TSTP Solution File: SWW322+1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SWW322+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 : Tue May 21 06:45:18 EDT 2024
% Result : ContradictoryAxioms 6.13s 2.18s
% Output : CNFRefutation 6.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 117 ( 69 unt; 0 def)
% Number of atoms : 185 ( 88 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 142 ( 74 ~; 49 |; 8 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 10 con; 0-3 aty)
% Number of variables : 224 ( 31 sgn 118 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ComplE,axiom,
! [X19,X23,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).
fof(fact_Collect__neg__eq,axiom,
! [X30,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X30)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_Collect__def,axiom,
! [X30,X5] : hAPP(c_Set_OCollect(X5),X30) = X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_mem__def,axiom,
! [X19,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),X19))
<=> hBOOL(hAPP(X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(help_c__COMBB__1,axiom,
! [X37,X29,X30,X25,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X25),X30),X29),X37) = hAPP(X30,hAPP(X29,X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_all__not__in__conv,axiom,
! [X19,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
<=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(help_c__fNot__2,axiom,
! [X30] :
( ~ ~ hBOOL(X30)
| hBOOL(hAPP(c_fNot,X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(fact_bex__UNIV,axiom,
! [X30,X5] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
& hBOOL(hAPP(X30,X3)) )
<=> ? [X77] : hBOOL(hAPP(X30,X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__UNIV) ).
fof(fact_UNIV__I,axiom,
! [X20,X5] : hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(help_c__fNot__1,axiom,
! [X30] :
( ~ hBOOL(hAPP(c_fNot,X30))
| ~ hBOOL(X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(help_c__COMBK__1,axiom,
! [X303,X302,X161,X56] : hAPP(hAPP(c_COMBK(X56,X161),X302),X303) = X302,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__empty__eq,axiom,
! [X30,X5] :
( hAPP(c_Set_OCollect(X5),X30) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X30,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(conj_2,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_double__complement,axiom,
! [X19,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)),X19)) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_Zero__neq__Suc,axiom,
! [X86] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X86),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_filter__id__conv,axiom,
! [X224,X30,X5] :
( hAPP(c_List_Ofilter(X5,X30),X224) = X224
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X224)))
=> hBOOL(hAPP(X30,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__id__conv) ).
fof(fact_top1I,axiom,
! [X20,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_add__eq__self__zero,axiom,
! [X92,X86] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92) = X86
=> X92 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_n__not__Suc__n,axiom,
! [X92] : X92 != hAPP(c_Nat_OSuc,X92),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_add__Suc__right,axiom,
! [X92,X86] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),hAPP(c_Nat_OSuc,X92)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X86),X92)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
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/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(c_0_24,plain,
! [X19,X23,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X19)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X19)) ),
inference(fof_simplification,[status(thm)],[fact_ComplE]) ).
fof(c_0_25,plain,
! [X2120,X2121] : hAPP(c_Set_OCollect(X2121),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2121),c_fNot),X2120)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2121,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2121),X2120)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_26,plain,
! [X4825,X4826] : hAPP(c_Set_OCollect(X4826),X4825) = X4825,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_27,plain,
! [X1827,X1828,X1829] :
( ~ hBOOL(hAPP(hAPP(c_member(X1829),X1828),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1829,tc_HOL_Obool)),X1827)))
| ~ hBOOL(hAPP(hAPP(c_member(X1829),X1828),X1827)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
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_25]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,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_27]) ).
cnf(c_0_31,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_29]),c_0_29]) ).
fof(c_0_32,plain,
! [X666,X667,X668] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X668),X667),X666))
| hBOOL(hAPP(X666,X667)) )
& ( ~ hBOOL(hAPP(X666,X667))
| hBOOL(hAPP(hAPP(c_member(X668),X667),X666)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
cnf(c_0_33,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_30,c_0_31]) ).
cnf(c_0_34,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X819,X820,X821,X822,X823,X824] : hAPP(hAPP(hAPP(c_COMBB(X824,X823,X822),X821),X820),X819) = hAPP(X821,hAPP(X820,X819)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(c_0_36,plain,
! [X19,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
<=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
cnf(c_0_37,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_33,c_0_34]) ).
cnf(c_0_38,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
! [X366,X367,X369,X370,X371] :
( ( hBOOL(hAPP(hAPP(c_member(X367),esk7_2(X366,X367)),X366))
| X366 = c_Orderings_Obot__class_Obot(tc_fun(X367,tc_HOL_Obool)) )
& ( X369 != c_Orderings_Obot__class_Obot(tc_fun(X370,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X370),X371),X369)) ) ),
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_36])])])])])]) ).
