TSTP Solution File: SWW299+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW299+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.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 20:09:02 EDT 2023
% Result : ContradictoryAxioms 92.08s 15.05s
% Output : CNFRefutation 92.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 88 ( 72 unt; 0 def)
% Number of atoms : 112 ( 89 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 18 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 153 ( 17 sgn; 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X23,X5] :
( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.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.TEF7AUx8rn/E---3.1_23576.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X23,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X23)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X23)),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X23,X2,X17,X5] : hAPP(c_Set_Ovimage(X5,X17,X2),hAPP(c_Set_OCollect(X17),X23)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X17,tc_HOL_Obool,X5),X23),X2)),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_vimage__Collect__eq) ).
fof(help_c__COMBK__1,axiom,
! [X299,X298,X5,X38] : hAPP(hAPP(c_COMBK(X38,X5),X298),X299) = X298,
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',help_c__COMBK__1) ).
fof(fact_double__complement,axiom,
! [X18,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)),X18)) = X18,
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X18,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X18) = X18,
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_vimage__id) ).
fof(help_c__fNot__1,axiom,
! [X23] :
( ~ hBOOL(hAPP(c_fNot,X23))
| ~ hBOOL(X23) ),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.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.TEF7AUx8rn/E---3.1_23576.p',fact_UNIV__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X67] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X67),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_Zero__neq__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/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.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.TEF7AUx8rn/E---3.1_23576.p',fact_Pls__def) ).
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.TEF7AUx8rn/E---3.1_23576.p',fact_Compl__empty__eq) ).
fof(fact_add__0__iff,axiom,
! [X6,X21,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X68,X67] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),hAPP(c_Nat_OSuc,X68)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),X68)),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_add__Suc__right) ).
fof(fact_id__apply,axiom,
! [X37,X38] : hAPP(c_Fun_Oid(X38),X37) = X37,
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_id__apply) ).
fof(help_c__COMBB__1,axiom,
! [X26,X27,X23,X126,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X126),X23),X27),X26) = hAPP(X23,hAPP(X27,X26)),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.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/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X67] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X67,
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X68] : X68 != hAPP(c_Nat_OSuc,X68),
file('/export/starexec/sandbox2/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p',fact_n__not__Suc__n) ).
fof(c_0_21,plain,
! [X23,X5] :
( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X10915] : c_Orderings_Obot__class_Obot(tc_fun(X10915,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10915),hAPP(c_COMBK(tc_HOL_Obool,X10915),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_23,plain,
! [X10931,X10932] : hAPP(c_Set_OCollect(X10932),X10931) = X10931,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_24,plain,
! [X10938,X10939] : hAPP(c_Set_OCollect(X10939),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10939),c_fNot),X10938)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10939,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10939),X10938)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_25,plain,
! [X10934,X10935,X10936,X10937] : hAPP(c_Set_Ovimage(X10937,X10936,X10935),hAPP(c_Set_OCollect(X10936),X10934)) = hAPP(c_Set_OCollect(X10937),hAPP(hAPP(c_COMBB(X10936,tc_HOL_Obool,X10937),X10934),X10935)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_26,plain,
! [X10925,X10926,X10927,X10928,X10930] :
( ( hAPP(c_Set_OCollect(X10926),X10925) != c_Orderings_Obot__class_Obot(tc_fun(X10926,tc_HOL_Obool))
| ~ hBOOL(hAPP(X10925,X10927)) )
& ( hBOOL(hAPP(X10928,esk290_1(X10928)))
| hAPP(c_Set_OCollect(X10930),X10928) = c_Orderings_Obot__class_Obot(tc_fun(X10930,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_21])])])])]) ).
fof(c_0_27,plain,
! [X17509,X17510,X17511,X17512] : hAPP(hAPP(c_COMBK(X17512,X17511),X17510),X17509) = X17510,
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_22]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X5929,X5930] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5930,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5930,tc_HOL_Obool)),X5929)) = X5929,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_31,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_24]) ).
fof(c_0_32,plain,
! [X11124,X11125] : hAPP(c_Set_Ovimage(X11125,X11125,c_Fun_Oid(X11125)),X11124) = X11124,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_33,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_25]) ).
fof(c_0_34,plain,
! [X23] :
( ~ hBOOL(hAPP(c_fNot,X23))
| ~ hBOOL(X23) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_35,plain,
( hBOOL(hAPP(X1,esk290_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_26]) ).
cnf(c_0_36,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
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_28,c_0_29]) ).
fof(c_0_38,plain,
! [X10933] : c_Orderings_Otop__class_Otop(tc_fun(X10933,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10933),hAPP(c_COMBK(tc_HOL_Obool,X10933),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_39,plain,
! [X3121] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3121),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_40,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_41,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_42,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_30]) ).
cnf(c_0_43,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_31,c_0_29]),c_0_29]) ).
cnf(c_0_44,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,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_33,c_0_29]),c_0_29]) ).
