TSTP Solution File: SWW316+1 by E-SAT---3.2.0
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%------------------------------------------------------------------------------
% File : E-SAT---3.2.0
% Problem : SWW316+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d SAT
% Computer : n013.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 18:14:10 EDT 2024
% Result : ContradictoryAxioms 73.43s 11.40s
% Output : CNFRefutation 73.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 28
% Syntax : Number of formulae : 158 ( 91 unt; 0 def)
% Number of atoms : 262 ( 94 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 202 ( 98 ~; 79 |; 13 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 8 con; 0-3 aty)
% Number of variables : 289 ( 52 sgn 139 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_bex__UNIV,axiom,
! [X17,X10] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
& hBOOL(hAPP(X17,X3)) )
<=> ? [X57] : hBOOL(hAPP(X17,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_bex__UNIV) ).
fof(fact_UNIV__I,axiom,
! [X18,X10] : hBOOL(hAPP(hAPP(c_member(X10),X18),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_UNIV__I) ).
fof(help_c__fNot__2,axiom,
! [X17] :
( ~ ~ hBOOL(X17)
| hBOOL(hAPP(c_fNot,X17)) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',help_c__fNot__2) ).
fof(fact_Collect__empty__eq,axiom,
! [X17,X10] :
( hAPP(c_Set_OCollect(X10),X17) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_Collect__empty__eq) ).
fof(help_c__fNot__1,axiom,
! [X17] :
( ~ hBOOL(hAPP(c_fNot,X17))
| ~ hBOOL(X17) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',help_c__fNot__1) ).
fof(fact_Compl__iff,axiom,
! [X20,X50,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X50),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X20)))
<=> ~ hBOOL(hAPP(hAPP(c_member(X10),X50),X20)) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_Compl__iff) ).
fof(fact_Collect__neg__eq,axiom,
! [X17,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X17)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X17)),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_Collect__neg__eq) ).
fof(fact_Collect__def,axiom,
! [X17,X10] : hAPP(c_Set_OCollect(X10),X17) = X17,
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_Collect__def) ).
fof(fact_mem__def,axiom,
! [X20,X18,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X18),X20))
<=> hBOOL(hAPP(X20,X18)) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_mem__def) ).
fof(fact_all__nat,axiom,
! [X17] :
( ! [X57] : hBOOL(hAPP(X17,X57))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
=> hBOOL(hAPP(X17,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_all__nat) ).
fof(fact_zero__zle__int,axiom,
! [X56] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X56))),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_zero__zle__int) ).
fof(help_c__COMBK__1,axiom,
! [X309,X45,X10,X23] : hAPP(hAPP(c_COMBK(X23,X10),X45),X309) = X45,
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',help_c__COMBK__1) ).
fof(help_c__COMBB__1,axiom,
! [X59,X16,X17,X32,X10,X21] : hAPP(hAPP(hAPP(c_COMBB(X21,X10,X32),X17),X16),X59) = hAPP(X17,hAPP(X16,X59)),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',help_c__COMBB__1) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_Pls__def) ).
fof(fact_nat__int,axiom,
! [X56] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X56)) = X56,
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_nat__int) ).
fof(fact_double__complement,axiom,
! [X20,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X20)) = X20,
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_double__complement) ).
fof(fact_insertI1,axiom,
! [X19,X51,X10] : hBOOL(hAPP(hAPP(c_member(X10),X51),hAPP(hAPP(c_Set_Oinsert(X10),X51),X19))),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_insertI1) ).
fof(fact_filter__id__conv,axiom,
! [X248,X17,X10] :
( hAPP(c_List_Ofilter(X10,X17),X248) = X248
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X248)))
=> hBOOL(hAPP(X17,X3)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_filter__id__conv) ).
fof(fact_top1I,axiom,
! [X18,X10] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X18)),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_top1I) ).
fof(fact_n__not__Suc__n,axiom,
! [X56] : X56 != hAPP(c_Nat_OSuc,X56),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_n__not__Suc__n) ).
fof(fact_ex__nat,axiom,
! [X17] :
( ? [X57] : hBOOL(hAPP(X17,X57))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
& hBOOL(hAPP(X17,hAPP(c_Int_Onat,X3))) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_ex__nat) ).
fof(fact_Zero__neq__Suc,axiom,
! [X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X85),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.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.kGaXEpYAsl/E---3.1_11989.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(help_c__fconj__2,axiom,
! [X16,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X16))
| hBOOL(X17) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',help_c__fconj__2) ).
