%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW377+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:25 PM UTC 2026
% Result : ContradictoryAxioms 102.22s 17.82s
% Output : CNFRefutation 102.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 101 ( 75 unt; 0 def)
% Number of atoms : 129 ( 97 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 35 ~; 21 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 153 ( 20 sgn 86 !; 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,
! [X16,X10] : hAPP(c_Set_OCollect(X10),X16) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X16,X10] :
( hAPP(c_Set_OCollect(X10),X16) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X16,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X323,X19,X23,X10] : hAPP(hAPP(c_COMBK(X10,X23),X19),X323) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__neg__eq,axiom,
! [X16,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X16)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__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_compl__bot__eq,axiom,
! [X10] :
( class_Lattices_Oboolean__algebra(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Orderings_Obot__class_Obot(X10)) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(fact_bot__fun__def,axiom,
! [X28,X23,X10] :
( class_Orderings_Obot(X10)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X23,X10)),X28) = c_Orderings_Obot__class_Obot(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X102] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X102),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X30,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)),X30)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X16] :
( ~ hBOOL(X16)
| ~ hBOOL(hAPP(c_fNot,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
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_Compl__UNIV__eq,axiom,
! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X54,X102] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X54) = X102
=> X54 = 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,
! [X57,X15,X16,X41,X10,X23] : hAPP(hAPP(hAPP(c_COMBB(X23,X10,X41),X16),X15),X57) = hAPP(X16,hAPP(X15,X57)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_top__apply,axiom,
! [X28,X23,X10] :
( class_Orderings_Otop(X10)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X23,X10)),X28) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__Suc__right,axiom,
! [X54,X102] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),hAPP(c_Nat_OSuc,X54)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X248,X10] : hAPP(c_List_Orev(X10),hAPP(c_List_Orev(X10),X248)) = X248,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X102] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X102),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X102,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X54] : X54 != hAPP(c_Nat_OSuc,X54),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_24,plain,
! [X7597] : c_Orderings_Obot__class_Obot(tc_fun(X7597,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7597),hAPP(c_COMBK(tc_HOL_Obool,X7597),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_25,plain,
! [X7476,X7477] : hAPP(c_Set_OCollect(X7477),X7476) = X7476,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_26,plain,
! [X16,X10] :
( hAPP(c_Set_OCollect(X10),X16) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X16,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_27,plain,
! [X17642,X17643,X17644,X17645] : hAPP(hAPP(c_COMBK(X17645,X17644),X17643),X17642) = X17643,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_28,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_24]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X7880,X7881] : hAPP(c_Set_OCollect(X7881),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7881),c_fNot),X7880)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7881,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7881),X7880)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_31,plain,
! [X7564,X7565,X7566,X7567,X7569] :
( ( hAPP(c_Set_OCollect(X7569),X7567) = c_Orderings_Obot__class_Obot(tc_fun(X7569,tc_HOL_Obool))
| hBOOL(hAPP(X7567,esk213_1(X7567))) )
& ( ~ hBOOL(hAPP(X7564,X7566))
| hAPP(c_Set_OCollect(X7565),X7564) != c_Orderings_Obot__class_Obot(tc_fun(X7565,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_26])])])])])]) ).
fof(c_0_32,plain,
! [X7605] : c_Orderings_Otop__class_Otop(tc_fun(X7605,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7605),hAPP(c_COMBK(tc_HOL_Obool,X7605),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_33,plain,
! [X7670] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X7670),c_Orderings_Obot__class_Obot(X7670)) = c_Orderings_Otop__class_Otop(X7670)
| ~ class_Lattices_Oboolean__algebra(X7670) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])]) ).
fof(c_0_34,plain,
! [X887,X888,X889] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X888,X889)),X887) = c_Orderings_Obot__class_Obot(X889)
| ~ class_Orderings_Obot(X889) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])])]) ).
cnf(c_0_35,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,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_28,c_0_29]) ).
fof(c_0_37,plain,
! [X102] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X102),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_38,plain,
! [X7992,X7993] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7993,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7993,tc_HOL_Obool)),X7992)) = X7992,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_39,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_30]) ).
fof(c_0_40,plain,
! [X16] :
( ~ hBOOL(X16)
| ~ hBOOL(hAPP(c_fNot,X16)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_41,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk213_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,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_32]) ).
cnf(c_0_43,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(c_0_45,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_34]) ).
