%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW384+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 : n018.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 67.33s 12.94s
% Output : CNFRefutation 67.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 106 ( 80 unt; 0 def)
% Number of atoms : 134 ( 102 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 : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 165 ( 22 sgn 90 !; 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,
! [X33,X5] : hAPP(c_Set_OCollect(X5),X33) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Diff__cancel,axiom,
! [X15,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X15),X15) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(fact_Collect__empty__eq,axiom,
! [X33,X5] :
( hAPP(c_Set_OCollect(X5),X33) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X33,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X321,X81,X13,X5] : hAPP(hAPP(c_COMBK(X5,X13),X81),X321) = X81,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__neg__eq,axiom,
! [X33,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X33)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
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_bot__fun__def,axiom,
! [X16,X13,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X13,X5)),X16) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Zero__neq__Suc,axiom,
! [X94] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X94),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X15,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)),X15)) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X33] :
( ~ hBOOL(X33)
| ~ hBOOL(hAPP(c_fNot,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_compl__bot__eq,axiom,
! [X5] :
( class_Lattices_Oboolean__algebra(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Orderings_Obot__class_Obot(X5)) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
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_add__eq__self__zero,axiom,
! [X93,X94] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93) = X94
=> X93 = 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,X32,X33,X22,X5,X13] : hAPP(hAPP(hAPP(c_COMBB(X13,X5,X22),X33),X32),X31) = hAPP(X33,hAPP(X32,X31)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_top__apply,axiom,
! [X16,X13,X5] :
( class_Orderings_Otop(X5)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13,X5)),X16) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
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(fact_add__Suc__right,axiom,
! [X93,X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),hAPP(c_Nat_OSuc,X93)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X93)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X258,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X258)) = X258,
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,
! [X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X94,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X93] : X93 != hAPP(c_Nat_OSuc,X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_25,plain,
! [X6318] : c_Orderings_Obot__class_Obot(tc_fun(X6318,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6318),hAPP(c_COMBK(tc_HOL_Obool,X6318),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_26,plain,
! [X6305,X6306] : hAPP(c_Set_OCollect(X6306),X6305) = X6305,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_27,plain,
! [X1249,X1250] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1250,tc_HOL_Obool)),X1249),X1249) = c_Orderings_Obot__class_Obot(tc_fun(X1250,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
fof(c_0_28,plain,
! [X33,X5] :
( hAPP(c_Set_OCollect(X5),X33) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X33,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_29,plain,
! [X17580,X17581,X17582,X17583] : hAPP(hAPP(c_COMBK(X17583,X17582),X17581),X17580) = X17581,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_30,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_25]) ).
cnf(c_0_31,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X6936,X6937] : hAPP(c_Set_OCollect(X6937),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6937),c_fNot),X6936)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6937,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6937),X6936)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_34,plain,
! [X6293,X6294,X6295,X6296,X6298] :
( ( hAPP(c_Set_OCollect(X6298),X6296) = c_Orderings_Obot__class_Obot(tc_fun(X6298,tc_HOL_Obool))
| hBOOL(hAPP(X6296,esk185_1(X6296))) )
& ( ~ hBOOL(hAPP(X6293,X6295))
| hAPP(c_Set_OCollect(X6294),X6293) != c_Orderings_Obot__class_Obot(tc_fun(X6294,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_28])])])])])]) ).
cnf(c_0_35,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
fof(c_0_37,plain,
! [X6325] : c_Orderings_Otop__class_Otop(tc_fun(X6325,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6325),hAPP(c_COMBK(tc_HOL_Obool,X6325),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_38,plain,
! [X640,X641,X642] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X641,X642)),X640) = c_Orderings_Obot__class_Obot(X642)
| ~ class_Orderings_Obot(X642) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])])]) ).
fof(c_0_39,plain,
! [X7019] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7019,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7019,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7019,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(c_0_40,plain,
! [X94] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X94),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_41,plain,
! [X6687,X6688] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6688,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6688,tc_HOL_Obool)),X6687)) = X6687,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_42,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_33]) ).
fof(c_0_43,plain,
! [X33] :
( ~ hBOOL(X33)
| ~ hBOOL(hAPP(c_fNot,X33)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_44,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk185_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,plain,
hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_47,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_37]) ).
fof(c_0_48,plain,
! [X6992] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X6992),c_Orderings_Obot__class_Obot(X6992)) = c_Orderings_Otop__class_Otop(X6992)
| ~ class_Lattices_Oboolean__algebra(X6992) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])]) ).
cnf(c_0_49,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_38]) ).
cnf(c_0_50,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
cnf(c_0_51,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_39]) ).
fof(c_0_52,plain,
! [X4466,X4467] :
( X4466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4467),X4466) != X4467 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_53,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_54,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_55,plain,
! [X4455] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4455),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
fof(c_0_56,plain,
! [X17584,X17585,X17586,X17587,X17588,X17589] : hAPP(hAPP(hAPP(c_COMBB(X17589,X17588,X17587),X17586),X17585),X17584) = hAPP(X17586,hAPP(X17585,X17584)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_57,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_41]) ).
