%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET887+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 03:38:07 EDT 2022
% Result : Theorem 0.38s 0.53s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 20
% Syntax : Number of formulae : 96 ( 24 unt; 0 def)
% Number of atoms : 276 ( 224 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 297 ( 117 ~; 136 |; 29 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 133 ( 9 sgn 77 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ) ).
fof(l46_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ) ).
fof(t10_zfmisc_1,axiom,
! [A,B,C,D] :
~ ( unordered_pair(A,B) = unordered_pair(C,D)
& A != C
& A != D ) ).
fof(t28_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( subset(unordered_pair(A,B),unordered_pair(C,D))
& A != C
& A != D ) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ) ).
fof(subgoal_0,plain,
! [A,B,C,D] :
( ( subset(unordered_pair(A,B),unordered_pair(C,D))
& A != C )
=> A = D ),
inference(strip,[],[t28_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,D] :
( ( subset(unordered_pair(A,B),unordered_pair(C,D))
& A != C )
=> A = D ),
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 != B
| in(D,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(canonicalize,[],[t8_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( singleton(A) != unordered_pair(B,C)
| A = B ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( unordered_pair(A,B) != unordered_pair(C,D)
| A = C
| A = D ),
inference(canonicalize,[],[t10_zfmisc_1]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( unordered_pair(A,B) != unordered_pair(C,D)
| A = C
| A = D ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [A,B,C,D] :
( A != C
& A != D
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C
& skolemFOFtoCNF_A_2 != skolemFOFtoCNF_D_1
& subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
<=> ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(canonicalize,[],[l46_zfmisc_1]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
<=> ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ( A != empty_set
| subset(A,unordered_pair(B,C)) )
& ( A != singleton(B)
| subset(A,unordered_pair(B,C)) )
& ( A != singleton(C)
| subset(A,unordered_pair(B,C)) )
& ( A != unordered_pair(B,C)
| subset(A,unordered_pair(B,C)) )
& ( ~ subset(A,unordered_pair(B,C))
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_17,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_D_1,
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_18,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_19,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
( C != unordered_pair(A,B)
| D != B
| in(D,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( B != B
| unordered_pair(A,B) != unordered_pair(A,B)
| in(B,unordered_pair(A,B)) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(unordered_pair(A,B))),bind(D,$fot(B))]]) ).
cnf(refute_0_2,plain,
B = B,
introduced(tautology,[refl,[$fot(B)]]) ).
cnf(refute_0_3,plain,
( unordered_pair(A,B) != unordered_pair(A,B)
| in(B,unordered_pair(A,B)) ),
inference(resolve,[$cnf( $equal(B,B) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
unordered_pair(A,B) = unordered_pair(A,B),
introduced(tautology,[refl,[$fot(unordered_pair(A,B))]]) ).
cnf(refute_0_5,plain,
in(B,unordered_pair(A,B)),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_7,plain,
( singleton(A) != unordered_pair(B,C)
| A = B ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( singleton(A) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| A = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_7:[bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_9,plain,
( unordered_pair(A,B) != unordered_pair(C,D)
| A = C
| A = D ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( unordered_pair(A,B) != unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)
| A = skolemFOFtoCNF_C
| A = skolemFOFtoCNF_D_1 ),
inference(subst,[],[refute_0_9:[bind(C,$fot(skolemFOFtoCNF_C)),bind(D,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_11,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
( ~ subset(A,unordered_pair(B,C))
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1))
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))),bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_14,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_16,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))),bind(Y,$fot(unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)))]]) ).
cnf(refute_0_19,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( unordered_pair(A,B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| unordered_pair(A,B) = unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(unordered_pair(A,B),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) ),[1],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_21,plain,
( unordered_pair(A,B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| unordered_pair(A,B) = unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( unordered_pair(A,B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| A = skolemFOFtoCNF_C
| A = skolemFOFtoCNF_D_1
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(skolemFOFtoCNF_C,skolemFOFtoCNF_D_1)) )],[refute_0_21,refute_0_10]) ).