fof(fact_add__eq__self__zero,axiom,
! [X56,X85] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X56) = X85
=> X56 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_add__eq__self__zero) ).
fof(fact_add__Suc__right,axiom,
! [X56,X85] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),hAPP(c_Nat_OSuc,X56)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X56)),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_add__Suc__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X85] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X85,
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_Nat_Oadd__0__right) ).
fof(fact_nat__add__commute,axiom,
! [X56,X85] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),X85),
file('/export/starexec/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p',fact_nat__add__commute) ).
fof(c_0_28,plain,
! [X1732,X1733,X1734,X1736,X1737,X1738] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1733),X1734),c_Orderings_Otop__class_Otop(tc_fun(X1733,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X1732,X1734))
| hBOOL(hAPP(X1732,esk37_1(X1732))) )
& ( hBOOL(hAPP(hAPP(c_member(X1738),esk38_2(X1736,X1738)),c_Orderings_Otop__class_Otop(tc_fun(X1738,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X1736,X1737)) )
& ( hBOOL(hAPP(X1736,esk38_2(X1736,X1738)))
| ~ hBOOL(hAPP(X1736,X1737)) ) ),
inference(distribute,[status(thm)],[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)],[fact_bex__UNIV])])])])])])]) ).
fof(c_0_29,plain,
! [X1700,X1701] : hBOOL(hAPP(hAPP(c_member(X1701),X1700),c_Orderings_Otop__class_Otop(tc_fun(X1701,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(c_0_30,plain,
! [X17] :
( hBOOL(X17)
| hBOOL(hAPP(c_fNot,X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(c_0_31,plain,
! [X17,X10] :
( hAPP(c_Set_OCollect(X10),X17) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_32,plain,
! [X17] :
( ~ hBOOL(hAPP(c_fNot,X17))
| ~ hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_33,plain,
( hBOOL(hAPP(X3,esk37_1(X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X2537] :
( hBOOL(X2537)
| hBOOL(hAPP(c_fNot,X2537)) ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X20,X50,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X50),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X20)))
<=> ~ hBOOL(hAPP(hAPP(c_member(X10),X50),X20)) ),
inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).
fof(c_0_37,plain,
! [X2526,X2527] : hAPP(c_Set_OCollect(X2527),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2527),c_fNot),X2526)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2527,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2527),X2526)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_38,plain,
! [X4556,X4557] : hAPP(c_Set_OCollect(X4557),X4556) = X4556,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_39,plain,
! [X4564,X4565,X4566,X4567,X4569] :
( ( hAPP(c_Set_OCollect(X4565),X4564) != c_Orderings_Obot__class_Obot(tc_fun(X4565,tc_HOL_Obool))
| ~ hBOOL(hAPP(X4564,X4566)) )
& ( hBOOL(hAPP(X4567,esk135_1(X4567)))
| hAPP(c_Set_OCollect(X4569),X4567) = c_Orderings_Obot__class_Obot(tc_fun(X4569,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_31])])])])])]) ).
fof(c_0_40,plain,
! [X2536] :
( ~ hBOOL(hAPP(c_fNot,X2536))
| ~ hBOOL(X2536) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).
cnf(c_0_41,plain,
( hBOOL(hAPP(X1,esk37_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_42,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X1748,X1749,X1750] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1750),X1749),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1750,tc_HOL_Obool)),X1748)))
| ~ hBOOL(hAPP(hAPP(c_member(X1750),X1749),X1748)) )
& ( hBOOL(hAPP(hAPP(c_member(X1750),X1749),X1748))
| hBOOL(hAPP(hAPP(c_member(X1750),X1749),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1750,tc_HOL_Obool)),X1748))) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
cnf(c_0_44,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_37]) ).
cnf(c_0_45,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( hAPP(c_Set_OCollect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(X1,esk135_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_39]) ).
cnf(c_0_48,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( hBOOL(hAPP(c_fNot,esk37_1(c_fNot)))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,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_44,c_0_45]),c_0_45]) ).
