TSTP Solution File: SWW331+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWW331+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 20:11:03 EDT 2023
% Result : ContradictoryAxioms 11.29s 3.18s
% Output : CNFRefutation 11.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 81 ( 67 unt; 0 def)
% Number of atoms : 104 ( 57 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 51 ( 28 ~; 16 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 6 con; 0-3 aty)
% Number of variables : 127 ( 15 sgn; 68 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__add__less1,axiom,
! [X122,X123] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X123),X122)),X123)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_not__add__less1) ).
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.bWS1P9r0Ga/E---3.1_18755.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.bWS1P9r0Ga/E---3.1_18755.p',fact_Pls__def) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X7] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X7) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X7)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Collect__mem__eq,axiom,
! [X19,X8] : hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X19)) = X19,
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X6,X8] : hAPP(c_Set_OCollect(X8),X6) = X6,
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_Collect__def) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_One__nat__def) ).
fof(fact_add__Suc__right,axiom,
! [X16,X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),hAPP(c_Nat_OSuc,X16)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X16)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_add__Suc__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X58] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X58,
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_Nat_Oadd__0__right) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X118] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X118))
<=> ? [X130] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X118))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X130)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_finite__nat__set__iff__bounded) ).
fof(help_c__COMBC__1,axiom,
! [X27,X4,X6,X8,X40,X21] : hAPP(hAPP(hAPP(c_COMBC(X21,X40,X8),X6),X4),X27) = hAPP(hAPP(X6,X27),X4),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',help_c__COMBC__1) ).
fof(fact_number__of__is__id,axiom,
! [X106] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X106) = X106,
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_number__of__is__id) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_nat__number__of__def,axiom,
! [X142] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X142) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X142)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_nat__number__of__def) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_one__is__num__one) ).
fof(fact_card__infinite,axiom,
! [X19,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X19))
=> hAPP(c_Finite__Set_Ocard(X8),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_card__infinite) ).
fof(fact_rangeI,axiom,
! [X21,X22,X2,X8] : hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X22)),hAPP(c_Set_Oimage(X21,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X21,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_rangeI) ).
fof(fact_semiring__norm_I115_J,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_semiring__norm_I115_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X58] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X58),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_Zero__not__Suc) ).
fof(fact_card__UNIV__bool,axiom,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_card__UNIV__bool) ).
fof(fact_finite__imageI,axiom,
! [X107,X21,X111,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X111))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X21),hAPP(c_Set_Oimage(X8,X21,X107),X111))) ),
file('/export/starexec/sandbox2/tmp/tmp.bWS1P9r0Ga/E---3.1_18755.p',fact_finite__imageI) ).
fof(c_0_21,plain,
! [X122,X123] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X123),X122)),X123)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
cnf(c_0_22,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_23,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_24,plain,
! [X1595,X1596] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1596),X1595)),X1596)),
inference(variable_rename,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X1069] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1069) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1069)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_26,plain,
! [X4686,X4687] : hAPP(c_Set_OCollect(X4687),hAPP(hAPP(c_COMBC(X4687,tc_fun(X4687,tc_HOL_Obool),tc_HOL_Obool),c_member(X4687)),X4686)) = X4686,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_27,plain,
! [X4663,X4664] : hAPP(c_Set_OCollect(X4664),X4663) = X4663,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
cnf(c_0_28,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
cnf(c_0_29,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X950,X951] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X951),hAPP(c_Nat_OSuc,X950)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X951),X950)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(c_0_33,plain,
! [X1575] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1575),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1575,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_34,plain,
! [X2029,X2031,X2032,X2033] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2029))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2031),X2029))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2031),esk50_1(X2029))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk51_2(X2032,X2033)),X2032))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2032)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk51_2(X2032,X2033)),X2033))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2032)) ) ),
inference(distribute,[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_finite__nat__set__iff__bounded])])])])])]) ).
fof(c_0_35,plain,
! [X2433,X2434,X2435,X2436,X2437,X2438] : hAPP(hAPP(hAPP(c_COMBC(X2438,X2437,X2436),X2435),X2434),X2433) = hAPP(hAPP(X2435,X2433),X2434),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_36,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_38,plain,
! [X3099] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X3099) = X3099,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(c_0_39,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).
