TSTP Solution File: SET878+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET878+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 03:38:04 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 23 unt; 0 def)
% Number of atoms : 93 ( 72 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 90 ( 40 ~; 38 |; 5 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 5 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ) ).
fof(l32_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ) ).
fof(t19_zfmisc_1,conjecture,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A) ).
fof(subgoal_0,plain,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(strip,[],[t19_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) != singleton(A),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(canonicalize,[],[d2_tarski]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ( C != unordered_pair(A,B)
| D != A
| in(D,C) )
& ( C != unordered_pair(A,B)
| D != B
| in(D,C) )
& ( skolemFOFtoCNF_D(A,B,C) != A
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = unordered_pair(A,B) )
& ( skolemFOFtoCNF_D(A,B,C) != B
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = unordered_pair(A,B) )
& ( C != unordered_pair(A,B)
| ~ in(D,C)
| D = A
| D = B )
& ( C = unordered_pair(A,B)
| skolemFOFtoCNF_D(A,B,C) = A
| skolemFOFtoCNF_D(A,B,C) = B
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( C != unordered_pair(A,B)
| D != A
| in(D,C) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ in(A,B)
| set_intersection2(B,singleton(A)) = singleton(A) ),
inference(canonicalize,[],[l32_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ in(A,B)
| set_intersection2(B,singleton(A)) = singleton(A) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_9,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( C != unordered_pair(A,B)
| D != A
| in(D,C) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( A != A
| unordered_pair(A,B) != unordered_pair(A,B)
| in(A,unordered_pair(A,B)) ),
inference(subst,[],[refute_0_1:[bind(C,$fot(unordered_pair(A,B))),bind(D,$fot(A))]]) ).
cnf(refute_0_3,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_4,plain,
( unordered_pair(A,B) != unordered_pair(A,B)
| in(A,unordered_pair(A,B)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
unordered_pair(A,B) = unordered_pair(A,B),
introduced(tautology,[refl,[$fot(unordered_pair(A,B))]]) ).
cnf(refute_0_6,plain,
in(A,unordered_pair(A,B)),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
in(X_12,unordered_pair(X_12,B)),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_8,plain,
( ~ in(A,B)
| set_intersection2(B,singleton(A)) = singleton(A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
( ~ in(X_12,unordered_pair(X_12,B))
| set_intersection2(unordered_pair(X_12,B),singleton(X_12)) = singleton(X_12) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_12)),bind(B,$fot(unordered_pair(X_12,B)))]]) ).
cnf(refute_0_10,plain,
set_intersection2(unordered_pair(X_12,B),singleton(X_12)) = singleton(X_12),
inference(resolve,[$cnf( in(X_12,unordered_pair(X_12,B)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_16,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
set_intersection2(unordered_pair(X_12,B),singleton(X_12)) = set_intersection2(singleton(X_12),unordered_pair(X_12,B)),
inference(subst,[],[refute_0_16:[bind(A,$fot(singleton(X_12))),bind(B,$fot(unordered_pair(X_12,B)))]]) ).
cnf(refute_0_18,plain,
( set_intersection2(unordered_pair(X_12,B),singleton(X_12)) != set_intersection2(singleton(X_12),unordered_pair(X_12,B))
| set_intersection2(unordered_pair(X_12,B),singleton(X_12)) != singleton(X_12)
| set_intersection2(singleton(X_12),unordered_pair(X_12,B)) = singleton(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(unordered_pair(X_12,B),singleton(X_12)),singleton(X_12)) ),[0],$fot(set_intersection2(singleton(X_12),unordered_pair(X_12,B)))]]) ).
cnf(refute_0_19,plain,
( set_intersection2(unordered_pair(X_12,B),singleton(X_12)) != singleton(X_12)
| set_intersection2(singleton(X_12),unordered_pair(X_12,B)) = singleton(X_12) ),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(X_12,B),singleton(X_12)),set_intersection2(singleton(X_12),unordered_pair(X_12,B))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
set_intersection2(singleton(X_12),unordered_pair(X_12,B)) = singleton(X_12),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(X_12,B),singleton(X_12)),singleton(X_12)) )],[refute_0_10,refute_0_19]) ).
cnf(refute_0_21,plain,
set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_20:[bind(B,$fot(skolemFOFtoCNF_B)),bind(X_12,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_22,plain,
( set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_23,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_23,refute_0_0]) ).
cnf(refute_0_25,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_25,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET878+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n006.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 : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 23:35:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37
% 0.14/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------