%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW378+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 : n017.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 138.65s 21.96s
% Output : CNFRefutation 138.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of formulae : 113 ( 80 unt; 0 def)
% Number of atoms : 148 ( 111 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 40 ~; 26 |; 1 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 170 ( 23 sgn 95 !; 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(help_c__COMBK__1,axiom,
! [X325,X19,X28,X10] : hAPP(hAPP(c_COMBK(X10,X28),X19),X325) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
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,
! [X25,X28,X10] :
( class_Orderings_Obot(X10)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X28,X10)),X25) = c_Orderings_Obot__class_Obot(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
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_top__apply,axiom,
! [X25,X28,X10] :
( class_Orderings_Otop(X10)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X28,X10)),X25) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_sup__top__left,axiom,
! [X33,X10] :
( class_Lattices_Obounded__lattice__top(X10)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Orderings_Otop__class_Otop(X10)),X33) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__left) ).
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_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(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_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
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_Zero__neq__Suc,axiom,
! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X27,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)),X27)) = X27,
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(fact_add__eq__self__zero,axiom,
! [X51,X100] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X51) = X100
=> X51 = 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,
! [X54,X15,X16,X40,X10,X28] : hAPP(hAPP(hAPP(c_COMBB(X28,X10,X40),X16),X15),X54) = hAPP(X16,hAPP(X15,X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X51,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),hAPP(c_Nat_OSuc,X51)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X250,X10] : hAPP(c_List_Orev(X10),hAPP(c_List_Orev(X10),X250)) = X250,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X100,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X51] : X51 != hAPP(c_Nat_OSuc,X51),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_27,plain,
! [X7169] : c_Orderings_Obot__class_Obot(tc_fun(X7169,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7169),hAPP(c_COMBK(tc_HOL_Obool,X7169),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_28,plain,
! [X7150,X7151] : hAPP(c_Set_OCollect(X7151),X7150) = X7150,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_29,plain,
! [X17639,X17640,X17641,X17642] : hAPP(hAPP(c_COMBK(X17642,X17641),X17640),X17639) = X17640,
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_27]) ).
cnf(c_0_31,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X7796] : c_Orderings_Otop__class_Otop(tc_fun(X7796,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7796),hAPP(c_COMBK(tc_HOL_Obool,X7796),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_33,plain,
! [X8752] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X8752),c_Orderings_Obot__class_Obot(X8752)) = c_Orderings_Otop__class_Otop(X8752)
| ~ class_Lattices_Oboolean__algebra(X8752) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])]) ).
fof(c_0_34,plain,
! [X792,X793,X794] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X793,X794)),X792) = c_Orderings_Obot__class_Obot(X794)
| ~ class_Orderings_Obot(X794) ),
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_29]) ).
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_30,c_0_31]) ).
cnf(c_0_37,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_38,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_39,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(c_0_40,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_41,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
cnf(c_0_42,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_43,plain,
! [X7554,X7555,X7556] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7555,X7556)),X7554) = c_Orderings_Otop__class_Otop(X7556)
| ~ class_Orderings_Otop(X7556) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])])]) ).
cnf(c_0_44,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_37,c_0_31]) ).
cnf(c_0_45,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_38,c_0_39]) ).
cnf(c_0_46,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
fof(c_0_47,plain,
! [X7804,X7805] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X7805),c_Orderings_Otop__class_Otop(X7805)),X7804) = c_Orderings_Otop__class_Otop(X7805)
| ~ class_Lattices_Obounded__lattice__top(X7805) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])])]) ).
cnf(c_0_48,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_43]) ).
cnf(c_0_49,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).
cnf(c_0_50,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_44]) ).
cnf(c_0_51,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_45,c_0_46]) ).
fof(c_0_52,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_53,plain,
! [X8668,X8669] : hAPP(c_Set_OCollect(X8669),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8669),c_fNot),X8668)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8669,tc_HOL_Obool)),hAPP(c_Set_OCollect(X8669),X8668)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_54,plain,
! [X326,X327] :
( X327 = X326
| hAPP(X327,esk1_2(X326,X327)) != hAPP(X326,esk1_2(X326,X327)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_55,plain,
( ~ class_Lattices_Obounded__lattice__top(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).
cnf(c_0_57,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_48,c_0_49]),c_0_50]),c_0_51]) ).
fof(c_0_58,plain,
! [X7142,X7143,X7144,X7145,X7147] :
( ( hAPP(c_Set_OCollect(X7147),X7145) = c_Orderings_Obot__class_Obot(tc_fun(X7147,tc_HOL_Obool))
| hBOOL(hAPP(X7145,esk195_1(X7145))) )
& ( ~ hBOOL(hAPP(X7142,X7144))
| hAPP(c_Set_OCollect(X7143),X7142) != c_Orderings_Obot__class_Obot(tc_fun(X7143,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_52])])])])])]) ).
