TSTP Solution File: SWW335+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWW335+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 20:11:04 EDT 2023
% Result : ContradictoryAxioms 87.84s 13.38s
% Output : CNFRefutation 87.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 95 ( 76 unt; 0 def)
% Number of atoms : 122 ( 94 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 59 ( 32 ~; 20 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 164 ( 21 sgn; 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_empty__def,axiom,
! [X6] : c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fFalse)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X12,X6] : hAPP(c_Set_OCollect(X6),X12) = X12,
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Collect__def) ).
fof(fact_bot__fun__def,axiom,
! [X4,X5,X6] :
( class_Orderings_Obot(X6)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,X6)),X4) = c_Orderings_Obot__class_Obot(X6) ),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_bot__fun__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X12,X6] :
( hAPP(c_Set_OCollect(X6),X12) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X12,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X281,X280,X6,X27] : hAPP(hAPP(c_COMBK(X27,X6),X280),X281) = X280,
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',help_c__COMBK__1) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_Collect__neg__eq,axiom,
! [X12,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),X12)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6),X12)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X12,X2,X5,X6] : hAPP(c_Set_Ovimage(X6,X5,X2),hAPP(c_Set_OCollect(X5),X12)) = hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X6),X12),X2)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_vimage__Collect__eq) ).
fof(fact_double__complement,axiom,
! [X14,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),X14)) = X14,
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X14,X6] : hAPP(c_Set_Ovimage(X6,X6,c_Fun_Oid(X6)),X14) = X14,
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_vimage__id) ).
fof(help_c__fNot__1,axiom,
! [X12] :
( ~ hBOOL(hAPP(c_fNot,X12))
| ~ hBOOL(X12) ),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X6] : c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fTrue)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_UNIV__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X86] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X86),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Zero__not__Suc) ).
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/tmp/tmp.moOSbv1ZMB/E---3.1_1532.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/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Pls__def) ).
fof(fact_Compl__empty__eq,axiom,
! [X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Compl__empty__eq) ).
fof(fact_add__0__iff,axiom,
! [X8,X28,X6] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6)
=> ( X28 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X28),X8)
<=> X8 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X85,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X85)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X85)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_add__Suc__right) ).
fof(fact_id__apply,axiom,
! [X26,X27] : hAPP(c_Fun_Oid(X27),X26) = X26,
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_id__apply) ).
fof(help_c__COMBB__1,axiom,
! [X44,X42,X12,X20,X6,X5] : hAPP(hAPP(hAPP(c_COMBB(X5,X6,X20),X12),X42),X44) = hAPP(X12,hAPP(X42,X44)),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',help_c__COMBB__1) ).
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/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X86,
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X85] : X85 != hAPP(c_Nat_OSuc,X85),
file('/export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p',fact_n__not__Suc__n) ).
fof(c_0_23,plain,
! [X2138] : c_Orderings_Obot__class_Obot(tc_fun(X2138,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2138),hAPP(c_COMBK(tc_HOL_Obool,X2138),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_24,plain,
! [X2113,X2114] : hAPP(c_Set_OCollect(X2114),X2113) = X2113,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_25,plain,
! [X285,X286,X287] :
( ~ class_Orderings_Obot(X287)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X286,X287)),X285) = c_Orderings_Obot__class_Obot(X287) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(c_0_26,plain,
! [X12,X6] :
( hAPP(c_Set_OCollect(X6),X12) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X12,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_27,plain,
! [X17487,X17488,X17489,X17490] : hAPP(hAPP(c_COMBK(X17490,X17489),X17488),X17487) = X17488,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_28,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
fof(c_0_32,plain,
! [X4064,X4065] : hAPP(c_Set_OCollect(X4065),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4065),c_fNot),X4064)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4065,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4065),X4064)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_33,plain,
! [X3173,X3174,X3175,X3176] : hAPP(c_Set_Ovimage(X3176,X3175,X3174),hAPP(c_Set_OCollect(X3175),X3173)) = hAPP(c_Set_OCollect(X3176),hAPP(hAPP(c_COMBB(X3175,tc_HOL_Obool,X3176),X3173),X3174)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_34,plain,
! [X2115,X2116,X2117,X2118,X2120] :
( ( hAPP(c_Set_OCollect(X2116),X2115) != c_Orderings_Obot__class_Obot(tc_fun(X2116,tc_HOL_Obool))
| ~ hBOOL(hAPP(X2115,X2117)) )
& ( hBOOL(hAPP(X2118,esk52_1(X2118)))
| hAPP(c_Set_OCollect(X2120),X2118) = c_Orderings_Obot__class_Obot(tc_fun(X2120,tc_HOL_Obool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])]) ).