fof(c_0_52,plain,
! [X1264,X1265,X1266] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1266),X1265),X1264))
| hBOOL(hAPP(X1264,X1265)) )
& ( ~ hBOOL(hAPP(X1264,X1265))
| hBOOL(hAPP(hAPP(c_member(X1266),X1265),X1264)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
fof(c_0_53,plain,
! [X5347,X5349,X5350,X5352] :
( ( ~ hBOOL(hAPP(X5347,esk171_1(X5347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5349))
| hBOOL(hAPP(X5347,hAPP(c_Int_Onat,X5349))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk172_1(X5350)))
| hBOOL(hAPP(X5350,X5352)) )
& ( ~ hBOOL(hAPP(X5350,hAPP(c_Int_Onat,esk172_1(X5350))))
| hBOOL(hAPP(X5350,X5352)) ) ),
inference(distribute,[status(thm)],[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)],[fact_all__nat])])])])])])]) ).
fof(c_0_54,plain,
! [X5249] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5249))),
inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).
cnf(c_0_55,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_45])]) ).
cnf(c_0_56,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk135_1(X1))) ),
inference(rw,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_57,plain,
( hBOOL(hAPP(X1,esk38_2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_58,plain,
hBOOL(hAPP(c_fNot,esk37_1(c_fNot))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_49]) ).
fof(c_0_59,plain,
! [X2475,X2476,X2477,X2478] : hAPP(hAPP(c_COMBK(X2478,X2477),X2476),X2475) = X2476,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_60,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_62,plain,
! [X544,X545,X546,X547,X548,X549] : hAPP(hAPP(hAPP(c_COMBB(X549,X548,X547),X546),X545),X544) = hAPP(X546,hAPP(X545,X544)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_63,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(X1,esk171_1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
cnf(c_0_65,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_66,plain,
! [X5285] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5285)) = X5285,
inference(variable_rename,[status(thm)],[fact_nat__int]) ).
cnf(c_0_67,plain,
( hBOOL(hAPP(X1,esk135_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
hBOOL(hAPP(c_fNot,esk38_2(c_fNot,X1))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
fof(c_0_69,plain,
! [X1746,X1747] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1747,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1747,tc_HOL_Obool)),X1746)) = X1746,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_70,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_71,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_73,plain,
! [X962,X963,X964] : hBOOL(hAPP(hAPP(c_member(X964),X963),hAPP(hAPP(c_Set_Oinsert(X964),X963),X962))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
cnf(c_0_74,plain,
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))
| ~ hBOOL(hAPP(X1,esk171_1(X1))) ),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_75,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),
inference(rw,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_76,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,plain,
hBOOL(hAPP(c_fNot,esk135_1(c_fNot))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_78,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_69]) ).
fof(c_0_79,plain,
! [X5126,X5127,X5128,X5129,X5130,X5131,X5132] :
( ( hAPP(c_List_Ofilter(X5128,X5127),X5126) != X5126
| ~ hBOOL(hAPP(hAPP(c_member(X5128),X5129),hAPP(c_List_Oset(X5128),X5126)))
| hBOOL(hAPP(X5127,X5129)) )
& ( hBOOL(hAPP(hAPP(c_member(X5132),esk153_3(X5130,X5131,X5132)),hAPP(c_List_Oset(X5132),X5130)))
| hAPP(c_List_Ofilter(X5132,X5131),X5130) = X5130 )
& ( ~ hBOOL(hAPP(X5131,esk153_3(X5130,X5131,X5132)))
| hAPP(c_List_Ofilter(X5132,X5131),X5130) = X5130 ) ),
inference(distribute,[status(thm)],[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)],[fact_filter__id__conv])])])])])])]) ).
fof(c_0_80,plain,
! [X1698,X1699] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1699,tc_HOL_Obool)),X1698)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_81,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = X3
| hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_56]),c_0_70]) ).
cnf(c_0_82,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_fNot,hAPP(X3,X2))) ),
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_83,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_84,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,esk171_1(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
fof(c_0_85,plain,
! [X56] : X56 != hAPP(c_Nat_OSuc,X56),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_86,plain,
~ hBOOL(esk135_1(c_fNot)),
inference(spm,[status(thm)],[c_0_48,c_0_77]) ).
cnf(c_0_87,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_78,c_0_51]),c_0_51]) ).
cnf(c_0_88,plain,
( hAPP(c_List_Ofilter(X3,X1),X2) = X2
| ~ hBOOL(hAPP(X1,esk153_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_90,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_81]) ).
cnf(c_0_91,plain,
~ hBOOL(hAPP(c_fNot,hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2))),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
( hBOOL(hAPP(c_fNot,X1))
| hBOOL(esk171_1(c_fNot)) ),
inference(spm,[status(thm)],[c_0_84,c_0_42]) ).
