%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW305+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 03:10:16 PM UTC 2026
% Result : ContradictoryAxioms 111.19s 20.07s
% Output : CNFRefutation 111.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of formulae : 115 ( 81 unt; 0 def)
% Number of atoms : 151 ( 114 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 41 ~; 27 |; 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 : 177 ( 28 sgn 95 !; 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,
! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(help_c__COMBK__1,axiom,
! [X325,X54,X5,X35] : hAPP(hAPP(c_COMBK(X35,X5),X54),X325) = X54,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
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_compl__bot__eq,axiom,
! [X35] :
( class_Lattices_Oboolean__algebra(X35)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X35),c_Orderings_Obot__class_Obot(X35)) = c_Orderings_Otop__class_Otop(X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(fact_bot__fun__def,axiom,
! [X23,X21,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X21,X5)),X23) = c_Orderings_Obot__class_Obot(X5) ),
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,
! [X23,X21,X5] :
( class_Orderings_Otop(X5)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X21,X5)),X23) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_Collect__empty__eq,axiom,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_Collect__neg__eq,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_sup__top__left,axiom,
! [X34,X35] :
( class_Lattices_Obounded__lattice__top(X35)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X35),c_Orderings_Otop__class_Otop(X35)),X34) = c_Orderings_Otop__class_Otop(X35) ),
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_Compl__empty__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
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_Zero__not__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__not__Suc) ).
fof(fact_double__complement,axiom,
! [X22,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)),X22)) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_add__eq__self__zero,axiom,
! [X76,X100] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X76) = X100
=> X76 = 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,
! [X30,X17,X18,X39,X5,X21] : hAPP(hAPP(hAPP(c_COMBB(X21,X5,X39),X18),X17),X30) = hAPP(X18,hAPP(X17,X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X76,X100] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),hAPP(c_Nat_OSuc,X76)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),X76)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X249,X35] : hAPP(c_List_Orev(X35),hAPP(c_List_Orev(X35),X249)) = X249,
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,
! [X76] : X76 != hAPP(c_Nat_OSuc,X76),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_27,plain,
! [X3143] : c_Orderings_Obot__class_Obot(tc_fun(X3143,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X3143),hAPP(c_COMBK(tc_HOL_Obool,X3143),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_28,plain,
! [X3118,X3119] : hAPP(c_Set_OCollect(X3119),X3118) = X3118,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_29,plain,
! [X17703,X17704,X17705,X17706] : hAPP(hAPP(c_COMBK(X17706,X17705),X17704),X17703) = X17704,
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,
! [X3147] : c_Orderings_Otop__class_Otop(tc_fun(X3147,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X3147),hAPP(c_COMBK(tc_HOL_Obool,X3147),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_33,plain,
! [X2752] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X2752),c_Orderings_Obot__class_Obot(X2752)) = c_Orderings_Otop__class_Otop(X2752)
| ~ class_Lattices_Oboolean__algebra(X2752) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])]) ).
fof(c_0_34,plain,
! [X379,X380,X381] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X380,X381)),X379) = c_Orderings_Obot__class_Obot(X381)
| ~ class_Orderings_Obot(X381) ),
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,
! [X1784,X1785,X1786] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1785,X1786)),X1784) = c_Orderings_Otop__class_Otop(X1786)
| ~ class_Orderings_Otop(X1786) ),
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,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_48,plain,
! [X3154,X3155] : hAPP(c_Set_OCollect(X3155),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3155),c_fNot),X3154)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3155,tc_HOL_Obool)),hAPP(c_Set_OCollect(X3155),X3154)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_49,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])])])]) ).
fof(c_0_50,plain,
! [X2174,X2175] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2175),c_Orderings_Otop__class_Otop(X2175)),X2174) = c_Orderings_Otop__class_Otop(X2175)
| ~ class_Lattices_Obounded__lattice__top(X2175) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])])]) ).
cnf(c_0_51,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_52,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).
cnf(c_0_53,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_54,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_55,plain,
! [X3120,X3121,X3122,X3123,X3125] :
( ( hAPP(c_Set_OCollect(X3125),X3123) = c_Orderings_Obot__class_Obot(tc_fun(X3125,tc_HOL_Obool))
| hBOOL(hAPP(X3123,esk46_1(X3123))) )
& ( ~ hBOOL(hAPP(X3120,X3122))
| hAPP(c_Set_OCollect(X3121),X3120) != c_Orderings_Obot__class_Obot(tc_fun(X3121,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_47])])])])])]) ).
fof(c_0_56,plain,
! [X2766] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2766,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2766,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2766,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_57,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_48]) ).
cnf(c_0_58,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,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_50]) ).
cnf(c_0_60,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).