fof(c_0_40,plain,
! [X30] :
( hBOOL(X30)
| hBOOL(hAPP(c_fNot,X30)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
fof(c_0_41,plain,
! [X1816,X1817,X1818,X1820,X1821,X1822] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1817),X1818),c_Orderings_Otop__class_Otop(tc_fun(X1817,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X1816,X1818))
| hBOOL(hAPP(X1816,esk38_1(X1816))) )
& ( hBOOL(hAPP(hAPP(c_member(X1822),esk39_2(X1820,X1822)),c_Orderings_Otop__class_Otop(tc_fun(X1822,tc_HOL_Obool))))
| ~ hBOOL(hAPP(X1820,X1821)) )
& ( hBOOL(hAPP(X1820,esk39_2(X1820,X1822)))
| ~ hBOOL(hAPP(X1820,X1821)) ) ),
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_42,plain,
! [X1784,X1785] : hBOOL(hAPP(hAPP(c_member(X1785),X1784),c_Orderings_Otop__class_Otop(tc_fun(X1785,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
cnf(c_0_43,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(c_fNot,hAPP(X3,X2))) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk7_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_45,plain,
! [X2142] :
( hBOOL(X2142)
| hBOOL(hAPP(c_fNot,X2142)) ),
inference(variable_rename,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( hBOOL(hAPP(X3,esk38_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_41]) ).
cnf(c_0_47,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_42]) ).
cnf(c_0_48,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_fNot,hAPP(X1,esk7_2(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_50,plain,
! [X30] :
( ~ hBOOL(hAPP(c_fNot,X30))
| ~ hBOOL(X30) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_51,plain,
! [X2056,X2057,X2058,X2059] : hAPP(hAPP(c_COMBK(X2059,X2058),X2057),X2056) = X2057,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_52,plain,
( hBOOL(hAPP(X1,esk38_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_53,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk7_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_54,plain,
! [X2141] :
( ~ hBOOL(hAPP(c_fNot,X2141))
| ~ hBOOL(X2141) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_50])]) ).
cnf(c_0_55,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk38_1(X1))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,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_55,c_0_56]),c_0_55]) ).
fof(c_0_59,plain,
! [X30,X5] :
( hAPP(c_Set_OCollect(X5),X30) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X30,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_60,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
inference(fof_simplification,[status(thm)],[conj_2]) ).
cnf(c_0_61,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_fNot,X3)
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
inference(split_conjunct,[status(thm)],[conj_1]) ).
fof(c_0_63,plain,
! [X1847,X1848] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1848,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1848,tc_HOL_Obool)),X1847)) = X1847,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
fof(c_0_64,plain,
! [X4819,X4820,X4821,X4822,X4824] :
( ( hAPP(c_Set_OCollect(X4820),X4819) != c_Orderings_Obot__class_Obot(tc_fun(X4820,tc_HOL_Obool))
| ~ hBOOL(hAPP(X4819,X4821)) )
& ( hBOOL(hAPP(X4822,esk147_1(X4822)))
| hAPP(c_Set_OCollect(X4824),X4822) = c_Orderings_Obot__class_Obot(tc_fun(X4824,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_59])])])])])]) ).
fof(c_0_65,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
inference(fof_nnf,[status(thm)],[c_0_60]) ).
cnf(c_0_66,hypothesis,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_fNot,hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_67,plain,
! [X86] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X86),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_68,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_63]) ).
fof(c_0_69,plain,
! [X5127,X5128,X5129,X5130,X5131,X5132,X5133] :
( ( hAPP(c_List_Ofilter(X5129,X5128),X5127) != X5127
| ~ hBOOL(hAPP(hAPP(c_member(X5129),X5130),hAPP(c_List_Oset(X5129),X5127)))
| hBOOL(hAPP(X5128,X5130)) )
& ( hBOOL(hAPP(hAPP(c_member(X5133),esk167_3(X5131,X5132,X5133)),hAPP(c_List_Oset(X5133),X5131)))
| hAPP(c_List_Ofilter(X5133,X5132),X5131) = X5131 )
& ( ~ hBOOL(hAPP(X5132,esk167_3(X5131,X5132,X5133)))
| hAPP(c_List_Ofilter(X5133,X5132),X5131) = X5131 ) ),
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_70,plain,
! [X1782,X1783] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1783,tc_HOL_Obool)),X1782)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_71,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_64]) ).
cnf(c_0_72,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
( hAPP(c_fNot,hAPP(c_Finite__Set_Ofinite(t_a),v_F)) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_58,c_0_66]) ).
fof(c_0_74,plain,
! [X2387,X2388] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2388),X2387) != X2388
| X2387 = 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_75,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_76,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_77,plain,
! [X2292] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2292),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_67])]) ).
fof(c_0_78,plain,
! [X92] : X92 != hAPP(c_Nat_OSuc,X92),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_79,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_68,c_0_31]),c_0_31]) ).
