TSTP Solution File: SEU152+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU152+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 12:38:49 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 69 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 29 ~; 19 |; 3 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(l23_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(t12_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ) ).
fof(subgoal_0,plain,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(strip,[],[l23_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != skolemFOFtoCNF_B
& in(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[t12_xboole_1]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_10,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_3,plain,
subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ subset(A,B)
| set_union2(A,B) = B ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B)
| set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
inference(subst,[],[refute_0_4:[bind(A,$fot(singleton(skolemFOFtoCNF_A))),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_6,plain,
set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( set_union2(A,B) != set_union2(B,A)
| set_union2(B,A) = set_union2(A,B) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(set_union2(A,B))),bind(Y,$fot(set_union2(B,A)))]]) ).
cnf(refute_0_12,plain,
set_union2(B,A) = set_union2(A,B),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) = set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(singleton(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_14,plain,
( set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A))
| set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),[0],$fot(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_15,plain,
( set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != skolemFOFtoCNF_B
| set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)) = skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != skolemFOFtoCNF_B,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
( set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) != set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A))
| set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)) != skolemFOFtoCNF_B
| set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),skolemFOFtoCNF_B) ),[0],$fot(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_19,plain,
( set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)) != skolemFOFtoCNF_B
| set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) = skolemFOFtoCNF_B ),
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A))) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)) != skolemFOFtoCNF_B,
inference(resolve,[$cnf( $equal(set_union2(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),skolemFOFtoCNF_B) )],[refute_0_19,refute_0_17]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A)),skolemFOFtoCNF_B) )],[refute_0_16,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU152+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % 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 : Mon Jun 20 02:47:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------