cnf(c_0_35,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_38,plain,
! [X3987,X3988] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3988,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3988,tc_HOL_Obool)),X3987)) = X3987,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_39,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_40,plain,
! [X10680,X10681] : hAPP(c_Set_Ovimage(X10681,X10681,c_Fun_Oid(X10681)),X10680) = X10680,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_41,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_42,plain,
! [X12] :
( ~ hBOOL(hAPP(c_fNot,X12))
| ~ hBOOL(X12) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_43,plain,
( hBOOL(hAPP(X1,esk52_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_45,plain,
! [X2142] : c_Orderings_Otop__class_Otop(tc_fun(X2142,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2142),hAPP(c_COMBK(tc_HOL_Obool,X2142),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_46,plain,
! [X6273] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X6273),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_47,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_48,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_49,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_50,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_29]),c_0_29]) ).
cnf(c_0_51,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_29]),c_0_29]) ).
fof(c_0_53,plain,
! [X17513] :
( ~ hBOOL(hAPP(c_fNot,X17513))
| ~ hBOOL(X17513) ),
inference(variable_rename,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk52_1(X1))) ),
inference(rw,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_55,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(rw,[status(thm)],[c_0_37,c_0_44]) ).
fof(c_0_56,plain,
! [X4106] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4106,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4106,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X4106,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_57,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_45]) ).
fof(c_0_58,plain,
! [X6228,X6229,X6230] :
( ( X6229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6230),X6229),X6228)
| X6228 = c_Groups_Ozero__class_Ozero(X6230)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6230) )
& ( X6228 != c_Groups_Ozero__class_Ozero(X6230)
| X6229 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6230),X6229),X6228)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(c_0_59,plain,
! [X5807,X5808] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5808),hAPP(c_Nat_OSuc,X5807)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5808),X5807)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_60,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_61,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_62,plain,
! [X10682,X10683] : hAPP(c_Fun_Oid(X10683),X10682) = X10682,
inference(variable_rename,[status(thm)],[fact_id__apply]) ).
cnf(c_0_63,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_49,c_0_50]),c_0_50]) ).
cnf(c_0_64,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_65,plain,
! [X17491,X17492,X17493,X17494,X17495,X17496] : hAPP(hAPP(hAPP(c_COMBB(X17496,X17495,X17494),X17493),X17492),X17491) = hAPP(X17493,hAPP(X17492,X17491)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_66,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_67,plain,
( c_fFalse = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_55]),c_0_35]) ).
cnf(c_0_68,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_69,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_57,c_0_29]) ).
cnf(c_0_70,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,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_59]) ).
cnf(c_0_72,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_73,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_74,plain,
! [X6292] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6292),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6292,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
cnf(c_0_75,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,plain,
c_Fun_Oid(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_77,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_78,plain,
( hAPP(c_fNot,X1) = c_fFalse
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_79,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_68,c_0_50]) ).
cnf(c_0_80,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_69]) ).
cnf(c_0_81,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_70,c_0_71]),c_0_61]),c_0_72])]),c_0_73]) ).
cnf(c_0_82,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_74]) ).
fof(c_0_83,plain,
! [X5778] : X5778 != hAPP(c_Nat_OSuc,X5778),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_84,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_85,plain,
( hAPP(c_fNot,X1) = c_fFalse
| c_fFalse = X1 ),
inference(spm,[status(thm)],[c_0_78,c_0_67]) ).
cnf(c_0_86,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_79]),c_0_80]),c_0_37]),c_0_44]) ).
cnf(c_0_87,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_81,c_0_71]) ).
cnf(c_0_88,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_82,c_0_61]) ).
cnf(c_0_89,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,plain,
( c_fFalse = X1
| c_fTrue = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).
cnf(c_0_91,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90])]) ).
cnf(c_0_93,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_94,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_90]),c_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SWW335+1 : TPTP v8.1.2. Released v5.2.0.
% 0.02/0.10 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n008.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 2400
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Oct 2 22:49:58 EDT 2023
% 0.09/0.30 % CPUTime :
% 1.32/1.49 Running first-order model finding
% 1.32/1.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.moOSbv1ZMB/E---3.1_1532.p
% 87.84/13.38 # Version: 3.1pre001
% 87.84/13.38 # Preprocessing class: FMLMSMSMSSSNFFN.
% 87.84/13.38 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 87.84/13.38 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 87.84/13.38 # Starting new_bool_3 with 300s (1) cores
% 87.84/13.38 # Starting new_bool_1 with 300s (1) cores
% 87.84/13.38 # Starting sh5l with 300s (1) cores
% 87.84/13.38 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1609 completed with status 0
% 87.84/13.38 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 87.84/13.38 # Preprocessing class: FMLMSMSMSSSNFFN.
% 87.84/13.38 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 87.84/13.38 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 87.84/13.38 # No SInE strategy applied
% 87.84/13.38 # Search class: FGHSM-SMLM33-DFFFFFNN
% 87.84/13.38 # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 87.84/13.38 # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 87.84/13.38 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 87.84/13.38 # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 87.84/13.38 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 87.84/13.38 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 135s (1) cores
% 87.84/13.38 # SAT001_CA_MinMin_p005000_rr with pid 1618 completed with status 0
% 87.84/13.38 # Result found by SAT001_CA_MinMin_p005000_rr
% 87.84/13.38 # Preprocessing class: FMLMSMSMSSSNFFN.