cnf(c_0_40,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_41,plain,
! [X5412] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X5412) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X5412)),
inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).
cnf(c_0_42,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_43,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_32]) ).
cnf(c_0_44,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_33]) ).
cnf(c_0_45,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk50_1(X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_48,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).
cnf(c_0_49,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_50,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_51,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_52,plain,
! [X19,X8] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X19))
=> hAPP(c_Finite__Set_Ocard(X8),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
cnf(c_0_53,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),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_42,c_0_43]) ).
cnf(c_0_54,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_44,c_0_29]) ).
cnf(c_0_55,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),esk50_1(X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2)) ),
inference(rw,[status(thm)],[c_0_45,c_0_31]) ).
cnf(c_0_56,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_57,plain,
! [X598,X599,X600,X601] : hBOOL(hAPP(hAPP(c_member(X601),hAPP(X600,X599)),hAPP(c_Set_Oimage(X598,X601,X600),c_Orderings_Otop__class_Otop(tc_fun(X598,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
cnf(c_0_58,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_59,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_60,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X1),
inference(rw,[status(thm)],[c_0_51,c_0_49]) ).
fof(c_0_61,plain,
! [X3688,X3689] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3689),X3688))
| hAPP(c_Finite__Set_Ocard(X3689),X3688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])]) ).
fof(c_0_62,plain,
! [X940] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X940),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_63,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1)),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),esk50_1(X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__bool]) ).
cnf(c_0_67,plain,
hAPP(c_Int_Onat,c_Int_OBit0(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_29]) ).
cnf(c_0_68,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk50_1(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
hBOOL(hAPP(hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
inference(rw,[status(thm)],[c_0_65,c_0_56]) ).
fof(c_0_72,plain,
! [X552,X553,X554,X555] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X555),X554))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X553),hAPP(c_Set_Oimage(X555,X553,X552),X554))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
cnf(c_0_73,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_59]),c_0_60]),c_0_67]) ).
cnf(c_0_74,plain,
( hAPP(c_Finite__Set_Ocard(X1),X2) = hAPP(c_Int_Onat,c_Int_OPls)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(rw,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_75,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_69,c_0_29]) ).
cnf(c_0_76,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(X1,X2,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_79,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,plain,
$false,
inference(sr,[status(thm)],[c_0_78,c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW331+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 2400
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Oct 2 22:27:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 1.01/1.20 Running first-order model finding
% 1.01/1.20 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.bWS1P9r0Ga/E---3.1_18755.p
% 11.29/3.18 # Version: 3.1pre001
% 11.29/3.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 11.29/3.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.29/3.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.29/3.18 # Starting new_bool_3 with 300s (1) cores
% 11.29/3.18 # Starting new_bool_1 with 300s (1) cores
% 11.29/3.18 # Starting sh5l with 300s (1) cores
% 11.29/3.18 # new_bool_1 with pid 18839 completed with status 0
% 11.29/3.18 # Result found by new_bool_1
% 11.29/3.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 11.29/3.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.29/3.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.29/3.18 # Starting new_bool_3 with 300s (1) cores
% 11.29/3.18 # Starting new_bool_1 with 300s (1) cores
% 11.29/3.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.29/3.18 # Search class: FGHSM-SMLM33-DFFFFFNN
% 11.29/3.18 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 11.29/3.18 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 11.29/3.18 # SAT001_MinMin_p005000_rr with pid 18842 completed with status 0
% 11.29/3.18 # Result found by SAT001_MinMin_p005000_rr
% 11.29/3.18 # Preprocessing class: FMLMSMSMSSSNFFN.
% 11.29/3.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.29/3.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 11.29/3.18 # Starting new_bool_3 with 300s (1) cores
% 11.29/3.18 # Starting new_bool_1 with 300s (1) cores
% 11.29/3.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 11.29/3.18 # Search class: FGHSM-SMLM33-DFFFFFNN
% 11.29/3.18 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 11.29/3.18 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 11.29/3.18 # Preprocessing time : 0.032 s
% 11.29/3.18 # Presaturation interreduction done
% 11.29/3.18
% 11.29/3.18 # Proof found!
