%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW379+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 100.05s 18.13s
% Output : CNFRefutation 100.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 114 ( 82 unt; 0 def)
% Number of atoms : 154 ( 111 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 83 ( 43 ~; 29 |; 2 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 172 ( 23 sgn 97 !; 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/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(help_c__COMBK__1,axiom,
! [X323,X22,X29,X5] : hAPP(hAPP(c_COMBK(X5,X29),X22),X323) = X22,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
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/sandbox/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(fact_bot__fun__def,axiom,
! [X31,X29,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X29,X5)),X31) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_top__apply,axiom,
! [X31,X29,X5] :
( class_Orderings_Otop(X5)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X29,X5)),X31) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_sup__top__left,axiom,
! [X40,X5] :
( class_Lattices_Obounded__lattice__top(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Otop__class_Otop(X5)),X40) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__left) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
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/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Zero__not__Suc,axiom,
! [X110] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X110),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X30,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)),X30)) = X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X36,X16,X18,X47,X5,X29] : hAPP(hAPP(hAPP(c_COMBB(X29,X5,X47),X18),X16),X36) = hAPP(X18,hAPP(X16,X36)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__0__iff,axiom,
! [X6,X33,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X33 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X108,X110] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),hAPP(c_Nat_OSuc,X108)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),X108)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X250,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X250)) = X250,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X110] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X110,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X108] : X108 != hAPP(c_Nat_OSuc,X108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_28,plain,
! [X7102] : c_Orderings_Obot__class_Obot(tc_fun(X7102,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7102),hAPP(c_COMBK(tc_HOL_Obool,X7102),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_29,plain,
! [X7089,X7090] : hAPP(c_Set_OCollect(X7090),X7089) = X7089,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_30,plain,
! [X17645,X17646,X17647,X17648] : hAPP(hAPP(c_COMBK(X17648,X17647),X17646),X17645) = X17646,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_31,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_28]) ).
cnf(c_0_32,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,plain,
! [X7109] : c_Orderings_Otop__class_Otop(tc_fun(X7109,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7109),hAPP(c_COMBK(tc_HOL_Obool,X7109),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_34,plain,
! [X7848] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X7848),c_Orderings_Obot__class_Obot(X7848)) = c_Orderings_Otop__class_Otop(X7848)
| ~ class_Lattices_Oboolean__algebra(X7848) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])])]) ).
fof(c_0_35,plain,
! [X407,X408,X409] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X408,X409)),X407) = c_Orderings_Obot__class_Obot(X409)
| ~ class_Orderings_Obot(X409) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])])]) ).
cnf(c_0_36,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,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_31,c_0_32]) ).
cnf(c_0_38,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_33]) ).
cnf(c_0_39,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_34]) ).
cnf(c_0_40,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(c_0_41,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_35]) ).
cnf(c_0_42,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
cnf(c_0_43,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_44,plain,
! [X2867,X2868,X2869] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2868,X2869)),X2867) = c_Orderings_Otop__class_Otop(X2869)
| ~ class_Orderings_Otop(X2869) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])])]) ).
cnf(c_0_45,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_38,c_0_32]) ).
cnf(c_0_46,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_39,c_0_40]) ).
cnf(c_0_47,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
fof(c_0_48,plain,
! [X3012,X3013] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X3013),c_Orderings_Otop__class_Otop(X3013)),X3012) = c_Orderings_Otop__class_Otop(X3013)
| ~ class_Lattices_Obounded__lattice__top(X3013) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])])]) ).
cnf(c_0_49,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_44]) ).
cnf(c_0_50,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).
cnf(c_0_51,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
cnf(c_0_52,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_46,c_0_47]) ).
fof(c_0_53,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_54,plain,
! [X7759,X7760] : hAPP(c_Set_OCollect(X7760),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7760),c_fNot),X7759)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7760,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7760),X7759)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_55,plain,
! [X324,X325] :
( X325 = X324
| hAPP(X325,esk1_2(X324,X325)) != hAPP(X324,esk1_2(X324,X325)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_56,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_48]) ).
cnf(c_0_57,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).
cnf(c_0_58,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_49,c_0_50]),c_0_51]),c_0_52]) ).
fof(c_0_59,plain,
! [X7083,X7084,X7085,X7086,X7088] :
( ( hAPP(c_Set_OCollect(X7088),X7086) = c_Orderings_Obot__class_Obot(tc_fun(X7088,tc_HOL_Obool))
| hBOOL(hAPP(X7086,esk206_1(X7086))) )
& ( ~ hBOOL(hAPP(X7083,X7085))
| hAPP(c_Set_OCollect(X7084),X7083) != c_Orderings_Obot__class_Obot(tc_fun(X7084,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_53])])])])])]) ).