% 87.84/13.38 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 87.84/13.38 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 87.84/13.38 # No SInE strategy applied
% 87.84/13.38 # Search class: FGHSM-SMLM33-DFFFFFNN
% 87.84/13.38 # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 87.84/13.38 # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 87.84/13.38 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 87.84/13.38 # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 87.84/13.38 # Preprocessing time : 0.163 s
% 87.84/13.38 # Presaturation interreduction done
% 87.84/13.38
% 87.84/13.38 # Proof found!
% 87.84/13.38 # SZS status ContradictoryAxioms
% 87.84/13.38 # SZS output start CNFRefutation
% See solution above
% 87.84/13.38 # Parsed axioms : 5224
% 87.84/13.38 # Removed by relevancy pruning/SinE : 0
% 87.84/13.38 # Initial clauses : 7603
% 87.84/13.38 # Removed in clause preprocessing : 245
% 87.84/13.38 # Initial clauses in saturation : 7358
% 87.84/13.38 # Processed clauses : 21173
% 87.84/13.38 # ...of these trivial : 470
% 87.84/13.38 # ...subsumed : 8347
% 87.84/13.38 # ...remaining for further processing : 12356
% 87.84/13.38 # Other redundant clauses eliminated : 1349
% 87.84/13.38 # Clauses deleted for lack of memory : 0
% 87.84/13.38 # Backward-subsumed : 186
% 87.84/13.38 # Backward-rewritten : 564
% 87.84/13.38 # Generated clauses : 194746
% 87.84/13.38 # ...of the previous two non-redundant : 184716
% 87.84/13.38 # ...aggressively subsumed : 0
% 87.84/13.38 # Contextual simplify-reflections : 28
% 87.84/13.38 # Paramodulations : 193429
% 87.84/13.38 # Factorizations : 2
% 87.84/13.38 # NegExts : 0
% 87.84/13.38 # Equation resolutions : 1381
% 87.84/13.38 # Total rewrite steps : 64405
% 87.84/13.38 # Propositional unsat checks : 3
% 87.84/13.38 # Propositional check models : 2
% 87.84/13.38 # Propositional check unsatisfiable : 0
% 87.84/13.38 # Propositional clauses : 0
% 87.84/13.38 # Propositional clauses after purity: 0
% 87.84/13.38 # Propositional unsat core size : 0
% 87.84/13.38 # Propositional preprocessing time : 0.000
% 87.84/13.38 # Propositional encoding time : 0.225
% 87.84/13.38 # Propositional solver time : 0.104
% 87.84/13.38 # Success case prop preproc time : 0.000
% 87.84/13.38 # Success case prop encoding time : 0.000
% 87.84/13.38 # Success case prop solver time : 0.000
% 87.84/13.38 # Current number of processed clauses : 5174
% 87.84/13.38 # Positive orientable unit clauses : 1723
% 87.84/13.38 # Positive unorientable unit clauses: 128
% 87.84/13.38 # Negative unit clauses : 638
% 87.84/13.38 # Non-unit-clauses : 2685
% 87.84/13.38 # Current number of unprocessed clauses: 167667
% 87.84/13.38 # ...number of literals in the above : 317829
% 87.84/13.38 # Current number of archived formulas : 0
% 87.84/13.38 # Current number of archived clauses : 6725
% 87.84/13.38 # Clause-clause subsumption calls (NU) : 4346654
% 87.84/13.38 # Rec. Clause-clause subsumption calls : 2265980
% 87.84/13.38 # Non-unit clause-clause subsumptions : 8121
% 87.84/13.38 # Unit Clause-clause subsumption calls : 114066
% 87.84/13.38 # Rewrite failures with RHS unbound : 461
% 87.84/13.38 # BW rewrite match attempts : 41772
% 87.84/13.38 # BW rewrite match successes : 1359
% 87.84/13.38 # Condensation attempts : 217049
% 87.84/13.38 # Condensation successes : 1716
% 87.84/13.38 # Termbank termtop insertions : 6876247
% 87.84/13.38
% 87.84/13.38 # -------------------------------------------------
% 87.84/13.38 # User time : 11.129 s
% 87.84/13.38 # System time : 0.278 s
% 87.84/13.38 # Total time : 11.407 s
% 87.84/13.38 # Maximum resident set size: 40092 pages
% 87.84/13.38
% 87.84/13.38 # -------------------------------------------------
% 87.84/13.38 # User time : 50.438 s
% 87.84/13.38 # System time : 1.316 s
% 87.84/13.38 # Total time : 51.754 s
% 87.84/13.38 # Maximum resident set size: 9456 pages
% 87.84/13.38 % E---3.1 exiting
%------------------------------------------------------------------------------