fof(c_0_93,plain,
! [X5341,X5342,X5344,X5345] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk169_1(X5341)))
| ~ hBOOL(hAPP(X5341,X5342)) )
& ( hBOOL(hAPP(X5341,hAPP(c_Int_Onat,esk169_1(X5341))))
| ~ hBOOL(hAPP(X5341,X5342)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X5345))
| ~ hBOOL(hAPP(X5344,hAPP(c_Int_Onat,X5345)))
| hBOOL(hAPP(X5344,esk170_1(X5344))) ) ),
inference(distribute,[status(thm)],[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)],[fact_ex__nat])])])])])])]) ).
fof(c_0_94,plain,
! [X1930] : X1930 != hAPP(c_Nat_OSuc,X1930),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_85])]) ).
cnf(c_0_95,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = esk135_1(c_fNot),
inference(spm,[status(thm)],[c_0_86,c_0_81]) ).
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_72,c_0_87]),c_0_72]) ).
cnf(c_0_97,plain,
hAPP(c_List_Ofilter(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))),X3) = X3,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_98,plain,
( X1 = hAPP(c_fNot,X2)
| hBOOL(X1)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_90]) ).
cnf(c_0_99,plain,
hBOOL(esk171_1(c_fNot)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,plain,
( hBOOL(hAPP(X2,esk170_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_101,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_102,plain,
( esk135_1(c_fNot) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_95]) ).
fof(c_0_103,plain,
! [X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X85),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_104,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_105,plain,
( X1 = hAPP(c_fNot,esk171_1(c_fNot))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,plain,
( hBOOL(hAPP(X1,esk170_1(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X2))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2))) ),
inference(rw,[status(thm)],[c_0_100,c_0_64]) ).
cnf(c_0_107,plain,
hBOOL(hAPP(c_Nat_OSuc,esk135_1(c_fNot))),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102])]) ).
fof(c_0_108,plain,
! [X1950] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1950),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_103])]) ).
cnf(c_0_109,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_110,plain,
( hAPP(c_fNot,X1) = esk171_1(c_fNot)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,plain,
( hBOOL(hAPP(X1,esk170_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_75]),c_0_76]) ).
cnf(c_0_112,plain,
hBOOL(hAPP(c_Nat_OSuc,esk135_1(c_Nat_OSuc))),
inference(spm,[status(thm)],[c_0_67,c_0_107]) ).
cnf(c_0_113,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_114,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_109,c_0_64]) ).
cnf(c_0_115,plain,
( X1 = esk171_1(c_fNot)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_110]),c_0_104]) ).
cnf(c_0_116,plain,
hBOOL(hAPP(c_Nat_OSuc,esk170_1(c_Nat_OSuc))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_117,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,plain,
hAPP(c_Nat_OSuc,esk170_1(c_Nat_OSuc)) = esk171_1(c_fNot),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,plain,
esk171_1(c_fNot) != hAPP(c_Int_Onat,c_Int_OPls),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
fof(c_0_120,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X17),X16))
| hBOOL(X17) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
cnf(c_0_121,plain,
( hBOOL(X1)
| hAPP(c_fNot,X1) != hAPP(c_Int_Onat,c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_119,c_0_110]) ).
cnf(c_0_122,plain,
hAPP(c_Nat_OSuc,esk135_1(c_Nat_OSuc)) = esk171_1(c_fNot),
inference(spm,[status(thm)],[c_0_115,c_0_112]) ).
fof(c_0_123,plain,
! [X2084,X2085] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2085),X2084) != X2085
| X2084 = 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])])]) ).
fof(c_0_124,plain,
! [X2590,X2591] :
( ~ hBOOL(hAPP(hAPP(c_fconj,X2591),X2590))
| hBOOL(X2591) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_120])]) ).
cnf(c_0_125,plain,
~ hBOOL(hAPP(c_Int_Onat,c_Int_OPls)),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_121]),c_0_104])]) ).
cnf(c_0_126,plain,
esk171_1(c_fNot) != esk135_1(c_Nat_OSuc),
inference(spm,[status(thm)],[c_0_101,c_0_122]) ).
cnf(c_0_127,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_123]) ).
fof(c_0_128,plain,
! [X2008,X2009] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2009),hAPP(c_Nat_OSuc,X2008)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2009),X2008)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_129,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_130,plain,
( hAPP(c_Int_Onat,c_Int_OPls) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_90]) ).
