TSTP Solution File: SET920+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 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 03:38:21 EDT 2022
% Result : Theorem 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 19 unt; 0 def)
% Number of atoms : 138 ( 73 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 148 ( 60 ~; 58 |; 15 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 4 sgn 51 !; 7 ?)
% 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(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ) ).
fof(t63_zfmisc_1,conjecture,
! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
inference(strip,[],[t63_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(canonicalize,[],[d2_tarski]) ).
fof(normalize_0_1,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [A,B,C,D] :
( C != unordered_pair(A,B)
| D != A
| in(D,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D_1(A,B,C),A)
| in(skolemFOFtoCNF_D_1(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D_1(A,B,C),B)
| in(skolemFOFtoCNF_D_1(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D_1(A,B,C),A)
| ~ in(skolemFOFtoCNF_D_1(A,B,C),B)
| ~ in(skolemFOFtoCNF_D_1(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A,B,C] :
( ~ in(A,C)
& set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_12,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( C != unordered_pair(A,B)
| D != A
| in(D,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( A != A
| unordered_pair(A,B) != unordered_pair(A,B)
| in(A,unordered_pair(A,B)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(unordered_pair(A,B))),bind(D,$fot(A))]]) ).
cnf(refute_0_2,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_3,plain,
( unordered_pair(A,B) != unordered_pair(A,B)
| in(A,unordered_pair(A,B)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
unordered_pair(A,B) = unordered_pair(A,B),
introduced(tautology,[refl,[$fot(unordered_pair(A,B))]]) ).
cnf(refute_0_5,plain,
in(A,unordered_pair(A,B)),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_7,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_7:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_9,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_0_10,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ in(X_14,set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))
| in(X_14,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),bind(D,$fot(X_14))]]) ).
cnf(refute_0_12,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_18,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_20,plain,
( set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_21,plain,
( set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( $equal(set_intersection2(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_12,refute_0_21]) ).
cnf(refute_0_23,plain,
( set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| ~ in(X_14,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(X_14,set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) ),
introduced(tautology,[equality,[$cnf( ~ in(X_14,set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) ),[1],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_24,plain,
( ~ in(X_14,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(X_14,set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ in(X_14,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(X_14,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( in(X_14,set_intersection2(skolemFOFtoCNF_C,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))) )],[refute_0_24,refute_0_11]) ).
cnf(refute_0_26,plain,
( ~ in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_25:[bind(X_14,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_27,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_6,refute_0_26]) ).
cnf(refute_0_28,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_27,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 14:43:42 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.35
% 0.19/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.35
%------------------------------------------------------------------------------