% 11.29/3.18 # SZS status ContradictoryAxioms
% 11.29/3.18 # SZS output start CNFRefutation
% See solution above
% 11.29/3.18 # Parsed axioms : 5228
% 11.29/3.18 # Removed by relevancy pruning/SinE : 3761
% 11.29/3.18 # Initial clauses : 2236
% 11.29/3.18 # Removed in clause preprocessing : 70
% 11.29/3.18 # Initial clauses in saturation : 2166
% 11.29/3.18 # Processed clauses : 9514
% 11.29/3.18 # ...of these trivial : 364
% 11.29/3.18 # ...subsumed : 4855
% 11.29/3.18 # ...remaining for further processing : 4295
% 11.29/3.18 # Other redundant clauses eliminated : 1847
% 11.29/3.18 # Clauses deleted for lack of memory : 0
% 11.29/3.18 # Backward-subsumed : 100
% 11.29/3.18 # Backward-rewritten : 181
% 11.29/3.18 # Generated clauses : 96704
% 11.29/3.18 # ...of the previous two non-redundant : 90528
% 11.29/3.18 # ...aggressively subsumed : 0
% 11.29/3.18 # Contextual simplify-reflections : 9
% 11.29/3.18 # Paramodulations : 94834
% 11.29/3.18 # Factorizations : 12
% 11.29/3.18 # NegExts : 0
% 11.29/3.18 # Equation resolutions : 1881
% 11.29/3.18 # Total rewrite steps : 22057
% 11.29/3.18 # Propositional unsat checks : 0
% 11.29/3.18 # Propositional check models : 0
% 11.29/3.18 # Propositional check unsatisfiable : 0
% 11.29/3.18 # Propositional clauses : 0
% 11.29/3.18 # Propositional clauses after purity: 0
% 11.29/3.18 # Propositional unsat core size : 0
% 11.29/3.18 # Propositional preprocessing time : 0.000
% 11.29/3.18 # Propositional encoding time : 0.000
% 11.29/3.18 # Propositional solver time : 0.000
% 11.29/3.18 # Success case prop preproc time : 0.000
% 11.29/3.18 # Success case prop encoding time : 0.000
% 11.29/3.18 # Success case prop solver time : 0.000
% 11.29/3.18 # Current number of processed clauses : 2272
% 11.29/3.18 # Positive orientable unit clauses : 551
% 11.29/3.18 # Positive unorientable unit clauses: 45
% 11.29/3.18 # Negative unit clauses : 710
% 11.29/3.18 # Non-unit-clauses : 966
% 11.29/3.18 # Current number of unprocessed clauses: 73360
% 11.29/3.18 # ...number of literals in the above : 158209
% 11.29/3.18 # Current number of archived formulas : 0
% 11.29/3.18 # Current number of archived clauses : 1855
% 11.29/3.18 # Clause-clause subsumption calls (NU) : 318334
% 11.29/3.18 # Rec. Clause-clause subsumption calls : 190509
% 11.29/3.18 # Non-unit clause-clause subsumptions : 1009
% 11.29/3.18 # Unit Clause-clause subsumption calls : 80881
% 11.29/3.18 # Rewrite failures with RHS unbound : 320
% 11.29/3.18 # BW rewrite match attempts : 9315
% 11.29/3.18 # BW rewrite match successes : 655
% 11.29/3.18 # Condensation attempts : 0
% 11.29/3.18 # Condensation successes : 0
% 11.29/3.18 # Termbank termtop insertions : 2455829
% 11.29/3.18
% 11.29/3.18 # -------------------------------------------------
% 11.29/3.18 # User time : 1.706 s
% 11.29/3.18 # System time : 0.067 s
% 11.29/3.18 # Total time : 1.773 s
% 11.29/3.18 # Maximum resident set size: 15864 pages
% 11.29/3.18
% 11.29/3.18 # -------------------------------------------------
% 11.29/3.18 # User time : 1.811 s
% 11.29/3.18 # System time : 0.077 s
% 11.29/3.18 # Total time : 1.887 s
% 11.29/3.18 # Maximum resident set size: 9520 pages
% 11.29/3.18 % E---3.1 exiting
%------------------------------------------------------------------------------