cnf(refute_0_23,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_D_1
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_22:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_24,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_D_1
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_A_2 = skolemFOFtoCNF_D_1
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_D_1,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_29,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( singleton(A) != singleton(skolemFOFtoCNF_C)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_C)
| singleton(A) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(A),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),[1],$fot(singleton(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_31,plain,
( singleton(A) != singleton(skolemFOFtoCNF_C)
| singleton(A) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_C)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( singleton(A) != singleton(skolemFOFtoCNF_C)
| A = skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(singleton(A),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_31,refute_0_8]) ).
cnf(refute_0_33,plain,
( singleton(skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_C)
| skolemFOFtoCNF_C = skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(subst,[],[refute_0_32:[bind(A,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_34,plain,
singleton(skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_C = skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_C)) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_C)),bind(Y,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_37,plain,
skolemFOFtoCNF_C != skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_36,refute_0_26]) ).
cnf(refute_0_38,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| ~ in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))
| in(skolemFOFtoCNF_B_1,empty_set) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_40,plain,
( ~ in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1)
| in(skolemFOFtoCNF_B_1,empty_set) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1)
| in(skolemFOFtoCNF_B_1,empty_set) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_6,refute_0_40]) ).
cnf(refute_0_42,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_43,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_0_42:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_44,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_45,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_44,refute_0_43]) ).
cnf(refute_0_46,plain,
~ in(skolemFOFtoCNF_B_1,empty_set),
inference(subst,[],[refute_0_45:[bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_47,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = singleton(skolemFOFtoCNF_D_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,empty_set) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
( singleton(A) != singleton(skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_D_1)
| singleton(A) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(singleton(A),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) ),[1],$fot(singleton(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_49,plain,
( singleton(A) != singleton(skolemFOFtoCNF_D_1)
| singleton(A) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_D_1)) )],[refute_0_38,refute_0_48]) ).
cnf(refute_0_50,plain,
( singleton(A) != singleton(skolemFOFtoCNF_D_1)
| A = skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(resolve,[$cnf( $equal(singleton(A),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_49,refute_0_8]) ).
cnf(refute_0_51,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_D_1)
| singleton(skolemFOFtoCNF_D_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) ),[0],$fot(singleton(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_52,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| singleton(skolemFOFtoCNF_D_1) = empty_set ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_D_1)) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( singleton(A) != singleton(skolemFOFtoCNF_D_1)
| A = skolemFOFtoCNF_A_2
| singleton(skolemFOFtoCNF_D_1) = empty_set ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
( singleton(skolemFOFtoCNF_D_1) != singleton(skolemFOFtoCNF_D_1)
| singleton(skolemFOFtoCNF_D_1) = empty_set
| skolemFOFtoCNF_D_1 = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_53:[bind(A,$fot(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_55,plain,
singleton(skolemFOFtoCNF_D_1) = singleton(skolemFOFtoCNF_D_1),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_D_1))]]) ).
cnf(refute_0_56,plain,
( singleton(skolemFOFtoCNF_D_1) = empty_set
| skolemFOFtoCNF_D_1 = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_D_1),singleton(skolemFOFtoCNF_D_1)) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( skolemFOFtoCNF_D_1 != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_D_1 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_D_1)),bind(Y,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_58,plain,
skolemFOFtoCNF_D_1 != skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_D_1) )],[refute_0_57,refute_0_28]) ).
cnf(refute_0_59,plain,
singleton(skolemFOFtoCNF_D_1) = empty_set,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_1,skolemFOFtoCNF_A_2) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
( singleton(skolemFOFtoCNF_D_1) != empty_set
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_D_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_61,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != singleton(skolemFOFtoCNF_D_1)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_D_1),empty_set) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),singleton(skolemFOFtoCNF_D_1)) )],[refute_0_47,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))
| in(skolemFOFtoCNF_B_1,empty_set) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_62,refute_0_39]) ).
cnf(refute_0_64,plain,
in(skolemFOFtoCNF_B_1,empty_set),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_6,refute_0_63]) ).
cnf(refute_0_65,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,empty_set) )],[refute_0_64,refute_0_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET887+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 16:48:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.53
% 0.38/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.38/0.54
%------------------------------------------------------------------------------