TSTP Solution File: SET921+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 03:38:22 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 102 ( 37 unt; 0 def)
% Number of atoms : 293 ( 119 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 338 ( 147 ~; 117 |; 43 &)
% ( 25 <=>; 6 =>; 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 : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 170 ( 4 sgn 90 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ) ).
fof(t64_zfmisc_1,conjecture,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( in(A,B)
& A != C ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
=> in(A,B) ),
inference(strip,[],[t64_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( in(A,set_difference(B,singleton(C)))
& in(A,B) )
=> A != C ),
inference(strip,[],[t64_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C] :
( ( in(A,B)
& A != C )
=> in(A,set_difference(B,singleton(C))) ),
inference(strip,[],[t64_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
=> in(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( ~ in(A,B)
& ? [C] : in(A,set_difference(B,singleton(C))) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
& ? [C] : in(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B,singleton(C))) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [C] : in(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B,singleton(C))),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
in(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_C_1))),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_C_1))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,set_difference(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_1:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_0_3,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_0_4,plain,
( ~ in(D,set_difference(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ in(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_C_1)))
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(singleton(skolemFOFtoCNF_C_1))),bind(D,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_C_1))) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_6,refute_0_7]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( in(A,set_difference(B,singleton(C)))
& in(A,B) )
=> A != C ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C] :
( A = C
& in(A,B)
& in(A,set_difference(B,singleton(C))) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( skolemFOFtoCNF_A_3 = skolemFOFtoCNF_C_2
& in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)))
& in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
skolemFOFtoCNF_A_3 = skolemFOFtoCNF_C_2,
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_4,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_1_5,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_1_9,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_1_10]) ).
cnf(refute_1_0,plain,
in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
skolemFOFtoCNF_A_3 = skolemFOFtoCNF_C_2,
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( skolemFOFtoCNF_A_3 != skolemFOFtoCNF_C_2
| skolemFOFtoCNF_C_2 = skolemFOFtoCNF_A_3 ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_A_3)),bind(Y,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_6,plain,
skolemFOFtoCNF_C_2 = skolemFOFtoCNF_A_3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_2) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_C_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_1_8,plain,
( singleton(skolemFOFtoCNF_C_2) != singleton(skolemFOFtoCNF_C_2)
| skolemFOFtoCNF_C_2 != skolemFOFtoCNF_A_3
| singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_A_3) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_C_2)) ),[1,0],$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_9,plain,
( skolemFOFtoCNF_C_2 != skolemFOFtoCNF_A_3
| singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_C_2)) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
singleton(skolemFOFtoCNF_C_2) = singleton(skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_2,skolemFOFtoCNF_A_3) )],[refute_1_6,refute_1_9]) ).
cnf(refute_1_11,plain,
set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)) = set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)),
introduced(tautology,[refl,[$fot(set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_1_12,plain,
( set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)) != set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))
| singleton(skolemFOFtoCNF_C_2) != singleton(skolemFOFtoCNF_A_3)
| set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)) = set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3)) ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))) ),[1,1],$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_13,plain,
( singleton(skolemFOFtoCNF_C_2) != singleton(skolemFOFtoCNF_A_3)
| set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)) = set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)) = set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C_2),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_10,refute_1_13]) ).
cnf(refute_1_15,plain,
( set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)) != set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3))
| ~ in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)))
| in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3))) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))) ),[1],$fot(set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3)))]]) ).
cnf(refute_1_16,plain,
( ~ in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)))
| in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3))) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2)),set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3))) )],[refute_1_14,refute_1_15]) ).
cnf(refute_1_17,plain,
in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_C_2))) )],[refute_1_0,refute_1_16]) ).
cnf(refute_1_18,plain,
( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_19,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(subst,[],[refute_1_18:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_1_20,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_1_21,plain,
( ~ in(D,B)
| ~ in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_1_20,refute_1_19]) ).
cnf(refute_1_22,plain,
( ~ in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3)))
| ~ in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_A_3)) ),
inference(subst,[],[refute_1_21:[bind(A,$fot(skolemFOFtoCNF_B_1)),bind(B,$fot(singleton(skolemFOFtoCNF_A_3))),bind(D,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_23,plain,
~ in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,set_difference(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3))) )],[refute_1_17,refute_1_22]) ).
