TSTP Solution File: SET881+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:38:05 EDT 2022
% Result : Theorem 0.15s 0.37s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 79 ( 55 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 85 ( 38 ~; 32 |; 6 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 59 ( 4 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ) ).
fof(l36_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ) ).
fof(t22_zfmisc_1,conjecture,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set ).
fof(subgoal_0,plain,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(strip,[],[t22_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] : set_difference(singleton(A),unordered_pair(A,B)) != empty_set,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != empty_set,
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] :
( set_difference(singleton(A),B) != empty_set
<=> ~ in(A,B) ),
inference(canonicalize,[],[l36_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B] :
( set_difference(singleton(A),B) != empty_set
<=> ~ in(A,B) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ( set_difference(singleton(A),B) != empty_set
| in(A,B) )
& ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set ),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != empty_set,
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( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
in(X_9,unordered_pair(X_9,B)),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_8,plain,
( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ in(X_9,unordered_pair(X_9,B))
| set_difference(singleton(X_9),unordered_pair(X_9,B)) = empty_set ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_9)),bind(B,$fot(unordered_pair(X_9,B)))]]) ).
cnf(refute_0_10,plain,
set_difference(singleton(X_9),unordered_pair(X_9,B)) = empty_set,
inference(resolve,[$cnf( in(X_9,unordered_pair(X_9,B)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = empty_set,
inference(subst,[],[refute_0_10:[bind(B,$fot(skolemFOFtoCNF_B)),bind(X_9,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_12,plain,
( empty_set != empty_set
| set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != empty_set
| set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_13,plain,
( empty_set != empty_set
| set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),empty_set) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(set_difference(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),empty_set) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_15,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 12:14:41 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37
% 0.15/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.37
%------------------------------------------------------------------------------