cnf(c_0_80,plain,
( hAPP(c_List_Ofilter(X3,X1),X2) = X2
| ~ hBOOL(hAPP(X1,esk167_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_81,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_82,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_71,c_0_29])]) ).
cnf(c_0_83,hypothesis,
~ hBOOL(hAPP(v_F,v_x)),
inference(spm,[status(thm)],[c_0_72,c_0_34]) ).
cnf(c_0_84,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_73]) ).
cnf(c_0_85,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_74]) ).
cnf(c_0_86,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
fof(c_0_87,plain,
! [X2231,X2232] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2232),hAPP(c_Nat_OSuc,X2231)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2232),X2231)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_88,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_89,plain,
! [X2202] : X2202 != hAPP(c_Nat_OSuc,X2202),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_78])]) ).
cnf(c_0_90,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_79]),c_0_38]) ).
cnf(c_0_91,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_80,c_0_81]) ).
cnf(c_0_92,plain,
~ hBOOL(hAPP(c_fNot,hAPP(c_Finite__Set_Ofinite(t_a),v_F))),
inference(rw,[status(thm)],[c_0_82,c_0_66]) ).
cnf(c_0_93,hypothesis,
( X1 = hAPP(v_F,v_x)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_94,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_85,c_0_86]) ).
cnf(c_0_95,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_87]) ).
cnf(c_0_96,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_88,c_0_86]) ).
cnf(c_0_97,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_98,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_99,hypothesis,
hAPP(c_fNot,hAPP(c_Finite__Set_Ofinite(t_a),v_F)) = hAPP(v_F,v_x),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
fof(c_0_101,plain,
! [X2391] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2391),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2391,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
cnf(c_0_102,hypothesis,
( hAPP(c_fNot,X1) = hAPP(v_F,v_x)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_93]) ).
cnf(c_0_103,plain,
hBOOL(hAPP(c_Nat_OSuc,hAPP(c_fNot,hAPP(c_Finite__Set_Ofinite(t_a),v_F)))),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_73])]) ).
cnf(c_0_104,hypothesis,
hAPP(c_Finite__Set_Ofinite(t_a),v_F) = hAPP(c_fNot,hAPP(v_F,v_x)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_100,c_0_95]) ).
cnf(c_0_106,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_101]) ).
cnf(c_0_107,hypothesis,
hAPP(c_fNot,hAPP(c_Nat_OSuc,hAPP(v_F,v_x))) = hAPP(v_F,v_x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_98]) ).
cnf(c_0_108,plain,
hAPP(c_Nat_OSuc,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_105,c_0_95]) ).
cnf(c_0_109,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_106,c_0_86]) ).
cnf(c_0_110,hypothesis,
( hAPP(c_fNot,X1) = hAPP(v_F,v_x)
| X1 = hAPP(v_F,v_x) ),
inference(spm,[status(thm)],[c_0_102,c_0_93]) ).
cnf(c_0_111,hypothesis,
hAPP(c_fNot,hAPP(v_F,v_x)) = hAPP(c_Nat_OSuc,hAPP(v_F,v_x)),
inference(spm,[status(thm)],[c_0_98,c_0_107]) ).
cnf(c_0_112,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,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_108,c_0_95]) ).
cnf(c_0_113,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) != X1,
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,hypothesis,
( hAPP(c_Nat_OSuc,hAPP(v_F,v_x)) = X1
| X1 = hAPP(v_F,v_x) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_110]),c_0_111]) ).
cnf(c_0_115,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))) != X1,
inference(spm,[status(thm)],[c_0_112,c_0_109]) ).
cnf(c_0_116,hypothesis,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114])]),c_0_115]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW322+1 : TPTP v8.2.0. Released v5.2.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat May 18 20:25:37 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.18/0.48 Running first-order model finding
% 0.18/0.48 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/benchmark/theBenchmark.p
% 6.13/2.18 # Version: 3.1.0
% 6.13/2.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 6.13/2.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/2.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.13/2.18 # Starting new_bool_3 with 300s (1) cores
% 6.13/2.18 # Starting new_bool_1 with 300s (1) cores
% 6.13/2.18 # Starting sh5l with 300s (1) cores
% 6.13/2.18 # new_bool_3 with pid 20739 completed with status 0
% 6.13/2.18 # Result found by new_bool_3
% 6.13/2.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 6.13/2.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/2.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.13/2.18 # Starting new_bool_3 with 300s (1) cores
% 6.13/2.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.13/2.18 # Search class: FGHSM-SMLM33-DFFFFFNN
% 6.13/2.18 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 6.13/2.18 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 6.13/2.18 # SAT001_MinMin_p005000_rr with pid 20742 completed with status 0
% 6.13/2.18 # Result found by SAT001_MinMin_p005000_rr
% 6.13/2.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 6.13/2.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/2.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.13/2.18 # Starting new_bool_3 with 300s (1) cores
% 6.13/2.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.13/2.18 # Search class: FGHSM-SMLM33-DFFFFFNN
% 6.13/2.18 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 6.13/2.18 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 6.13/2.18 # Preprocessing time : 0.040 s
% 6.13/2.18 # Presaturation interreduction done
% 6.13/2.18
% 6.13/2.18 # Proof found!