cnf(refute_1_24,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_25,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_1_24:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_1_26,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_1_27,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_1_26,refute_1_25]) ).
cnf(refute_1_28,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_1_29,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_1_28,refute_1_27]) ).
cnf(refute_1_30,plain,
in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_A_3)),
inference(subst,[],[refute_1_29:[bind(A,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_31,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_A_3)) )],[refute_1_30,refute_1_23]) ).
fof(negate_2_0,plain,
~ ! [A,B,C] :
( ( in(A,B)
& A != C )
=> in(A,set_difference(B,singleton(C))) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_2_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
? [A,B,C] :
( A != C
& ~ in(A,set_difference(B,singleton(C)))
& in(A,B) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_5,plain,
( skolemFOFtoCNF_A_4 != skolemFOFtoCNF_C_3
& ~ in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,singleton(skolemFOFtoCNF_C_3)))
& in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) ),
inference(skolemize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
~ in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,singleton(skolemFOFtoCNF_C_3))),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_8,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_xboole_0]) ).
fof(normalize_2_9,plain,
! [A,B,C] :
( C != set_difference(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
! [A,B,C,D] :
( ( C != set_difference(A,B)
| ~ in(D,B)
| ~ in(D,C) )
& ( C != set_difference(A,B)
| ~ in(D,C)
| in(D,A) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_difference(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B) ) ),
inference(clausify,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [A,B,C,D] :
( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
skolemFOFtoCNF_A_4 != skolemFOFtoCNF_C_3,
inference(conjunct,[],[normalize_2_5]) ).
cnf(refute_2_0,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_2_0:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_2_2,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_2_3,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_2_2,refute_2_1]) ).
cnf(refute_2_4,plain,
( ~ in(skolemFOFtoCNF_A_4,singleton(skolemFOFtoCNF_C_3))
| skolemFOFtoCNF_A_4 = skolemFOFtoCNF_C_3 ),
inference(subst,[],[refute_2_3:[bind(A,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_2_5,plain,
~ in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,singleton(skolemFOFtoCNF_C_3))),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_6,plain,
in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_7,plain,
( C != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_8,plain,
( set_difference(A,B) != set_difference(A,B)
| ~ in(D,A)
| in(D,B)
| in(D,set_difference(A,B)) ),
inference(subst,[],[refute_2_7:[bind(C,$fot(set_difference(A,B)))]]) ).
cnf(refute_2_9,plain,
set_difference(A,B) = set_difference(A,B),
introduced(tautology,[refl,[$fot(set_difference(A,B))]]) ).
cnf(refute_2_10,plain,
( ~ in(D,A)
| in(D,B)
| in(D,set_difference(A,B)) ),
inference(resolve,[$cnf( $equal(set_difference(A,B),set_difference(A,B)) )],[refute_2_9,refute_2_8]) ).
cnf(refute_2_11,plain,
( ~ in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_A_4,X_46)
| in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,X_46)) ),
inference(subst,[],[refute_2_10:[bind(A,$fot(skolemFOFtoCNF_B_2)),bind(B,$fot(X_46)),bind(D,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_2_12,plain,
( in(skolemFOFtoCNF_A_4,X_46)
| in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,X_46)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2) )],[refute_2_6,refute_2_11]) ).
cnf(refute_2_13,plain,
( in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,singleton(skolemFOFtoCNF_C_3)))
| in(skolemFOFtoCNF_A_4,singleton(skolemFOFtoCNF_C_3)) ),
inference(subst,[],[refute_2_12:[bind(X_46,$fot(singleton(skolemFOFtoCNF_C_3)))]]) ).
cnf(refute_2_14,plain,
in(skolemFOFtoCNF_A_4,singleton(skolemFOFtoCNF_C_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_4,set_difference(skolemFOFtoCNF_B_2,singleton(skolemFOFtoCNF_C_3))) )],[refute_2_13,refute_2_5]) ).
cnf(refute_2_15,plain,
skolemFOFtoCNF_A_4 = skolemFOFtoCNF_C_3,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_4,singleton(skolemFOFtoCNF_C_3)) )],[refute_2_14,refute_2_4]) ).
cnf(refute_2_16,plain,
skolemFOFtoCNF_A_4 != skolemFOFtoCNF_C_3,
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_17,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C_3) )],[refute_2_15,refute_2_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 20:55:22 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.40
%------------------------------------------------------------------------------