fof(c_0_46,plain,
! [X17535] :
( ~ hBOOL(hAPP(c_fNot,X17535))
| ~ hBOOL(X17535) ),
inference(variable_rename,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk290_1(X1))) ),
inference(rw,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_48,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_49,plain,
! [X6545] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6545,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6545,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X6545,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_50,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_38]) ).
fof(c_0_51,plain,
! [X3088,X3089,X3090] :
( ( X3089 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3090),X3089),X3088)
| X3088 = c_Groups_Ozero__class_Ozero(X3090)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3090) )
& ( X3088 != c_Groups_Ozero__class_Ozero(X3090)
| X3089 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3090),X3089),X3088)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3090) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(c_0_52,plain,
! [X2826,X2827] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2827),hAPP(c_Nat_OSuc,X2826)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2827),X2826)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_53,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_55,plain,
! [X11126,X11127] : hAPP(c_Fun_Oid(X11127),X11126) = X11126,
inference(variable_rename,[status(thm)],[fact_id__apply]) ).
cnf(c_0_56,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_42,c_0_43]),c_0_43]) ).
cnf(c_0_57,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_58,plain,
! [X17513,X17514,X17515,X17516,X17517,X17518] : hAPP(hAPP(hAPP(c_COMBB(X17518,X17517,X17516),X17515),X17514),X17513) = hAPP(X17515,hAPP(X17514,X17513)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_59,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,plain,
( c_fFalse = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_47]),c_0_48]),c_0_36]) ).
cnf(c_0_61,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_49]) ).
cnf(c_0_62,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_50,c_0_29]) ).
cnf(c_0_63,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_51]) ).
cnf(c_0_64,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_52]) ).
cnf(c_0_65,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_66,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_67,plain,
! [X3136] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3136),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3136,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
cnf(c_0_68,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_69,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_56,c_0_57]) ).
cnf(c_0_70,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_71,plain,
( hAPP(c_fNot,X1) = c_fFalse
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_72,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_61,c_0_43]) ).
cnf(c_0_73,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_62]) ).
cnf(c_0_74,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_63,c_0_64]),c_0_54]),c_0_65])]),c_0_66]) ).
cnf(c_0_75,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_67]) ).
fof(c_0_76,plain,
! [X2786] : X2786 != hAPP(c_Nat_OSuc,X2786),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_77,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_78,plain,
( hAPP(c_fNot,X1) = c_fFalse
| c_fFalse = X1 ),
inference(spm,[status(thm)],[c_0_71,c_0_60]) ).
cnf(c_0_79,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_72]),c_0_73]),c_0_48]) ).
cnf(c_0_80,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_74,c_0_64]) ).
cnf(c_0_81,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_75,c_0_54]) ).
cnf(c_0_82,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,plain,
( c_fFalse = X1
| c_fTrue = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_86,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_83]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.10/1.16 % Problem : SWW299+1 : TPTP v8.1.2. Released v5.2.0.
% 1.10/1.17 % Command : run_E %s %d THM
% 1.20/1.38 % Computer : n026.cluster.edu
% 1.20/1.38 % Model : x86_64 x86_64
% 1.20/1.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.20/1.38 % Memory : 8042.1875MB
% 1.20/1.38 % OS : Linux 3.10.0-693.el7.x86_64
% 1.20/1.38 % CPULimit : 2400
% 1.20/1.38 % WCLimit : 300
% 1.20/1.38 % DateTime : Mon Oct 2 22:39:00 EDT 2023
% 1.20/1.38 % CPUTime :
% 2.29/2.56 Running first-order theorem proving
% 2.29/2.56 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/tmp/tmp.TEF7AUx8rn/E---3.1_23576.p
% 92.08/15.05 # Version: 3.1pre001
% 92.08/15.05 # Preprocessing class: FMLMSMSMSSSNFFN.
% 92.08/15.05 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 92.08/15.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 92.08/15.05 # Starting new_bool_3 with 300s (1) cores
% 92.08/15.05 # Starting new_bool_1 with 300s (1) cores
% 92.08/15.05 # Starting sh5l with 300s (1) cores
% 92.08/15.05 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 23661 completed with status 0
% 92.08/15.05 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 92.08/15.05 # Preprocessing class: FMLMSMSMSSSNFFN.
% 92.08/15.05 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 92.08/15.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 92.08/15.05 # No SInE strategy applied
% 92.08/15.05 # Search class: FGHSM-SMLM33-DFFFFFNN
% 92.08/15.05 # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 92.08/15.05 # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 92.08/15.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 92.08/15.05 # Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 92.08/15.05 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 92.08/15.05 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 135s (1) cores
% 92.08/15.05 # SAT001_MinMin_p005000_rr with pid 23668 completed with status 0
% 92.08/15.05 # Result found by SAT001_MinMin_p005000_rr
% 92.08/15.05 # Preprocessing class: FMLMSMSMSSSNFFN.
