370
% 139.55/22.91 % ...subsumed : 6985
% 139.55/22.91 % ...remaining for further processing : 13767
% 139.55/22.91 % Other redundant clauses eliminated : 1525
% 139.55/22.91 % Clauses deleted for lack of memory : 0
% 139.55/22.91 % Backward-subsumed : 238
% 139.55/22.91 % Backward-rewritten : 430
% 139.55/22.91 % Generated clauses : 209637
% 139.55/22.91 % ...of the previous two non-redundant : 198914
% 139.55/22.91 % ...aggressively subsumed : 0
% 139.55/22.91 % Contextual simplify-reflections : 24
% 139.55/22.91 % Paramodulations : 208094
% 139.55/22.91 % Factorizations : 2
% 139.55/22.91 % NegExts : 0
% 139.55/22.91 % Equation resolutions : 1604
% 139.55/22.91 % Disequality decompositions : 0
% 139.55/22.91 % Total rewrite steps : 61626
% 139.55/22.91 % ...of those cached : 44335
% 139.55/22.91 % Propositional unsat checks : 3
% 139.55/22.91 % Propositional check models : 2
% 139.55/22.91 % Propositional check unsatisfiable : 0
% 139.55/22.91 % Propositional clauses : 0
% 139.55/22.91 % Propositional clauses after purity: 0
% 139.55/22.91 % Propositional unsat core size : 0
% 139.55/22.91 % Propositional preprocessing time : 0.000
% 139.55/22.91 % Propositional encoding time : 0.297
% 139.55/22.91 % Propositional solver time : 0.168
% 139.55/22.91 % Success case prop preproc time : 0.000
% 139.55/22.91 % Success case prop encoding time : 0.000
% 139.55/22.91 % Success case prop solver time : 0.000
% 139.55/22.91 % Current number of processed clauses : 6827
% 139.55/22.91 % Positive orientable unit clauses : 1631
% 139.55/22.91 % Positive unorientable unit clauses: 129
% 139.55/22.91 % Negative unit clauses : 1265
% 139.55/22.91 % Non-unit-clauses : 3802
% 139.55/22.91 % Current number of unprocessed clauses: 178592
% 139.55/22.91 % ...number of literals in the above : 327622
% 139.55/22.91 % Current number of archived formulas : 0
% 139.55/22.91 % Current number of archived clauses : 6489
% 139.55/22.91 % Clause-clause subsumption calls (NU) : 5186781
% 139.55/22.91 % Rec. Clause-clause subsumption calls : 2282492
% 139.55/22.91 % Non-unit clause-clause subsumptions : 4337
% 139.55/22.91 % Unit Clause-clause subsumption calls : 390783
% 139.55/22.91 % Rewrite failures with RHS unbound : 619
% 139.55/22.91 % BW rewrite match attempts : 44410
% 139.55/22.91 % BW rewrite match successes : 1342
% 139.55/22.91 % Condensation attempts : 231619
% 139.55/22.91 % Condensation successes : 994
% 139.55/22.91 % Termbank termtop insertions : 6982734
% 139.55/22.91 % Search garbage collected termcells : 99444
% 139.55/22.91
% 139.55/22.91 % -------------------------------------------------
% 139.55/22.91 % User time : 19.998 s
% 139.55/22.91 % System time : 0.551 s
% 139.55/22.91 % Total time : 20.548 s
% 139.55/22.91 % Maximum resident set size: 42412 pages
% 139.55/22.91
% 139.55/22.91 % -------------------------------------------------
% 139.55/22.91 % User time : 93.962 s
% 139.55/22.91 % System time : 2.658 s
% 139.55/22.91 % Total time : 96.620 s
% 139.55/22.91 % Maximum resident set size: 12288 pages
% 139.55/22.91 % E exiting
%------------------------------------------------------------------------------