cnf(c_0_46,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
cnf(c_0_47,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_48,plain,
! [X7885] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7885,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7885,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7885,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(c_0_49,plain,
! [X3519,X3520] :
( X3519 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3520),X3519) != X3520 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_50,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_51,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_52,plain,
! [X3504] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3504),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
fof(c_0_53,plain,
! [X17646,X17647,X17648,X17649,X17650,X17651] : hAPP(hAPP(hAPP(c_COMBB(X17651,X17650,X17649),X17648),X17647),X17646) = hAPP(X17648,hAPP(X17647,X17646)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_54,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_38]) ).
cnf(c_0_55,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_39,c_0_29]),c_0_29]) ).
fof(c_0_56,plain,
! [X17668] :
( ~ hBOOL(X17668)
| ~ hBOOL(hAPP(c_fNot,X17668)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
cnf(c_0_57,plain,
( hBOOL(hAPP(X1,esk213_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_41,c_0_29]) ).
fof(c_0_58,plain,
! [X895,X896,X897] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X896,X897)),X895) = c_Orderings_Otop__class_Otop(X897)
| ~ class_Orderings_Otop(X897) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])])]) ).
cnf(c_0_59,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_42,c_0_29]) ).
cnf(c_0_60,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_61,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_62,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_48]) ).
cnf(c_0_63,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_49]) ).
cnf(c_0_64,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_65,plain,
! [X2829,X2830] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2830),hAPP(c_Nat_OSuc,X2829)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2830),X2829)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_66,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_67,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,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_54,c_0_55]),c_0_55]) ).
fof(c_0_69,plain,
! [X16600,X16601] : hAPP(c_List_Orev(X16601),hAPP(c_List_Orev(X16601),X16600)) = X16600,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_70,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_71,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_57]),c_0_47]),c_0_35]) ).
cnf(c_0_72,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3) = c_Orderings_Otop__class_Otop(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_73,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).
cnf(c_0_74,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_35,c_0_59]) ).
cnf(c_0_75,plain,
c_Orderings_Otop__class_Otop(tc_HOL_Obool) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fFalse),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_76,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_62,c_0_55]) ).
cnf(c_0_77,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_63,c_0_64]) ).
cnf(c_0_78,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_65]) ).
cnf(c_0_79,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_66,c_0_64]) ).
fof(c_0_80,plain,
! [X3516] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3516),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3516,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_81,plain,
! [X54] : X54 != hAPP(c_Nat_OSuc,X54),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_82,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_67]) ).
cnf(c_0_83,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_84,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_85,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_75]) ).
cnf(c_0_86,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_76]),c_0_47]),c_0_74]) ).
cnf(c_0_87,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_77,c_0_78]),c_0_79]) ).
cnf(c_0_88,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_80]) ).
fof(c_0_89,plain,
! [X2268] : X2268 != hAPP(c_Nat_OSuc,X2268),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_81])]) ).
cnf(c_0_90,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_84,c_0_71]) ).
cnf(c_0_92,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_85]),c_0_86]) ).
cnf(c_0_93,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_87,c_0_78]) ).
cnf(c_0_94,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_88,c_0_64]) ).
cnf(c_0_95,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_96,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_97,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_99,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_100,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_96]),c_0_95]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW377+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 09:51:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 102.22/17.82 % Version: 3.5.1
% 102.22/17.82 % Preprocessing class: FMLMSLSMSSSNFFN.
% 102.22/17.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.22/17.82 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 102.22/17.82 % Starting new_bool_3 with 300s (1) cores
% 102.22/17.82 % Starting new_bool_1 with 300s (1) cores
% 102.22/17.82 % Starting sh5l with 300s (1) cores
% 102.22/17.82 % SAT001_MinMin_p005000_rr_RG with pid 2624359 completed with status 0
% 102.22/17.82 % Result found by SAT001_MinMin_p005000_rr_RG
% 102.22/17.82 % Preprocessing class: FMLMSLSMSSSNFFN.
% 102.22/17.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.22/17.82 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 102.22/17.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 102.22/17.82 % No SInE strategy applied
% 102.22/17.82 % Search class: FGHSM-SMLM33-DFFFFFNN
% 102.22/17.82 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 102.22/17.82 % Starting SubtermCWHack with 135s (1) cores
% 102.22/17.82 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 102.22/17.82 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 102.22/17.82 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 102.22/17.82 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 102.22/17.82 % SAT001_MinMin_p005000_rr_RG with pid 2624398 completed with status 0
% 102.22/17.82 % Result found by SAT001_MinMin_p005000_rr_RG
% 102.22/17.82 % Preprocessing class: FMLMSLSMSSSNFFN.