fof(c_0_60,plain,
! [X7875] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7875,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7875,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7875,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_61,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_54]) ).
cnf(c_0_62,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,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_56,c_0_57]),c_0_52]),c_0_58]),c_0_52]),c_0_58]) ).
fof(c_0_64,plain,
! [X110] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X110),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_65,plain,
! [X7382,X7383] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7383,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7383,tc_HOL_Obool)),X7382)) = X7382,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(c_0_66,plain,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_67,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk206_1(X1))) ),
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)),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_60]) ).
cnf(c_0_69,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_61,c_0_32]),c_0_32]) ).
cnf(c_0_70,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_62,c_0_63]) ).
fof(c_0_71,plain,
! [X3772] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3772),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
cnf(c_0_72,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_73,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_74,plain,
! [X17649,X17650,X17651,X17652,X17653,X17654] : hAPP(hAPP(hAPP(c_COMBB(X17654,X17653,X17652),X17651),X17650),X17649) = hAPP(X17651,hAPP(X17650,X17649)),
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_65]) ).
fof(c_0_76,plain,
! [X17671] :
( ~ hBOOL(X17671)
| ~ hBOOL(hAPP(c_fNot,X17671)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_66])]) ).
cnf(c_0_77,plain,
( hBOOL(hAPP(X1,esk206_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_67,c_0_32]) ).
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_68,c_0_69]) ).
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_70,c_0_51]) ).
fof(c_0_80,plain,
! [X3319,X3320,X3321] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3321)
| X3320 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3321),X3320),X3319)
| X3319 != c_Groups_Ozero__class_Ozero(X3321) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3321)
| X3319 = c_Groups_Ozero__class_Ozero(X3321)
| X3320 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3321),X3320),X3319) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
fof(c_0_81,plain,
! [X3799,X3800] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3800),hAPP(c_Nat_OSuc,X3799)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3800),X3799)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_82,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_83,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_72,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_69]),c_0_69]) ).
fof(c_0_86,plain,
! [X16607,X16608] : hAPP(c_List_Orev(X16608),hAPP(c_List_Orev(X16608),X16607)) = X16607,
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_36,c_0_77]),c_0_43]),c_0_36]) ).
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,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
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_81]) ).
cnf(c_0_92,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_93,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_94,plain,
! [X2951] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2951),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2951,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_95,plain,
! [X108] : X108 != hAPP(c_Nat_OSuc,X108),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_96,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_97,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_98,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_99,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))) = hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_fTrue),
inference(spm,[status(thm)],[c_0_85,c_0_89]) ).
cnf(c_0_100,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_83]),c_0_92])]),c_0_93]) ).
cnf(c_0_101,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_94]) ).
fof(c_0_102,plain,
! [X3643] : X3643 != hAPP(c_Nat_OSuc,X3643),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_95])]) ).
cnf(c_0_103,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_98,c_0_88]) ).
cnf(c_0_105,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_99]),c_0_63]),c_0_43]) ).
cnf(c_0_106,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_100,c_0_91]) ).
cnf(c_0_107,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_101,c_0_83]) ).
cnf(c_0_108,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_109,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]) ).
cnf(c_0_110,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_112,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_113,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_109]),c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW379+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n010.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 09:50:10 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.54 Running first-order theorem proving
% 0.24/0.54 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 100.05/18.13 % Version: 3.5.1
% 100.05/18.13 % Preprocessing class: FMLMSLSMSSSNFFN.
% 100.05/18.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.05/18.13 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 100.05/18.13 % Starting new_bool_3 with 300s (1) cores
% 100.05/18.13 % Starting new_bool_1 with 300s (1) cores
% 100.05/18.13 % Starting sh5l with 300s (1) cores
% 100.05/18.13 % SAT001_MinMin_p005000_rr_RG with pid 602894 completed with status 0
% 100.05/18.13 % Result found by SAT001_MinMin_p005000_rr_RG
% 100.05/18.13 % Preprocessing class: FMLMSLSMSSSNFFN.
% 100.05/18.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.05/18.13 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 100.05/18.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 100.05/18.13 % No SInE strategy applied
% 100.05/18.13 % Search class: FGHSM-SMLM33-DFFFFFNN
% 100.05/18.13 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 100.05/18.13 % Starting SubtermCWHack with 135s (1) cores
% 100.05/18.13 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 100.05/18.13 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 100.05/18.13 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 100.05/18.13 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 100.05/18.13 % SAT001_MinMin_p005000_rr_RG with pid 602902 completed with status 0
% 100.05/18.13 % Result found by SAT001_MinMin_p005000_rr_RG
% 100.05/18.13 % Preprocessing class: FMLMSLSMSSSNFFN.
