TSTP Solution File: NUN059+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 16:34:53 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 26 unt; 0 def)
% Number of atoms : 169 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 162 ( 64 ~; 51 |; 47 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 141 ( 7 sgn 48 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ) ).
fof(fermattothepoweroftwo,conjecture,
? [Y1,Y3,Y2,Y4] :
( ? [Y5] :
( r4(Y2,Y2,Y5)
& Y4 = Y5 )
& ? [Y6] :
( r4(Y3,Y3,Y6)
& ? [Y7] :
( r4(Y1,Y1,Y7)
& r3(Y7,Y6,Y4) ) ) ) ).
fof(subgoal_0,plain,
? [Y1,Y3,Y2,Y4] :
( ? [Y5] :
( r4(Y2,Y2,Y5)
& Y4 = Y5 )
& ? [Y6] :
( r4(Y3,Y3,Y6)
& ? [Y7] :
( r4(Y1,Y1,Y7)
& r3(Y7,Y6,Y4) ) ) ),
inference(strip,[],[fermattothepoweroftwo]) ).
fof(negate_0_0,plain,
~ ? [Y1,Y3,Y2,Y4] :
( ? [Y5] :
( r4(Y2,Y2,Y5)
& Y4 = Y5 )
& ? [Y6] :
( r4(Y3,Y3,Y6)
& ? [Y7] :
( r4(Y1,Y1,Y7)
& r3(Y7,Y6,Y4) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(canonicalize,[],[axiom_5a]) ).
fof(normalize_0_1,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X5] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) )
& ? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X5] :
? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X5] :
( r1(skolemFOFtoCNF_Y17(X5))
& r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X5] : r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X5] :
? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X5] :
( skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5)
& r1(skolemFOFtoCNF_Y18(X5)) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X5] : skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X5] : r1(skolemFOFtoCNF_Y17(X5)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_10,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_11,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X5] : r1(skolemFOFtoCNF_Y18(X5)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_16,plain,
! [Y1,Y2,Y3,Y4] :
( ! [Y5] :
( Y4 != Y5
| ~ r4(Y2,Y2,Y5) )
| ! [Y6] :
( ~ r4(Y3,Y3,Y6)
| ! [Y7] :
( ~ r3(Y7,Y6,Y4)
| ~ r4(Y1,Y1,Y7) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_17,plain,
! [Y1,Y2,Y3,Y4] :
( ! [Y5] :
( Y4 != Y5
| ~ r4(Y2,Y2,Y5) )
| ! [Y6] :
( ~ r4(Y3,Y3,Y6)
| ! [Y7] :
( ~ r3(Y7,Y6,Y4)
| ~ r4(Y1,Y1,Y7) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [Y1,Y2,Y3,Y4,Y5,Y6,Y7] :
( Y4 != Y5
| ~ r3(Y7,Y6,Y4)
| ~ r4(Y1,Y1,Y7)
| ~ r4(Y2,Y2,Y5)
| ~ r4(Y3,Y3,Y6) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(canonicalize,[],[axiom_4a]) ).
fof(normalize_0_20,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X4] :
( skolemFOFtoCNF_Y9(X4) = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
inference(skolemize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X4] :
? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X4] :
( r1(skolemFOFtoCNF_Y16(X4))
& r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),
inference(skolemize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X4] : r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X4] : skolemFOFtoCNF_Y9(X4) = X4,
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_26,plain,
! [X4] : r1(skolemFOFtoCNF_Y16(X4)),
inference(conjunct,[],[normalize_0_23]) ).
cnf(refute_0_0,plain,
r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y18(X5)
| ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5))
| r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) ),[2],$fot(skolemFOFtoCNF_Y18(X5))]]) ).
cnf(refute_0_3,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5))
| r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
r1(skolemFOFtoCNF_Y17(X5)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( ~ r1(skolemFOFtoCNF_Y17(X5))
| skolemFOFtoCNF_Y17(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_6:[bind(X19,$fot(skolemFOFtoCNF_Y17(X5)))]]) ).
cnf(refute_0_8,plain,
skolemFOFtoCNF_Y17(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y17(X5)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_Y17(X5) != skolemFOFtoCNF_Y24
| ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_10,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y24) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
r1(skolemFOFtoCNF_Y18(X5)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ r1(skolemFOFtoCNF_Y18(X5))
| skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_6:[bind(X19,$fot(skolemFOFtoCNF_Y18(X5)))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y18(X5)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( skolemFOFtoCNF_Y18(X5) != skolemFOFtoCNF_Y24
| ~ r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),[2],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_15,plain,
( ~ r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y18(X5),skolemFOFtoCNF_Y24) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
r4(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_17:[bind(X5,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_19,plain,
( Y4 != Y5
| ~ r3(Y7,Y6,Y4)
| ~ r4(Y1,Y1,Y7)
| ~ r4(Y2,Y2,Y5)
| ~ r4(Y3,Y3,Y6) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_20,plain,
( Y5 != Y5
| ~ r3(Y7,Y6,Y5)
| ~ r4(Y1,Y1,Y7)
| ~ r4(Y2,Y2,Y5)
| ~ r4(Y3,Y3,Y6) ),
inference(subst,[],[refute_0_19:[bind(Y4,$fot(Y5))]]) ).
cnf(refute_0_21,plain,
Y5 = Y5,
introduced(tautology,[refl,[$fot(Y5)]]) ).
cnf(refute_0_22,plain,
( ~ r3(Y7,Y6,Y5)
| ~ r4(Y1,Y1,Y7)
| ~ r4(Y2,Y2,Y5)
| ~ r4(Y3,Y3,Y6) ),
inference(resolve,[$cnf( $equal(Y5,Y5) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( ~ r3(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24)
| ~ r4(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_22:[bind(Y1,$fot(skolemFOFtoCNF_Y24)),bind(Y2,$fot(skolemFOFtoCNF_Y24)),bind(Y3,$fot(skolemFOFtoCNF_Y24)),bind(Y5,$fot(skolemFOFtoCNF_Y24)),bind(Y6,$fot(skolemFOFtoCNF_Y24)),bind(Y7,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_24,plain,
~ r3(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r4(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_Y9(X4) = X4,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_Y9(X4) != X4
| ~ r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4))
| r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),
introduced(tautology,[equality,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),[2],$fot(X4)]]) ).
cnf(refute_0_28,plain,
( ~ r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4))
| r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y9(X4),X4) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
r3(X4,skolemFOFtoCNF_Y16(X4),X4),
inference(resolve,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
r1(skolemFOFtoCNF_Y16(X4)),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_31,plain,
( ~ r1(skolemFOFtoCNF_Y16(X4))
| skolemFOFtoCNF_Y16(X4) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_6:[bind(X19,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).
cnf(refute_0_32,plain,
skolemFOFtoCNF_Y16(X4) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y16(X4)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_Y16(X4) != skolemFOFtoCNF_Y24
| ~ r3(X4,skolemFOFtoCNF_Y16(X4),X4)
| r3(X4,skolemFOFtoCNF_Y24,X4) ),
introduced(tautology,[equality,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_34,plain,
( ~ r3(X4,skolemFOFtoCNF_Y16(X4),X4)
| r3(X4,skolemFOFtoCNF_Y24,X4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
r3(X4,skolemFOFtoCNF_Y24,X4),
inference(resolve,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),X4) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
r3(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_35:[bind(X4,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( r3(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_36,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 07:54:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.38
% 0.20/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
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