cnf(c_0_61,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_51,c_0_52]),c_0_53]),c_0_54]) ).
fof(c_0_62,plain,
! [X100] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X100),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_63,plain,
! [X2602,X2603] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2603,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2603,tc_HOL_Obool)),X2602)) = X2602,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(c_0_64,plain,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_65,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk46_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,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_57,c_0_31]),c_0_31]) ).
cnf(c_0_68,plain,
( hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_fFalse
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_69,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_59,c_0_60]),c_0_54]),c_0_61]),c_0_54]),c_0_61]) ).
fof(c_0_70,plain,
! [X4100,X4101] :
( X4100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4101),X4100) != X4101 ),
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,
! [X2339] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2339),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_62])]) ).
fof(c_0_74,plain,
! [X17707,X17708,X17709,X17710,X17711,X17712] : hAPP(hAPP(hAPP(c_COMBB(X17712,X17711,X17710),X17709),X17708),X17707) = hAPP(X17709,hAPP(X17708,X17707)),
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_63]) ).
fof(c_0_76,plain,
! [X17729] :
( ~ hBOOL(X17729)
| ~ hBOOL(hAPP(c_fNot,X17729)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
cnf(c_0_77,plain,
( hBOOL(hAPP(X1,esk46_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_65,c_0_31]) ).
cnf(c_0_78,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_79,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_68,c_0_42]) ).
cnf(c_0_80,plain,
( hAPP(X1,esk1_2(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue),X1)) != c_fTrue
| X1 = hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue) ),
inference(spm,[status(thm)],[c_0_58,c_0_69]) ).
cnf(c_0_81,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_82,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_83,plain,
! [X4110,X4111] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4111),hAPP(c_Nat_OSuc,X4110)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4111),X4110)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_84,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_85,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_86,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_67]),c_0_67]) ).
fof(c_0_87,plain,
! [X16133,X16134] : hAPP(c_List_Orev(X16134),hAPP(c_List_Orev(X16134),X16133)) = X16133,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_88,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_89,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_90,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_91,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_80,c_0_53]) ).
cnf(c_0_92,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_81,c_0_82]) ).
cnf(c_0_93,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_83]) ).
cnf(c_0_94,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_84,c_0_82]) ).
fof(c_0_95,plain,
! [X4104] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4104),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4104,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_96,plain,
! [X76] : X76 != hAPP(c_Nat_OSuc,X76),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_97,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_85]) ).
cnf(c_0_98,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_99,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_100,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_101,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_92,c_0_93]),c_0_94]) ).
cnf(c_0_102,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_95]) ).
fof(c_0_103,plain,
! [X2483] : X2483 != hAPP(c_Nat_OSuc,X2483),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_96])]) ).
cnf(c_0_104,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_99,c_0_89]) ).
cnf(c_0_106,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_100]),c_0_69]),c_0_42]) ).
cnf(c_0_107,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_101,c_0_93]) ).
cnf(c_0_108,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_102,c_0_82]) ).
cnf(c_0_109,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_111,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_113,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_114,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_110]),c_0_109]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW305+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.48 % Computer : n018.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.48 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Mon Sep 21 09:48:59 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.56 Running first-order theorem proving
% 0.25/0.56 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
% 111.19/20.07 % Version: 3.5.1
% 111.19/20.07 % Preprocessing class: FMLMSMSMSSSNFFN.
% 111.19/20.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 111.19/20.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 111.19/20.07 % Starting new_bool_3 with 300s (1) cores
% 111.19/20.07 % Starting new_bool_1 with 300s (1) cores
% 111.19/20.07 % Starting sh5l with 300s (1) cores
% 111.19/20.07 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1583433 completed with status 0
% 111.19/20.07 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 111.19/20.07 % Preprocessing class: FMLMSMSMSSSNFFN.
% 111.19/20.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 111.19/20.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 111.19/20.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 111.19/20.07 % No SInE strategy applied
% 111.19/20.07 % Search class: FGHSM-SMLM33-DFFFFFNN
% 111.19/20.07 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 111.19/20.07 % Starting SubtermCWHack with 135s (1) cores
% 111.19/20.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 111.19/20.07 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 111.19/20.07 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 111.19/20.07 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 111.19/20.07 % SAT001_CA_MinMin_p005000_rr with pid 1583443 completed with status 0
% 111.19/20.07 % Result found by SAT001_CA_MinMin_p005000_rr
% 111.19/20.07 % Preprocessing class: FMLMSMSMSSSNFFN.