% 6.13/2.18 # SZS status ContradictoryAxioms
% 6.13/2.18 # SZS output start CNFRefutation
% See solution above
% 6.13/2.18 # Parsed axioms : 5233
% 6.13/2.18 # Removed by relevancy pruning/SinE : 3755
% 6.13/2.18 # Initial clauses : 2215
% 6.13/2.18 # Removed in clause preprocessing : 62
% 6.13/2.18 # Initial clauses in saturation : 2153
% 6.13/2.18 # Processed clauses : 5659
% 6.13/2.18 # ...of these trivial : 183
% 6.13/2.18 # ...subsumed : 2372
% 6.13/2.18 # ...remaining for further processing : 3104
% 6.13/2.18 # Other redundant clauses eliminated : 1274
% 6.13/2.18 # Clauses deleted for lack of memory : 0
% 6.13/2.18 # Backward-subsumed : 45
% 6.13/2.18 # Backward-rewritten : 271
% 6.13/2.18 # Generated clauses : 51543
% 6.13/2.18 # ...of the previous two non-redundant : 46505
% 6.13/2.18 # ...aggressively subsumed : 0
% 6.13/2.18 # Contextual simplify-reflections : 12
% 6.13/2.18 # Paramodulations : 50257
% 6.13/2.18 # Factorizations : 10
% 6.13/2.18 # NegExts : 0
% 6.13/2.18 # Equation resolutions : 1301
% 6.13/2.18 # Disequality decompositions : 0
% 6.13/2.18 # Total rewrite steps : 15471
% 6.13/2.18 # ...of those cached : 11914
% 6.13/2.18 # Propositional unsat checks : 0
% 6.13/2.18 # Propositional check models : 0
% 6.13/2.18 # Propositional check unsatisfiable : 0
% 6.13/2.18 # Propositional clauses : 0
% 6.13/2.18 # Propositional clauses after purity: 0
% 6.13/2.18 # Propositional unsat core size : 0
% 6.13/2.18 # Propositional preprocessing time : 0.000
% 6.13/2.18 # Propositional encoding time : 0.000
% 6.13/2.18 # Propositional solver time : 0.000
% 6.13/2.18 # Success case prop preproc time : 0.000
% 6.13/2.18 # Success case prop encoding time : 0.000
% 6.13/2.18 # Success case prop solver time : 0.000
% 6.13/2.18 # Current number of processed clauses : 1033
% 6.13/2.18 # Positive orientable unit clauses : 443
% 6.13/2.18 # Positive unorientable unit clauses: 42
% 6.13/2.18 # Negative unit clauses : 147
% 6.13/2.18 # Non-unit-clauses : 401
% 6.13/2.18 # Current number of unprocessed clauses: 37040
% 6.13/2.18 # ...number of literals in the above : 80503
% 6.13/2.18 # Current number of archived formulas : 0
% 6.13/2.18 # Current number of archived clauses : 1897
% 6.13/2.18 # Clause-clause subsumption calls (NU) : 239782
% 6.13/2.18 # Rec. Clause-clause subsumption calls : 137461
% 6.13/2.18 # Non-unit clause-clause subsumptions : 1394
% 6.13/2.18 # Unit Clause-clause subsumption calls : 8366
% 6.13/2.18 # Rewrite failures with RHS unbound : 170
% 6.13/2.18 # BW rewrite match attempts : 8157
% 6.13/2.18 # BW rewrite match successes : 616
% 6.13/2.18 # Condensation attempts : 0
% 6.13/2.18 # Condensation successes : 0
% 6.13/2.18 # Termbank termtop insertions : 1428504
% 6.13/2.18 # Search garbage collected termcells : 64194
% 6.13/2.18
% 6.13/2.18 # -------------------------------------------------
% 6.13/2.18 # User time : 1.400 s
% 6.13/2.18 # System time : 0.060 s
% 6.13/2.18 # Total time : 1.460 s
% 6.13/2.18 # Maximum resident set size: 16572 pages
% 6.13/2.18
% 6.13/2.18 # -------------------------------------------------
% 6.13/2.18 # User time : 1.603 s
% 6.13/2.18 # System time : 0.070 s
% 6.13/2.18 # Total time : 1.673 s
% 6.13/2.18 # Maximum resident set size: 9428 pages
% 6.13/2.18 % E---3.1 exiting
%------------------------------------------------------------------------------