% 100.05/18.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 100.05/18.13 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 100.05/18.13 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 100.05/18.13 % No SInE strategy applied
% 100.05/18.13 % Search class: FGHSM-SMLM33-DFFFFFNN
% 100.05/18.13 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 100.05/18.13 % Starting SubtermCWHack with 135s (1) cores
% 100.05/18.13 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 100.05/18.13 % Preprocessing time : 0.333 s
% 100.05/18.13 % Presaturation interreduction done
% 100.05/18.13
% 100.05/18.13 % Proof found!
% 100.05/18.13 % SZS status ContradictoryAxioms
% 100.05/18.13 % SZS output start CNFRefutation
% See solution above
% 100.05/18.13 % Parsed axioms : 5240
% 100.05/18.13 % Removed by relevancy pruning/SinE : 0
% 100.05/18.13 % Initial clauses : 7570
% 100.05/18.13 % Removed in clause preprocessing : 234
% 100.05/18.13 % Initial clauses in saturation : 7336
% 100.05/18.13 % Processed clauses : 21884
% 100.05/18.13 % ...of these trivial : 406
% 100.05/18.13 % ...subsumed : 8967
% 100.05/18.13 % ...remaining for further processing : 12511
% 100.05/18.13 % Other redundant clauses eliminated : 1861
% 100.05/18.13 % Clauses deleted for lack of memory : 0
% 100.05/18.13 % Backward-subsumed : 319
% 100.05/18.13 % Backward-rewritten : 428
% 100.05/18.13 % Generated clauses : 188967
% 100.05/18.13 % ...of the previous two non-redundant : 178080
% 100.05/18.13 % ...aggressively subsumed : 0
% 100.05/18.13 % Contextual simplify-reflections : 88
% 100.05/18.13 % Paramodulations : 187125
% 100.05/18.13 % Factorizations : 2
% 100.05/18.13 % NegExts : 0
% 100.05/18.13 % Equation resolutions : 1907
% 100.05/18.13 % Disequality decompositions : 0
% 100.05/18.13 % Total rewrite steps : 67386
% 100.05/18.13 % ...of those cached : 49056
% 100.05/18.13 % Propositional unsat checks : 3
% 100.05/18.13 % Propositional check models : 2
% 100.05/18.13 % Propositional check unsatisfiable : 0
% 100.05/18.13 % Propositional clauses : 0
% 100.05/18.13 % Propositional clauses after purity: 0
% 100.05/18.13 % Propositional unsat core size : 0
% 100.05/18.13 % Propositional preprocessing time : 0.000
% 100.05/18.13 % Propositional encoding time : 0.283
% 100.05/18.13 % Propositional solver time : 0.132
% 100.05/18.13 % Success case prop preproc time : 0.000
% 100.05/18.13 % Success case prop encoding time : 0.000
% 100.05/18.13 % Success case prop solver time : 0.000
% 100.05/18.13 % Current number of processed clauses : 5359
% 100.05/18.13 % Positive orientable unit clauses : 1563
% 100.05/18.13 % Positive unorientable unit clauses: 129
% 100.05/18.13 % Negative unit clauses : 664
% 100.05/18.13 % Non-unit-clauses : 3003
% 100.05/18.13 % Current number of unprocessed clauses: 164640
% 100.05/18.13 % ...number of literals in the above : 333244
% 100.05/18.13 % Current number of archived formulas : 0
% 100.05/18.13 % Current number of archived clauses : 6702
% 100.05/18.13 % Clause-clause subsumption calls (NU) : 7652944
% 100.05/18.13 % Rec. Clause-clause subsumption calls : 2690064
% 100.05/18.13 % Non-unit clause-clause subsumptions : 6794
% 100.05/18.13 % Unit Clause-clause subsumption calls : 112674
% 100.05/18.13 % Rewrite failures with RHS unbound : 0
% 100.05/18.13 % BW rewrite match attempts : 38464
% 100.05/18.13 % BW rewrite match successes : 1205
% 100.05/18.13 % Condensation attempts : 0
% 100.05/18.13 % Condensation successes : 0
% 100.05/18.13 % Termbank termtop insertions : 6841943
% 100.05/18.13 % Search garbage collected termcells : 100511
% 100.05/18.13
% 100.05/18.13 % -------------------------------------------------
% 100.05/18.13 % User time : 15.264 s
% 100.05/18.13 % System time : 0.421 s
% 100.05/18.13 % Total time : 15.685 s
% 100.05/18.13 % Maximum resident set size: 42368 pages
% 100.05/18.13
% 100.05/18.13 % -------------------------------------------------
% 100.05/18.13 % User time : 66.704 s
% 100.05/18.13 % System time : 1.857 s
% 100.05/18.13 % Total time : 68.562 s
% 100.05/18.13 % Maximum resident set size: 12288 pages
% 100.05/18.13 % E exiting
%------------------------------------------------------------------------------