% 92.08/15.05 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 92.08/15.05 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 92.08/15.05 # No SInE strategy applied
% 92.08/15.05 # Search class: FGHSM-SMLM33-DFFFFFNN
% 92.08/15.05 # Scheduled 6 strats onto 5 cores with 1499 seconds (1499 total)
% 92.08/15.05 # Starting SAT001_MinMin_p005000_rr with 810s (1) cores
% 92.08/15.05 # Preprocessing time : 0.171 s
% 92.08/15.05 # Presaturation interreduction done
% 92.08/15.05
% 92.08/15.05 # Proof found!
% 92.08/15.05 # SZS status ContradictoryAxioms
% 92.08/15.05 # SZS output start CNFRefutation
% See solution above
% 92.08/15.05 # Parsed axioms : 5224
% 92.08/15.05 # Removed by relevancy pruning/SinE : 0
% 92.08/15.05 # Initial clauses : 7581
% 92.08/15.05 # Removed in clause preprocessing : 250
% 92.08/15.05 # Initial clauses in saturation : 7331
% 92.08/15.05 # Processed clauses : 20608
% 92.08/15.05 # ...of these trivial : 429
% 92.08/15.05 # ...subsumed : 6990
% 92.08/15.05 # ...remaining for further processing : 13189
% 92.08/15.05 # Other redundant clauses eliminated : 1084
% 92.08/15.05 # Clauses deleted for lack of memory : 0
% 92.08/15.05 # Backward-subsumed : 138
% 92.08/15.05 # Backward-rewritten : 551
% 92.08/15.05 # Generated clauses : 209708
% 92.08/15.05 # ...of the previous two non-redundant : 201008
% 92.08/15.05 # ...aggressively subsumed : 0
% 92.08/15.05 # Contextual simplify-reflections : 42
% 92.08/15.05 # Paramodulations : 208644
% 92.08/15.05 # Factorizations : 4
% 92.08/15.05 # NegExts : 0
% 92.08/15.05 # Equation resolutions : 1126
% 92.08/15.05 # Total rewrite steps : 56900
% 92.08/15.05 # Propositional unsat checks : 3
% 92.08/15.05 # Propositional check models : 2
% 92.08/15.05 # Propositional check unsatisfiable : 0
% 92.08/15.05 # Propositional clauses : 0
% 92.08/15.05 # Propositional clauses after purity: 0
% 92.08/15.05 # Propositional unsat core size : 0
% 92.08/15.05 # Propositional preprocessing time : 0.000
% 92.08/15.05 # Propositional encoding time : 0.202
% 92.08/15.05 # Propositional solver time : 0.096
% 92.08/15.05 # Success case prop preproc time : 0.000
% 92.08/15.05 # Success case prop encoding time : 0.000
% 92.08/15.05 # Success case prop solver time : 0.000
% 92.08/15.05 # Current number of processed clauses : 6088
% 92.08/15.05 # Positive orientable unit clauses : 1620
% 92.08/15.05 # Positive unorientable unit clauses: 126
% 92.08/15.05 # Negative unit clauses : 737
% 92.08/15.05 # Non-unit-clauses : 3605
% 92.08/15.05 # Current number of unprocessed clauses: 179995
% 92.08/15.05 # ...number of literals in the above : 339584
% 92.08/15.05 # Current number of archived formulas : 0
% 92.08/15.05 # Current number of archived clauses : 6648
% 92.08/15.05 # Clause-clause subsumption calls (NU) : 4074553
% 92.08/15.05 # Rec. Clause-clause subsumption calls : 2241584
% 92.08/15.05 # Non-unit clause-clause subsumptions : 5175
% 92.08/15.05 # Unit Clause-clause subsumption calls : 198893
% 92.08/15.05 # Rewrite failures with RHS unbound : 421
% 92.08/15.05 # BW rewrite match attempts : 38648
% 92.08/15.05 # BW rewrite match successes : 1339
% 92.08/15.05 # Condensation attempts : 0
% 92.08/15.05 # Condensation successes : 0
% 92.08/15.05 # Termbank termtop insertions : 7048162
% 92.08/15.05
% 92.08/15.05 # -------------------------------------------------
% 92.08/15.05 # User time : 11.659 s
% 92.08/15.05 # System time : 0.340 s
% 92.08/15.05 # Total time : 11.999 s
% 92.08/15.05 # Maximum resident set size: 39968 pages
% 92.08/15.05
% 92.08/15.05 # -------------------------------------------------
% 92.08/15.05 # User time : 52.926 s
% 92.08/15.05 # System time : 1.476 s
% 92.08/15.05 # Total time : 54.402 s
% 92.08/15.05 # Maximum resident set size: 9452 pages
% 92.08/15.05 % E---3.1 exiting
% 92.08/15.06 % E---3.1 exiting
%------------------------------------------------------------------------------