cnf(c_0_58,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_42,c_0_31]),c_0_31]) ).
fof(c_0_59,plain,
! [X17606] :
( ~ hBOOL(X17606)
| ~ hBOOL(hAPP(c_fNot,X17606)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_43])]) ).
cnf(c_0_60,plain,
( hBOOL(hAPP(X1,esk185_1(X1)))
| X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_31]),c_0_32]) ).
cnf(c_0_61,plain,
hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2),X3) = c_fFalse,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_62,plain,
! [X3487,X3488,X3489] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X3488,X3489)),X3487) = c_Orderings_Otop__class_Otop(X3489)
| ~ class_Orderings_Otop(X3489) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])])]) ).
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_47,c_0_31]) ).
cnf(c_0_64,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_48]) ).
cnf(c_0_65,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(c_0_66,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32]),c_0_45]) ).
cnf(c_0_67,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[c_0_51,c_0_32]) ).
cnf(c_0_68,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_52]) ).
cnf(c_0_69,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_70,plain,
! [X4095,X4096] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4096),hAPP(c_Nat_OSuc,X4095)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4096),X4095)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_71,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_72,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_73,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_57,c_0_58]),c_0_58]) ).
fof(c_0_74,plain,
! [X15994,X15995] : hAPP(c_List_Orev(X15995),hAPP(c_List_Orev(X15995),X15994)) = X15994,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_75,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_76,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_60]),c_0_61]),c_0_35]) ).
cnf(c_0_77,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_62]) ).
cnf(c_0_78,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).
cnf(c_0_79,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_63]) ).
cnf(c_0_80,plain,
c_Orderings_Otop__class_Otop(tc_HOL_Obool) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_HOL_Obool),c_fFalse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_81,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))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[c_0_67,c_0_58]) ).
cnf(c_0_82,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_68,c_0_69]) ).
cnf(c_0_83,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_70]) ).
cnf(c_0_84,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_71,c_0_69]) ).
fof(c_0_85,plain,
! [X4470] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4470),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4470,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_86,plain,
! [X93] : X93 != hAPP(c_Nat_OSuc,X93),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_87,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_72]) ).
cnf(c_0_88,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_89,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_90,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_77,c_0_78]),c_0_79]),c_0_80]) ).
cnf(c_0_91,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_81]),c_0_45]),c_0_79]) ).
cnf(c_0_92,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_82,c_0_83]),c_0_84]) ).
cnf(c_0_93,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_85]) ).
fof(c_0_94,plain,
! [X4061] : X4061 != hAPP(c_Nat_OSuc,X4061),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_86])]) ).
cnf(c_0_95,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_89,c_0_76]) ).
cnf(c_0_97,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_90]),c_0_91]) ).
cnf(c_0_98,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_92,c_0_83]) ).
cnf(c_0_99,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_93,c_0_69]) ).
cnf(c_0_100,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_101,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_102,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_104,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_105,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_101]),c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW384+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 % Computer : n018.cluster.edu
% 0.22/0.51 % Model : x86_64 x86_64
% 0.22/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.51 % Memory : 8046.5625MB
% 0.22/0.51 % OS : Linux 6.8.0-71-generic
% 0.22/0.51 % CPULimit : 300
% 0.22/0.51 % WCLimit : 300
% 0.22/0.51 % DateTime : Mon Sep 21 09:52:45 UTC 2026
% 0.22/0.52 % CPUTime :
% 0.22/0.52 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.63 Running first-order theorem proving
% 0.22/0.63 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
% 67.33/12.94 % Version: 3.5.1
% 67.33/12.94 % Preprocessing class: FMLMSLSMSSSNFFN.
% 67.33/12.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.33/12.94 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 67.33/12.94 % Starting new_bool_3 with 300s (1) cores
% 67.33/12.94 % Starting new_bool_1 with 300s (1) cores
% 67.33/12.94 % Starting sh5l with 300s (1) cores
% 67.33/12.94 % SAT001_MinMin_p005000_rr_RG with pid 1589091 completed with status 0
% 67.33/12.94 % Result found by SAT001_MinMin_p005000_rr_RG
% 67.33/12.94 % Preprocessing class: FMLMSLSMSSSNFFN.
% 67.33/12.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.33/12.94 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 67.33/12.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.33/12.94 % No SInE strategy applied
% 67.33/12.94 % Search class: FGHSM-SMLM33-DFFFFFNN
% 67.33/12.94 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 67.33/12.94 % Starting SubtermCWHack with 135s (1) cores
% 67.33/12.94 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 67.33/12.94 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 67.33/12.94 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 67.33/12.94 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 67.33/12.94 % SAT001_MinMin_p005000_rr_RG with pid 1589099 completed with status 0
% 67.33/12.94 % Result found by SAT001_MinMin_p005000_rr_RG
% 67.33/12.94 % Preprocessing class: FMLMSLSMSSSNFFN.
