TSTP Solution File: SET930+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 03:38:27 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 82 ( 27 unt; 0 def)
% Number of atoms : 201 ( 128 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 215 ( 96 ~; 83 |; 25 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 4 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) ) ).
fof(t72_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(A,C)
& ~ in(B,C) ) ) ).
fof(t73_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(A,C)
& in(B,C) ) ) ).
fof(t74_zfmisc_1,conjecture,
! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B) )
=> set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(strip,[],[t74_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B) )
=> set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != empty_set
& set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
& set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_B)
& set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(canonicalize,[],[l39_zfmisc_1]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) )
& ( A != B
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) )
& ( set_difference(unordered_pair(A,B),C) != singleton(A)
| A = B
| in(B,C) )
& ( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
<=> ( in(A,C)
| in(B,C) ) ),
inference(canonicalize,[],[t72_zfmisc_1]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
<=> ( in(A,C)
| in(B,C) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
| ~ in(A,C) )
& ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
| ~ in(B,C) )
& ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(A,C)
| in(B,C) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(A,C)
| in(B,C) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[commutativity_k2_tarski]) ).
fof(normalize_0_14,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(canonicalize,[],[t73_zfmisc_1]) ).
fof(normalize_0_16,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != empty_set
| in(A,C) )
& ( set_difference(unordered_pair(A,B),C) != empty_set
| in(B,C) )
& ( ~ in(A,C)
| ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = empty_set ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B,C] :
( ~ in(A,C)
| ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = empty_set ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != empty_set,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_difference(unordered_pair(A,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = singleton(A)
| in(A,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_3,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| in(A,C)
| in(B,C) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_7,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_8,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ in(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| set_difference(unordered_pair(X_61,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(X_61)
| in(X_61,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_61)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_13,plain,
( set_difference(unordered_pair(X_61,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(X_61)
| in(X_61,skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_13:[bind(X_61,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_15,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_16,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_16,refute_0_3]) ).
cnf(refute_0_18,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_19,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( set_difference(unordered_pair(A,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = singleton(A)
| in(A,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_19,refute_0_2]) ).
cnf(refute_0_21,plain,
( set_difference(unordered_pair(X_65,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = singleton(X_65)
| in(X_65,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_65))]]) ).
cnf(refute_0_22,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
unordered_pair(skolemFOFtoCNF_A_2,X_65) = unordered_pair(X_65,skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(X_65))]]) ).
cnf(refute_0_24,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_26,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( unordered_pair(skolemFOFtoCNF_A_2,X_65) != unordered_pair(X_65,skolemFOFtoCNF_A_2)
| unordered_pair(X_65,skolemFOFtoCNF_A_2) = unordered_pair(skolemFOFtoCNF_A_2,X_65) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(unordered_pair(skolemFOFtoCNF_A_2,X_65))),bind(Y,$fot(unordered_pair(X_65,skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_28,plain,
unordered_pair(X_65,skolemFOFtoCNF_A_2) = unordered_pair(skolemFOFtoCNF_A_2,X_65),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,X_65),unordered_pair(X_65,skolemFOFtoCNF_A_2)) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( set_difference(unordered_pair(X_65,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) != singleton(X_65)
| unordered_pair(X_65,skolemFOFtoCNF_A_2) != unordered_pair(skolemFOFtoCNF_A_2,X_65)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,X_65),skolemFOFtoCNF_C) = singleton(X_65) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(unordered_pair(X_65,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),singleton(X_65)) ),[0,0],$fot(unordered_pair(skolemFOFtoCNF_A_2,X_65))]]) ).
cnf(refute_0_30,plain,
( set_difference(unordered_pair(X_65,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) != singleton(X_65)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,X_65),skolemFOFtoCNF_C) = singleton(X_65) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_65,skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,X_65)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,X_65),skolemFOFtoCNF_C) = singleton(X_65)
| in(X_65,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(X_65,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),singleton(X_65)) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_31:[bind(X_65,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_33,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_B)
| singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_B)) ),[0],$fot(singleton(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_34,plain,
( singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_B)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( singleton(skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_B)) )],[refute_0_34,refute_0_0]) ).
cnf(refute_0_36,plain,
singleton(skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_37,plain,
in(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_B)) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( ~ in(A,C)
| ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = empty_set ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_39,plain,
( ~ in(A,skolemFOFtoCNF_C)
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
| set_difference(unordered_pair(A,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = empty_set ),
inference(subst,[],[refute_0_38:[bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_40,plain,
( ~ in(A,skolemFOFtoCNF_C)
| set_difference(unordered_pair(A,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = empty_set ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_19,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ in(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = empty_set ),
inference(subst,[],[refute_0_40:[bind(A,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_42,plain,
set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = empty_set,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
( unordered_pair(A,B) != unordered_pair(B,A)
| unordered_pair(B,A) = unordered_pair(A,B) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(unordered_pair(A,B))),bind(Y,$fot(unordered_pair(B,A)))]]) ).
cnf(refute_0_44,plain,
unordered_pair(B,A) = unordered_pair(A,B),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(B,A)) )],[refute_0_22,refute_0_43]) ).
cnf(refute_0_45,plain,
unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_44:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_46,plain,
set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C))]]) ).
cnf(refute_0_47,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) != set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C)) ),[1,0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_48,plain,
( unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) = set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) != set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),empty_set) ),[0],$fot(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C))]]) ).
cnf(refute_0_51,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C) != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set,
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C),empty_set) )],[refute_0_42,refute_0_51]) ).
cnf(refute_0_53,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != empty_set,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),empty_set) )],[refute_0_52,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET930+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 21:33:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------