% 111.19/20.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 111.19/20.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 111.19/20.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 111.19/20.07 % No SInE strategy applied
% 111.19/20.07 % Search class: FGHSM-SMLM33-DFFFFFNN
% 111.19/20.07 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 111.19/20.07 % Starting SubtermCWHack with 135s (1) cores
% 111.19/20.07 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 111.19/20.07 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 111.19/20.07 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 111.19/20.07 % Preprocessing time : 0.321 s
% 111.19/20.07 % Presaturation interreduction done
% 111.19/20.07
% 111.19/20.07 % Proof found!
% 111.19/20.07 % SZS status ContradictoryAxioms
% 111.19/20.07 % SZS output start CNFRefutation
% See solution above
% 111.19/20.07 % Parsed axioms : 5225
% 111.19/20.07 % Removed by relevancy pruning/SinE : 0
% 111.19/20.07 % Initial clauses : 7610
% 111.19/20.07 % Removed in clause preprocessing : 236
% 111.19/20.07 % Initial clauses in saturation : 7374
% 111.19/20.07 % Processed clauses : 21624
% 111.19/20.07 % ...of these trivial : 412
% 111.19/20.07 % ...subsumed : 8812
% 111.19/20.07 % ...remaining for further processing : 12400
% 111.19/20.07 % Other redundant clauses eliminated : 1603
% 111.19/20.07 % Clauses deleted for lack of memory : 0
% 111.19/20.07 % Backward-subsumed : 275
% 111.19/20.07 % Backward-rewritten : 438
% 111.19/20.07 % Generated clauses : 190413
% 111.19/20.07 % ...of the previous two non-redundant : 180287
% 111.19/20.07 % ...aggressively subsumed : 0
% 111.19/20.07 % Contextual simplify-reflections : 29
% 111.19/20.07 % Paramodulations : 188826
% 111.19/20.07 % Factorizations : 2
% 111.19/20.07 % NegExts : 0
% 111.19/20.07 % Equation resolutions : 1650
% 111.19/20.07 % Disequality decompositions : 0
% 111.19/20.07 % Total rewrite steps : 65163
% 111.19/20.07 % ...of those cached : 47393
% 111.19/20.07 % Propositional unsat checks : 3
% 111.19/20.07 % Propositional check models : 2
% 111.19/20.07 % Propositional check unsatisfiable : 0
% 111.19/20.07 % Propositional clauses : 0
% 111.19/20.07 % Propositional clauses after purity: 0
% 111.19/20.07 % Propositional unsat core size : 0
% 111.19/20.07 % Propositional preprocessing time : 0.000
% 111.19/20.07 % Propositional encoding time : 0.262
% 111.19/20.07 % Propositional solver time : 0.128
% 111.19/20.07 % Success case prop preproc time : 0.000
% 111.19/20.07 % Success case prop encoding time : 0.000
% 111.19/20.07 % Success case prop solver time : 0.000
% 111.19/20.07 % Current number of processed clauses : 5255
% 111.19/20.07 % Positive orientable unit clauses : 1598
% 111.19/20.07 % Positive unorientable unit clauses: 129
% 111.19/20.07 % Negative unit clauses : 725
% 111.19/20.07 % Non-unit-clauses : 2803
% 111.19/20.07 % Current number of unprocessed clauses: 165240
% 111.19/20.07 % ...number of literals in the above : 322017
% 111.19/20.07 % Current number of archived formulas : 0
% 111.19/20.07 % Current number of archived clauses : 6699
% 111.19/20.07 % Clause-clause subsumption calls (NU) : 5096132
% 111.19/20.07 % Rec. Clause-clause subsumption calls : 2208160
% 111.19/20.07 % Non-unit clause-clause subsumptions : 6568
% 111.19/20.07 % Unit Clause-clause subsumption calls : 343317
% 111.19/20.07 % Rewrite failures with RHS unbound : 615
% 111.19/20.07 % BW rewrite match attempts : 36093
% 111.19/20.07 % BW rewrite match successes : 1170
% 111.19/20.07 % Condensation attempts : 212915
% 111.19/20.07 % Condensation successes : 681
% 111.19/20.07 % Termbank termtop insertions : 6998482
% 111.19/20.07 % Search garbage collected termcells : 102726
% 111.19/20.07
% 111.19/20.07 % -------------------------------------------------
% 111.19/20.07 % User time : 15.306 s
% 111.19/20.07 % System time : 0.470 s
% 111.19/20.07 % Total time : 15.776 s
% 111.19/20.07 % Maximum resident set size: 42364 pages
% 111.19/20.07
% 111.19/20.07 % -------------------------------------------------
% 111.19/20.07 % User time : 74.577 s
% 111.19/20.07 % System time : 2.197 s
% 111.19/20.07 % Total time : 76.774 s
% 111.19/20.07 % Maximum resident set size: 12544 pages
% 111.19/20.07 % E exiting
%------------------------------------------------------------------------------