% 67.33/12.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.33/12.94 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 67.33/12.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.33/12.94 % No SInE strategy applied
% 67.33/12.94 % Search class: FGHSM-SMLM33-DFFFFFNN
% 67.33/12.94 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 67.33/12.94 % Starting SubtermCWHack with 135s (1) cores
% 67.33/12.94 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 67.33/12.94 % Preprocessing time : 0.338 s
% 67.33/12.94 % Presaturation interreduction done
% 67.33/12.94
% 67.33/12.94 % Proof found!
% 67.33/12.94 % SZS status ContradictoryAxioms
% 67.33/12.94 % SZS output start CNFRefutation
% See solution above
% 67.33/12.94 % Parsed axioms : 5250
% 67.33/12.94 % Removed by relevancy pruning/SinE : 0
% 67.33/12.94 % Initial clauses : 7553
% 67.33/12.94 % Removed in clause preprocessing : 231
% 67.33/12.94 % Initial clauses in saturation : 7322
% 67.33/12.94 % Processed clauses : 21745
% 67.33/12.94 % ...of these trivial : 467
% 67.33/12.94 % ...subsumed : 7553
% 67.33/12.94 % ...remaining for further processing : 13725
% 67.33/12.94 % Other redundant clauses eliminated : 1349
% 67.33/12.94 % Clauses deleted for lack of memory : 0
% 67.33/12.94 % Backward-subsumed : 363
% 67.33/12.94 % Backward-rewritten : 535
% 67.33/12.94 % Generated clauses : 220873
% 67.33/12.94 % ...of the previous two non-redundant : 209364
% 67.33/12.94 % ...aggressively subsumed : 0
% 67.33/12.94 % Contextual simplify-reflections : 50
% 67.33/12.94 % Paramodulations : 219439
% 67.33/12.94 % Factorizations : 6
% 67.33/12.94 % NegExts : 0
% 67.33/12.94 % Equation resolutions : 1495
% 67.33/12.94 % Disequality decompositions : 0
% 67.33/12.94 % Total rewrite steps : 66339
% 67.33/12.94 % ...of those cached : 46379
% 67.33/12.94 % Propositional unsat checks : 3
% 67.33/12.94 % Propositional check models : 2
% 67.33/12.94 % Propositional check unsatisfiable : 0
% 67.33/12.94 % Propositional clauses : 0
% 67.33/12.94 % Propositional clauses after purity: 0
% 67.33/12.94 % Propositional unsat core size : 0
% 67.33/12.94 % Propositional preprocessing time : 0.000
% 67.33/12.94 % Propositional encoding time : 0.149
% 67.33/12.94 % Propositional solver time : 0.054
% 67.33/12.94 % Success case prop preproc time : 0.000
% 67.33/12.94 % Success case prop encoding time : 0.000
% 67.33/12.94 % Success case prop solver time : 0.000
% 67.33/12.94 % Current number of processed clauses : 6411
% 67.33/12.94 % Positive orientable unit clauses : 1759
% 67.33/12.94 % Positive unorientable unit clauses: 130
% 67.33/12.94 % Negative unit clauses : 1040
% 67.33/12.94 % Non-unit-clauses : 3482
% 67.33/12.94 % Current number of unprocessed clauses: 185938
% 67.33/12.94 % ...number of literals in the above : 345293
% 67.33/12.94 % Current number of archived formulas : 0
% 67.33/12.94 % Current number of archived clauses : 6866
% 67.33/12.94 % Clause-clause subsumption calls (NU) : 6310706
% 67.33/12.94 % Rec. Clause-clause subsumption calls : 2558337
% 67.33/12.94 % Non-unit clause-clause subsumptions : 4657
% 67.33/12.94 % Unit Clause-clause subsumption calls : 220756
% 67.33/12.94 % Rewrite failures with RHS unbound : 0
% 67.33/12.94 % BW rewrite match attempts : 41999
% 67.33/12.94 % BW rewrite match successes : 1451
% 67.33/12.94 % Condensation attempts : 0
% 67.33/12.94 % Condensation successes : 0
% 67.33/12.94 % Termbank termtop insertions : 7540393
% 67.33/12.94 % Search garbage collected termcells : 99465
% 67.33/12.94
% 67.33/12.94 % -------------------------------------------------
% 67.33/12.94 % User time : 10.624 s
% 67.33/12.94 % System time : 0.346 s
% 67.33/12.94 % Total time : 10.969 s
% 67.33/12.94 % Maximum resident set size: 42384 pages
% 67.33/12.94
% 67.33/12.94 % -------------------------------------------------
% 67.33/12.94 % User time : 42.709 s
% 67.33/12.94 % System time : 1.331 s
% 67.33/12.94 % Total time : 44.040 s
% 67.33/12.94 % Maximum resident set size: 12288 pages
% 67.33/12.94 % E exiting
%------------------------------------------------------------------------------