fof(c_0_59,plain,
! [X8787] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8787,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8787,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X8787,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_60,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_53]) ).
cnf(c_0_61,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue),X1) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_51]),c_0_57]),c_0_51]),c_0_57]) ).
fof(c_0_63,plain,
! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_64,plain,
! [X8586,X8587] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8587,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8587,tc_HOL_Obool)),X8586)) = X8586,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(c_0_65,plain,
! [X16] :
( ~ hBOOL(X16)
| ~ hBOOL(hAPP(c_fNot,X16)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_66,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk195_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
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))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,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_60,c_0_31]),c_0_31]) ).
cnf(c_0_69,plain,
( hAPP(X1,esk1_2(X1,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue))) != c_fTrue
| hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue) = X1 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_70,plain,
! [X3080,X3081] :
( X3080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3081),X3080) != X3081 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_71,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_72,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_73,plain,
! [X1174] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1174),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).
fof(c_0_74,plain,
! [X17643,X17644,X17645,X17646,X17647,X17648] : hAPP(hAPP(hAPP(c_COMBB(X17648,X17647,X17646),X17645),X17644),X17643) = hAPP(X17645,hAPP(X17644,X17643)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_75,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_64]) ).
fof(c_0_76,plain,
! [X17665] :
( ~ hBOOL(X17665)
| ~ hBOOL(hAPP(c_fNot,X17665)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_65])]) ).
cnf(c_0_77,plain,
( hBOOL(hAPP(X1,esk195_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_78,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_67,c_0_68]) ).
cnf(c_0_79,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue),
inference(spm,[status(thm)],[c_0_69,c_0_50]) ).
cnf(c_0_80,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_70]) ).
cnf(c_0_81,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
fof(c_0_82,plain,
! [X3116,X3117] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3117),hAPP(c_Nat_OSuc,X3116)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3117),X3116)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_83,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_84,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_85,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_75,c_0_68]),c_0_68]) ).
fof(c_0_86,plain,
! [X16608,X16609] : hAPP(c_List_Orev(X16609),hAPP(c_List_Orev(X16609),X16608)) = X16608,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_87,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_88,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_77]),c_0_42]),c_0_35]) ).
cnf(c_0_89,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,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_80,c_0_81]) ).
cnf(c_0_91,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_82]) ).
cnf(c_0_92,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_83,c_0_81]) ).
fof(c_0_93,plain,
! [X3084] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3084),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3084,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_94,plain,
! [X51] : X51 != hAPP(c_Nat_OSuc,X51),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_95,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_84]) ).
cnf(c_0_96,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_97,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_98,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_89]),c_0_42]),c_0_62]) ).
cnf(c_0_99,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_90,c_0_91]),c_0_92]) ).
cnf(c_0_100,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_93]) ).
fof(c_0_101,plain,
! [X1284] : X1284 != hAPP(c_Nat_OSuc,X1284),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_94])]) ).
cnf(c_0_102,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_97,c_0_88]) ).
cnf(c_0_104,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_57]),c_0_98]) ).
cnf(c_0_105,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_99,c_0_91]) ).
cnf(c_0_106,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_100,c_0_81]) ).
cnf(c_0_107,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_108,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_109,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_111,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_112,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_108]),c_0_107]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW378+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 09:45:13 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 138.65/21.96 % Version: 3.5.1
% 138.65/21.96 % Preprocessing class: FMLMSLSMSSSNFFN.
% 138.65/21.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 138.65/21.96 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 138.65/21.96 % Starting new_bool_3 with 300s (1) cores
% 138.65/21.96 % Starting new_bool_1 with 300s (1) cores
% 138.65/21.96 % Starting sh5l with 300s (1) cores
% 138.65/21.96 % SAT001_MinMin_p005000_rr_RG with pid 2023804 completed with status 0
% 138.65/21.96 % Result found by SAT001_MinMin_p005000_rr_RG
% 138.65/21.96 % Preprocessing class: FMLMSLSMSSSNFFN.
% 138.65/21.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 138.65/21.96 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 138.65/21.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 138.65/21.96 % No SInE strategy applied
% 138.65/21.96 % Search class: FGHSM-SMLM33-DFFFFFNN
% 138.65/21.96 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 138.65/21.96 % Starting SubtermCWHack with 135s (1) cores
% 138.65/21.96 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 138.65/21.96 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 138.65/21.96 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 138.65/21.96 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 138.65/21.96 % SAT001_MinMin_p005000_rr_RG with pid 2023820 completed with status 0
% 138.65/21.96 % Result found by SAT001_MinMin_p005000_rr_RG
% 138.65/21.96 % Preprocessing class: FMLMSLSMSSSNFFN.