% 102.22/17.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 102.22/17.82 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 102.22/17.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 102.22/17.82 % No SInE strategy applied
% 102.22/17.82 % Search class: FGHSM-SMLM33-DFFFFFNN
% 102.22/17.82 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 102.22/17.82 % Starting SubtermCWHack with 135s (1) cores
% 102.22/17.82 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 102.22/17.82 % Preprocessing time : 0.330 s
% 102.22/17.82 % Presaturation interreduction done
% 102.22/17.82
% 102.22/17.82 % Proof found!
% 102.22/17.82 % SZS status ContradictoryAxioms
% 102.22/17.82 % SZS output start CNFRefutation
% See solution above
% 102.22/17.82 % Parsed axioms : 5240
% 102.22/17.82 % Removed by relevancy pruning/SinE : 0
% 102.22/17.82 % Initial clauses : 7570
% 102.22/17.82 % Removed in clause preprocessing : 234
% 102.22/17.82 % Initial clauses in saturation : 7336
% 102.22/17.82 % Processed clauses : 21817
% 102.22/17.82 % ...of these trivial : 550
% 102.22/17.82 % ...subsumed : 7355
% 102.22/17.82 % ...remaining for further processing : 13912
% 102.22/17.82 % Other redundant clauses eliminated : 1307
% 102.22/17.82 % Clauses deleted for lack of memory : 0
% 102.22/17.82 % Backward-subsumed : 417
% 102.22/17.82 % Backward-rewritten : 578
% 102.22/17.82 % Generated clauses : 204445
% 102.22/17.82 % ...of the previous two non-redundant : 192992
% 102.22/17.82 % ...aggressively subsumed : 0
% 102.22/17.82 % Contextual simplify-reflections : 42
% 102.22/17.82 % Paramodulations : 203137
% 102.22/17.82 % Factorizations : 6
% 102.22/17.82 % NegExts : 0
% 102.22/17.82 % Equation resolutions : 1369
% 102.22/17.82 % Disequality decompositions : 0
% 102.22/17.82 % Total rewrite steps : 68721
% 102.22/17.82 % ...of those cached : 50307
% 102.22/17.82 % Propositional unsat checks : 3
% 102.22/17.82 % Propositional check models : 2
% 102.22/17.82 % Propositional check unsatisfiable : 0
% 102.22/17.82 % Propositional clauses : 0
% 102.22/17.82 % Propositional clauses after purity: 0
% 102.22/17.82 % Propositional unsat core size : 0
% 102.22/17.82 % Propositional preprocessing time : 0.000
% 102.22/17.82 % Propositional encoding time : 0.231
% 102.22/17.82 % Propositional solver time : 0.106
% 102.22/17.82 % Success case prop preproc time : 0.000
% 102.22/17.82 % Success case prop encoding time : 0.000
% 102.22/17.82 % Success case prop solver time : 0.000
% 102.22/17.82 % Current number of processed clauses : 6513
% 102.22/17.82 % Positive orientable unit clauses : 1674
% 102.22/17.82 % Positive unorientable unit clauses: 128
% 102.22/17.82 % Negative unit clauses : 1006
% 102.22/17.82 % Non-unit-clauses : 3705
% 102.22/17.82 % Current number of unprocessed clauses: 170789
% 102.22/17.82 % ...number of literals in the above : 321909
% 102.22/17.82 % Current number of archived formulas : 0
% 102.22/17.82 % Current number of archived clauses : 6949
% 102.22/17.82 % Clause-clause subsumption calls (NU) : 6292517
% 102.22/17.82 % Rec. Clause-clause subsumption calls : 2585956
% 102.22/17.82 % Non-unit clause-clause subsumptions : 4821
% 102.22/17.82 % Unit Clause-clause subsumption calls : 260169
% 102.22/17.82 % Rewrite failures with RHS unbound : 0
% 102.22/17.82 % BW rewrite match attempts : 41065
% 102.22/17.82 % BW rewrite match successes : 1375
% 102.22/17.82 % Condensation attempts : 0
% 102.22/17.82 % Condensation successes : 0
% 102.22/17.82 % Termbank termtop insertions : 6883694
% 102.22/17.82 % Search garbage collected termcells : 100418
% 102.22/17.82
% 102.22/17.82 % -------------------------------------------------
% 102.22/17.82 % User time : 15.157 s
% 102.22/17.82 % System time : 0.441 s
% 102.22/17.82 % Total time : 15.598 s
% 102.22/17.82 % Maximum resident set size: 42680 pages
% 102.22/17.82
% 102.22/17.82 % -------------------------------------------------
% 102.22/17.82 % User time : 67.824 s
% 102.22/17.82 % System time : 1.993 s
% 102.22/17.82 % Total time : 69.816 s
% 102.22/17.82 % Maximum resident set size: 12544 pages
% 102.22/17.82 % E exiting
%------------------------------------------------------------------------------