TSTP Solution File: SWW392+1 by E---3.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SWW392+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:11:52 EDT 2024
% Result : ContradictoryAxioms 59.43s 9.44s
% Output : CNFRefutation 59.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 64 unt; 0 def)
% Number of atoms : 100 ( 83 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 29 ~; 15 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 132 ( 16 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X6,X5] :
( hAPP(c_Set_OCollect(X5),X6) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X6,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Collect__empty__eq) ).
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/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X6,X5] : hAPP(c_Set_OCollect(X5),X6) = X6,
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X6)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X6)),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X307,X306,X5,X43] : hAPP(hAPP(c_COMBK(X43,X5),X306),X307) = X306,
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',help_c__COMBK__1) ).
fof(fact_Zero__neq__Suc,axiom,
! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X21,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)),X21)) = X21,
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X6] :
( ~ hBOOL(hAPP(c_fNot,X6))
| ~ hBOOL(X6) ),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',help_c__fNot__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/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X74,X73] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),X74) = X73
=> X74 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.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/tmp/tmp.F0giZVGGPE/E---3.1_20673.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/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X31,X26,X6,X132,X5,X20] : hAPP(hAPP(hAPP(c_COMBB(X20,X5,X132),X6),X26),X31) = hAPP(X6,hAPP(X26,X31)),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',help_c__COMBB__1) ).
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/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Compl__empty__eq) ).
fof(fact_add__Suc__right,axiom,
! [X74,X73] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),hAPP(c_Nat_OSuc,X74)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),X74)),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X230,X43] : hAPP(c_List_Orev(X43),hAPP(c_List_Orev(X43),X230)) = X230,
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X73] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X73,
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X74] : X74 != hAPP(c_Nat_OSuc,X74),
file('/export/starexec/sandbox2/tmp/tmp.F0giZVGGPE/E---3.1_20673.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X6,X5] :
( hAPP(c_Set_OCollect(X5),X6) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X6,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X2189] : c_Orderings_Obot__class_Obot(tc_fun(X2189,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2189),hAPP(c_COMBK(tc_HOL_Obool,X2189),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X5408,X5409] : hAPP(c_Set_OCollect(X5409),X5408) = X5408,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X2488,X2489] : hAPP(c_Set_OCollect(X2489),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2489),c_fNot),X2488)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2489,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2489),X2488)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X734,X735,X736,X737,X739] :
( ( hAPP(c_Set_OCollect(X735),X734) != c_Orderings_Obot__class_Obot(tc_fun(X735,tc_HOL_Obool))
| ~ hBOOL(hAPP(X734,X736)) )
& ( hBOOL(hAPP(X737,esk29_1(X737)))
| hAPP(c_Set_OCollect(X739),X737) = c_Orderings_Obot__class_Obot(tc_fun(X739,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_18])])])])])]) ).
fof(c_0_23,plain,
! [X2438,X2439,X2440,X2441] : hAPP(hAPP(c_COMBK(X2441,X2440),X2439),X2438) = X2439,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_27,plain,
! [X4395,X4396] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4396,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4396,tc_HOL_Obool)),X4395)) = X4395,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_28,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_21]) ).
fof(c_0_29,plain,
! [X6] :
( ~ hBOOL(hAPP(c_fNot,X6))
| ~ hBOOL(X6) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_30,plain,
( hBOOL(hAPP(X1,esk29_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_22]) ).
cnf(c_0_31,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,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_24,c_0_25]) ).
fof(c_0_33,plain,
! [X2442] : c_Orderings_Otop__class_Otop(tc_fun(X2442,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2442),hAPP(c_COMBK(tc_HOL_Obool,X2442),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_34,plain,
! [X3408,X3409] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3409),X3408) != X3409
| X3408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_35,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_36,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_37,plain,
! [X3403] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3403),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
fof(c_0_38,plain,
! [X2041,X2042,X2043,X2044,X2045,X2046] : hAPP(hAPP(hAPP(c_COMBB(X2046,X2045,X2044),X2043),X2042),X2041) = hAPP(X2043,hAPP(X2042,X2041)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_39,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_27]) ).
cnf(c_0_40,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_28,c_0_25]),c_0_25]) ).
fof(c_0_41,plain,
! [X2531] :
( ~ hBOOL(hAPP(c_fNot,X2531))
| ~ hBOOL(X2531) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_42,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk29_1(X1))) ),
inference(rw,[status(thm)],[c_0_30,c_0_25]) ).