cnf(c_0_131,plain,
( hBOOL(X1)
| hAPP(c_fNot,X1) != esk135_1(c_Nat_OSuc) ),
inference(spm,[status(thm)],[c_0_126,c_0_110]) ).
cnf(c_0_132,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_127,c_0_114]) ).
cnf(c_0_133,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_128]) ).
fof(c_0_134,plain,
! [X2088] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2088),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2088,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_135,plain,
! [X2178,X2179] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2179),X2178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2179),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_136,plain,
( hAPP(c_fconj,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_56]) ).
cnf(c_0_137,plain,
( hAPP(c_fNot,X1) = hAPP(c_Int_Onat,c_Int_OPls)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_130]) ).
cnf(c_0_138,plain,
hBOOL(hAPP(c_fNot,esk135_1(c_Nat_OSuc))),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_104])]) ).
cnf(c_0_139,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_132,c_0_133]),c_0_117]) ).
cnf(c_0_140,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_134]) ).
cnf(c_0_141,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_142,plain,
hAPP(c_fconj,esk135_1(c_fNot)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_86,c_0_136]) ).
cnf(c_0_143,plain,
esk135_1(c_Nat_OSuc) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_104]) ).
cnf(c_0_144,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_139,c_0_133]) ).
cnf(c_0_145,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_140,c_0_114]) ).
cnf(c_0_146,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X2,
inference(spm,[status(thm)],[c_0_139,c_0_141]) ).
cnf(c_0_147,plain,
~ hBOOL(hAPP(hAPP(c_fconj,esk135_1(c_fNot)),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_142]) ).
cnf(c_0_148,plain,
esk171_1(c_fNot) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)),
inference(rw,[status(thm)],[c_0_122,c_0_143]) ).
cnf(c_0_149,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_150,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != hAPP(c_Nat_OSuc,X2),
inference(spm,[status(thm)],[c_0_146,c_0_133]) ).
cnf(c_0_151,plain,
~ hBOOL(hAPP(hAPP(c_fconj,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_81]),c_0_86]) ).
cnf(c_0_152,plain,
( X1 = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_115,c_0_148]) ).
cnf(c_0_153,plain,
( hBOOL(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))
| hBOOL(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_90])]) ).
cnf(c_0_154,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)),
inference(spm,[status(thm)],[c_0_150,c_0_145]) ).
cnf(c_0_155,plain,
~ hBOOL(hAPP(hAPP(c_fconj,hAPP(c_fNot,esk171_1(c_fNot))),X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_105]),c_0_55]) ).
cnf(c_0_156,plain,
hBOOL(X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_157,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW316+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d SAT
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 08:05:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.10/1.32 Running first-order model finding
% 1.10/1.32 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.kGaXEpYAsl/E---3.1_11989.p
% 73.43/11.40 # Version: 3.2.0
% 73.43/11.40 # Preprocessing class: FMLMSMSMSSSNFFN.
% 73.43/11.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.43/11.40 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.43/11.40 # Starting new_bool_3 with 300s (1) cores
% 73.43/11.40 # Starting new_bool_1 with 300s (1) cores
% 73.43/11.40 # Starting sh5l with 300s (1) cores
% 73.43/11.40 # new_bool_1 with pid 12097 completed with status 0
% 73.43/11.40 # Result found by new_bool_1
% 73.43/11.40 # Preprocessing class: FMLMSMSMSSSNFFN.
% 73.43/11.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.43/11.40 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.43/11.40 # Starting new_bool_3 with 300s (1) cores
% 73.43/11.40 # Starting new_bool_1 with 300s (1) cores
% 73.43/11.40 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 73.43/11.40 # Search class: FGHSM-SMLM33-DFFFFFNN
% 73.43/11.40 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 73.43/11.40 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 73.43/11.40 # SAT001_MinMin_p005000_rr with pid 12102 completed with status 0
% 73.43/11.40 # Result found by SAT001_MinMin_p005000_rr
% 73.43/11.40 # Preprocessing class: FMLMSMSMSSSNFFN.
% 73.43/11.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.43/11.40 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.43/11.40 # Starting new_bool_3 with 300s (1) cores
% 73.43/11.40 # Starting new_bool_1 with 300s (1) cores
% 73.43/11.40 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 73.43/11.40 # Search class: FGHSM-SMLM33-DFFFFFNN
% 73.43/11.40 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 73.43/11.40 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 73.43/11.40 # Preprocessing time : 0.035 s
% 73.43/11.40 # Presaturation interreduction done
% 73.43/11.40
% 73.43/11.40 # Proof found!
