TSTP Solution File: SET912+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET912+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:38:18 EDT 2022
% Result : Theorem 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 18 unt; 0 def)
% Number of atoms : 89 ( 39 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 38 ~; 28 |; 10 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ) ).
fof(t53_zfmisc_1,conjecture,
! [A,B,C] :
( ( in(A,B)
& in(C,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( in(A,B)
& in(C,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
inference(strip,[],[t53_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( in(A,B)
& in(C,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[t28_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [A,B,C] :
( set_intersection2(unordered_pair(A,C),B) != unordered_pair(A,C)
& in(A,B)
& in(C,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& in(skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(canonicalize,[],[t38_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ( ~ subset(unordered_pair(A,B),C)
| in(A,C) )
& ( ~ subset(unordered_pair(A,B),C)
| in(B,C) )
& ( ~ in(A,C)
| ~ in(B,C)
| subset(unordered_pair(A,B),C) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ in(A,C)
| ~ in(B,C)
| subset(unordered_pair(A,B),C) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_11,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B)
| set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ in(A,C)
| ~ in(B,C)
| subset(unordered_pair(A,B),C) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ in(X_35,skolemFOFtoCNF_B)
| ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B)
| subset(unordered_pair(X_35,skolemFOFtoCNF_C),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_35)),bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_6,plain,
( ~ in(X_35,skolemFOFtoCNF_B)
| subset(unordered_pair(X_35,skolemFOFtoCNF_C),skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_6:[bind(X_35,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_8,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_15,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_17,plain,
( set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))
| set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) ),[0],$fot(set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_18,plain,
( set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_21,plain,
( set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) != set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))
| set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))) ),[1],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_22,plain,
( set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C))) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_22,refute_0_20]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)) )],[refute_0_19,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET912+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.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 : Sun Jul 10 05:04:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.36
% 0.20/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------