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_31,c_0_32]) ).
fof(c_0_44,plain,
! [X625] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X625,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X625,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X625,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_45,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_46,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_48,plain,
! [X3362,X3363] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3363),hAPP(c_Nat_OSuc,X3362)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3363),X3362)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_49,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,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_39,c_0_40]),c_0_40]) ).
fof(c_0_52,plain,
! [X10845,X10846] : hAPP(c_List_Orev(X10846),hAPP(c_List_Orev(X10846),X10845)) = X10845,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_53,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( c_fFalse = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_43]),c_0_31]) ).
cnf(c_0_55,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_44]) ).
cnf(c_0_56,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_45,c_0_25]) ).
cnf(c_0_57,plain,
( X1 = hAPP(c_Int_Onat,c_Int_OPls)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,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_48]) ).
cnf(c_0_59,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_49,c_0_47]) ).
fof(c_0_60,plain,
! [X3412] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3412),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3412,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_61,plain,
! [X74] : X74 != hAPP(c_Nat_OSuc,X74),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_62,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
cnf(c_0_63,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
( hAPP(c_fNot,X1) = c_fFalse
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,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_55,c_0_40]) ).
cnf(c_0_66,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_31,c_0_56]) ).
cnf(c_0_67,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_57,c_0_58]),c_0_59]) ).
cnf(c_0_68,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_60]) ).
fof(c_0_69,plain,
! [X6333] : X6333 != hAPP(c_Nat_OSuc,X6333),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_61])]) ).
cnf(c_0_70,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
( hAPP(c_fNot,X1) = c_fFalse
| c_fFalse = X1 ),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_72,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_65]),c_0_66]),c_0_43]) ).
cnf(c_0_73,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_67,c_0_58]) ).
cnf(c_0_74,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_68,c_0_47]) ).
cnf(c_0_75,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,plain,
( c_fFalse = X1
| c_fTrue = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_77,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_80,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_76]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SWW392+1 : TPTP v8.2.0. Released v5.2.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Jun 19 05:52:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.12/1.31 Running first-order theorem proving
% 1.12/1.31 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/tmp/tmp.F0giZVGGPE/E---3.1_20673.p
% 59.43/9.44 # Version: 3.2.0
% 59.43/9.44 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.43/9.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.43/9.44 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.43/9.44 # Starting new_bool_3 with 300s (1) cores
% 59.43/9.44 # Starting new_bool_1 with 300s (1) cores
% 59.43/9.44 # Starting sh5l with 300s (1) cores
% 59.43/9.44 # sh5l with pid 20754 completed with status 0
% 59.43/9.44 # Result found by sh5l
% 59.43/9.44 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.43/9.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.43/9.44 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.43/9.44 # Starting new_bool_3 with 300s (1) cores
% 59.43/9.44 # Starting new_bool_1 with 300s (1) cores
% 59.43/9.44 # Starting sh5l with 300s (1) cores
% 59.43/9.44 # SinE strategy is gf500_gu_R04_F100_L20000
% 59.43/9.44 # Search class: FGHSM-SMLM33-DFFFFFNN
% 59.43/9.44 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 59.43/9.44 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 59.43/9.44 # SAT001_MinMin_p005000_rr with pid 20757 completed with status 0
% 59.43/9.44 # Result found by SAT001_MinMin_p005000_rr
% 59.43/9.44 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.43/9.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.43/9.44 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.43/9.44 # Starting new_bool_3 with 300s (1) cores
% 59.43/9.44 # Starting new_bool_1 with 300s (1) cores
% 59.43/9.44 # Starting sh5l with 300s (1) cores
% 59.43/9.44 # SinE strategy is gf500_gu_R04_F100_L20000
% 59.43/9.44 # Search class: FGHSM-SMLM33-DFFFFFNN
% 59.43/9.44 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 59.43/9.44 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 59.43/9.44 # Preprocessing time : 0.155 s
% 59.43/9.44 # Presaturation interreduction done
% 59.43/9.44
% 59.43/9.44 # Proof found!