% 73.43/11.40 # SZS status ContradictoryAxioms
% 73.43/11.40 # SZS output start CNFRefutation
% See solution above
% 73.43/11.40 # Parsed axioms : 5227
% 73.43/11.40 # Removed by relevancy pruning/SinE : 3760
% 73.43/11.40 # Initial clauses : 2228
% 73.43/11.40 # Removed in clause preprocessing : 71
% 73.43/11.40 # Initial clauses in saturation : 2157
% 73.43/11.40 # Processed clauses : 16222
% 73.43/11.40 # ...of these trivial : 306
% 73.43/11.40 # ...subsumed : 9923
% 73.43/11.40 # ...remaining for further processing : 5993
% 73.43/11.40 # Other redundant clauses eliminated : 6612
% 73.43/11.40 # Clauses deleted for lack of memory : 0
% 73.43/11.40 # Backward-subsumed : 211
% 73.43/11.40 # Backward-rewritten : 2853
% 73.43/11.40 # Generated clauses : 339019
% 73.43/11.40 # ...of the previous two non-redundant : 321237
% 73.43/11.40 # ...aggressively subsumed : 0
% 73.43/11.40 # Contextual simplify-reflections : 13
% 73.43/11.40 # Paramodulations : 332339
% 73.43/11.40 # Factorizations : 18
% 73.43/11.40 # NegExts : 0
% 73.43/11.40 # Equation resolutions : 6686
% 73.43/11.40 # Disequality decompositions : 0
% 73.43/11.40 # Total rewrite steps : 42744
% 73.43/11.40 # ...of those cached : 32683
% 73.43/11.40 # Propositional unsat checks : 1
% 73.43/11.40 # Propositional check models : 0
% 73.43/11.40 # Propositional check unsatisfiable : 0
% 73.43/11.40 # Propositional clauses : 0
% 73.43/11.40 # Propositional clauses after purity: 0
% 73.43/11.40 # Propositional unsat core size : 0
% 73.43/11.40 # Propositional preprocessing time : 0.000
% 73.43/11.40 # Propositional encoding time : 0.595
% 73.43/11.40 # Propositional solver time : 0.225
% 73.43/11.40 # Success case prop preproc time : 0.000
% 73.43/11.40 # Success case prop encoding time : 0.000
% 73.43/11.40 # Success case prop solver time : 0.000
% 73.43/11.40 # Current number of processed clauses : 1202
% 73.43/11.40 # Positive orientable unit clauses : 355
% 73.43/11.40 # Positive unorientable unit clauses: 47
% 73.43/11.40 # Negative unit clauses : 311
% 73.43/11.40 # Non-unit-clauses : 489
% 73.43/11.40 # Current number of unprocessed clauses: 296580
% 73.43/11.40 # ...number of literals in the above : 909805
% 73.43/11.40 # Current number of archived formulas : 0
% 73.43/11.40 # Current number of archived clauses : 4623
% 73.43/11.40 # Clause-clause subsumption calls (NU) : 1638413
% 73.43/11.40 # Rec. Clause-clause subsumption calls : 712119
% 73.43/11.40 # Non-unit clause-clause subsumptions : 6967
% 73.43/11.40 # Unit Clause-clause subsumption calls : 80247
% 73.43/11.40 # Rewrite failures with RHS unbound : 424
% 73.43/11.40 # BW rewrite match attempts : 9251
% 73.43/11.40 # BW rewrite match successes : 2095
% 73.43/11.40 # Condensation attempts : 0
% 73.43/11.40 # Condensation successes : 0
% 73.43/11.40 # Termbank termtop insertions : 11044459
% 73.43/11.40 # Search garbage collected termcells : 64233
% 73.43/11.40
% 73.43/11.40 # -------------------------------------------------
% 73.43/11.40 # User time : 9.120 s
% 73.43/11.40 # System time : 0.340 s
% 73.43/11.40 # Total time : 9.460 s
% 73.43/11.40 # Maximum resident set size: 16600 pages
% 73.43/11.40
% 73.43/11.40 # -------------------------------------------------
% 73.43/11.40 # User time : 9.263 s
% 73.43/11.40 # System time : 0.345 s
% 73.43/11.40 # Total time : 9.608 s
% 73.43/11.40 # Maximum resident set size: 9520 pages
% 73.43/11.40 % E---3.1 exiting
% 73.43/11.40 % E exiting
%------------------------------------------------------------------------------