% 138.65/21.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 138.65/21.96 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 138.65/21.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 138.65/21.96 % No SInE strategy applied
% 138.65/21.96 % Search class: FGHSM-SMLM33-DFFFFFNN
% 138.65/21.96 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 138.65/21.96 % Starting SubtermCWHack with 135s (1) cores
% 138.65/21.96 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 138.65/21.96 % Preprocessing time : 0.315 s
% 138.65/21.96 % Presaturation interreduction done
% 138.65/21.96
% 138.65/21.96 % Proof found!
% 138.65/21.96 % SZS status ContradictoryAxioms
% 138.65/21.96 % SZS output start CNFRefutation
% See solution above
% 138.65/21.96 % Parsed axioms : 5243
% 138.65/21.96 % Removed by relevancy pruning/SinE : 0
% 138.65/21.96 % Initial clauses : 7568
% 138.65/21.96 % Removed in clause preprocessing : 237
% 138.65/21.96 % Initial clauses in saturation : 7331
% 138.65/21.96 % Processed clauses : 21931
% 138.65/21.96 % ...of these trivial : 520
% 138.65/21.96 % ...subsumed : 7234
% 138.65/21.96 % ...remaining for further processing : 14177
% 138.65/21.96 % Other redundant clauses eliminated : 1579
% 138.65/21.96 % Clauses deleted for lack of memory : 0
% 138.65/21.96 % Backward-subsumed : 386
% 138.65/21.96 % Backward-rewritten : 522
% 138.65/21.96 % Generated clauses : 221355
% 138.65/21.96 % ...of the previous two non-redundant : 209057
% 138.65/21.96 % ...aggressively subsumed : 0
% 138.65/21.96 % Contextual simplify-reflections : 46
% 138.65/21.96 % Paramodulations : 219764
% 138.65/21.96 % Factorizations : 6
% 138.65/21.96 % NegExts : 0
% 138.65/21.96 % Equation resolutions : 1651
% 138.65/21.96 % Disequality decompositions : 0
% 138.65/21.96 % Total rewrite steps : 67465
% 138.65/21.96 % ...of those cached : 48650
% 138.65/21.96 % Propositional unsat checks : 3
% 138.65/21.96 % Propositional check models : 2
% 138.65/21.96 % Propositional check unsatisfiable : 0
% 138.65/21.96 % Propositional clauses : 0
% 138.65/21.96 % Propositional clauses after purity: 0
% 138.65/21.96 % Propositional unsat core size : 0
% 138.65/21.96 % Propositional preprocessing time : 0.000
% 138.65/21.96 % Propositional encoding time : 0.300
% 138.65/21.96 % Propositional solver time : 0.178
% 138.65/21.96 % Success case prop preproc time : 0.000
% 138.65/21.96 % Success case prop encoding time : 0.000
% 138.65/21.96 % Success case prop solver time : 0.000
% 138.65/21.96 % Current number of processed clauses : 6873
% 138.65/21.96 % Positive orientable unit clauses : 1743
% 138.65/21.96 % Positive unorientable unit clauses: 128
% 138.65/21.96 % Negative unit clauses : 1083
% 138.65/21.96 % Non-unit-clauses : 3919
% 138.65/21.96 % Current number of unprocessed clauses: 185595
% 138.65/21.96 % ...number of literals in the above : 351133
% 138.65/21.96 % Current number of archived formulas : 0
% 138.65/21.96 % Current number of archived clauses : 6863
% 138.65/21.96 % Clause-clause subsumption calls (NU) : 6608302
% 138.65/21.96 % Rec. Clause-clause subsumption calls : 2853191
% 138.65/21.96 % Non-unit clause-clause subsumptions : 4760
% 138.65/21.96 % Unit Clause-clause subsumption calls : 197753
% 138.65/21.96 % Rewrite failures with RHS unbound : 0
% 138.65/21.96 % BW rewrite match attempts : 42428
% 138.65/21.96 % BW rewrite match successes : 1237
% 138.65/21.96 % Condensation attempts : 0
% 138.65/21.96 % Condensation successes : 0
% 138.65/21.96 % Termbank termtop insertions : 7241514
% 138.65/21.96 % Search garbage collected termcells : 100354
% 138.65/21.96
% 138.65/21.96 % -------------------------------------------------
% 138.65/21.96 % User time : 20.243 s
% 138.65/21.96 % System time : 0.570 s
% 138.65/21.96 % Total time : 20.813 s
% 138.65/21.96 % Maximum resident set size: 42392 pages
% 138.65/21.96
% 138.65/21.96 % -------------------------------------------------
% 138.65/21.96 % User time : 93.126 s
% 138.65/21.96 % System time : 2.188 s
% 138.65/21.96 % Total time : 95.315 s
% 138.65/21.96 % Maximum resident set size: 12544 pages
% 138.65/21.96 % E exiting
%------------------------------------------------------------------------------