% 59.43/9.44 # SZS status ContradictoryAxioms
% 59.43/9.44 # SZS output start CNFRefutation
% See solution above
% 59.43/9.44 # Parsed axioms : 5224
% 59.43/9.44 # Removed by relevancy pruning/SinE : 688
% 59.43/9.44 # Initial clauses : 6639
% 59.43/9.44 # Removed in clause preprocessing : 188
% 59.43/9.44 # Initial clauses in saturation : 6451
% 59.43/9.44 # Processed clauses : 19226
% 59.43/9.44 # ...of these trivial : 369
% 59.43/9.44 # ...subsumed : 6410
% 59.43/9.44 # ...remaining for further processing : 12447
% 59.43/9.44 # Other redundant clauses eliminated : 1232
% 59.43/9.44 # Clauses deleted for lack of memory : 0
% 59.43/9.44 # Backward-subsumed : 241
% 59.43/9.44 # Backward-rewritten : 451
% 59.43/9.44 # Generated clauses : 163661
% 59.43/9.44 # ...of the previous two non-redundant : 155703
% 59.43/9.44 # ...aggressively subsumed : 0
% 59.43/9.44 # Contextual simplify-reflections : 29
% 59.43/9.44 # Paramodulations : 162440
% 59.43/9.44 # Factorizations : 4
% 59.43/9.44 # NegExts : 0
% 59.43/9.44 # Equation resolutions : 1274
% 59.43/9.44 # Disequality decompositions : 0
% 59.43/9.44 # Total rewrite steps : 53413
% 59.43/9.44 # ...of those cached : 38068
% 59.43/9.44 # Propositional unsat checks : 3
% 59.43/9.44 # Propositional check models : 2
% 59.43/9.44 # Propositional check unsatisfiable : 0
% 59.43/9.44 # Propositional clauses : 0
% 59.43/9.44 # Propositional clauses after purity: 0
% 59.43/9.44 # Propositional unsat core size : 0
% 59.43/9.44 # Propositional preprocessing time : 0.000
% 59.43/9.44 # Propositional encoding time : 0.154
% 59.43/9.44 # Propositional solver time : 0.071
% 59.43/9.44 # Success case prop preproc time : 0.000
% 59.43/9.44 # Success case prop encoding time : 0.000
% 59.43/9.44 # Success case prop solver time : 0.000
% 59.43/9.44 # Current number of processed clauses : 6142
% 59.43/9.44 # Positive orientable unit clauses : 1389
% 59.43/9.44 # Positive unorientable unit clauses: 112
% 59.43/9.44 # Negative unit clauses : 832
% 59.43/9.44 # Non-unit-clauses : 3809
% 59.43/9.44 # Current number of unprocessed clauses: 140235
% 59.43/9.44 # ...number of literals in the above : 288129
% 59.43/9.44 # Current number of archived formulas : 0
% 59.43/9.44 # Current number of archived clauses : 5884
% 59.43/9.44 # Clause-clause subsumption calls (NU) : 4210630
% 59.43/9.44 # Rec. Clause-clause subsumption calls : 2502383
% 59.43/9.44 # Non-unit clause-clause subsumptions : 3953
% 59.43/9.44 # Unit Clause-clause subsumption calls : 260137
% 59.43/9.44 # Rewrite failures with RHS unbound : 585
% 59.43/9.44 # BW rewrite match attempts : 32277
% 59.43/9.44 # BW rewrite match successes : 1276
% 59.43/9.44 # Condensation attempts : 0
% 59.43/9.44 # Condensation successes : 0
% 59.43/9.44 # Termbank termtop insertions : 5362909
% 59.43/9.44 # Search garbage collected termcells : 96405
% 59.43/9.44
% 59.43/9.44 # -------------------------------------------------
% 59.43/9.44 # User time : 7.486 s
% 59.43/9.44 # System time : 0.221 s
% 59.43/9.44 # Total time : 7.707 s
% 59.43/9.44 # Maximum resident set size: 37500 pages
% 59.43/9.44
% 59.43/9.44 # -------------------------------------------------
% 59.43/9.44 # User time : 7.606 s
% 59.43/9.44 # System time : 0.232 s
% 59.43/9.44 # Total time : 7.838 s
% 59.43/9.44 # Maximum resident set size: 9488 pages
% 59.43/9.44 % E---3.1 exiting
% 59.43/9.44 % E exiting
%------------------------------------------------------------------------------