TSTP Solution File: SEU159+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 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 12:38:53 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 128 ( 37 unt; 0 def)
% Number of atoms : 354 ( 146 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 379 ( 153 ~; 155 |; 42 &)
% ( 22 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 183 ( 4 sgn 101 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t38_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
=> in(A,C) ),
inference(strip,[],[t38_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( subset(unordered_pair(A,B),C)
& in(A,C) )
=> in(B,C) ),
inference(strip,[],[t38_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C] :
( ( in(A,C)
& in(B,C) )
=> subset(unordered_pair(A,B),C) ),
inference(strip,[],[t38_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
=> 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] :
( ~ in(A,C)
& subset(unordered_pair(A,B),C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1)
& subset(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_0_5]) ).
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( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_A,unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_7,plain,
subset(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ in(X_18,unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
| ~ subset(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_C_1)
| in(X_18,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B))),bind(B,$fot(skolemFOFtoCNF_C_1)),bind(C,$fot(X_18))]]) ).
cnf(refute_0_10,plain,
( ~ in(X_18,unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
| in(X_18,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_C_1) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_A,unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_0_10:[bind(X_18,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_12,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,unordered_pair(skolemFOFtoCNF_A,skolemFOFtoCNF_B)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_C_1) )],[refute_0_12,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( subset(unordered_pair(A,B),C)
& in(A,C) )
=> in(B,C) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(canonicalize,[],[d2_tarski]) ).
fof(normalize_1_1,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_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_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C,D] :
( C != unordered_pair(A,B)
| D != B
| in(D,C) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C] :
( ~ in(B,C)
& in(A,C)
& subset(unordered_pair(A,B),C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2)
& in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_C_2)
& subset(unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
subset(unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_1_8,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( C != unordered_pair(A,B)
| D != B
| in(D,C) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( B != B
| unordered_pair(A,B) != unordered_pair(A,B)
| in(B,unordered_pair(A,B)) ),
inference(subst,[],[refute_1_0:[bind(C,$fot(unordered_pair(A,B))),bind(D,$fot(B))]]) ).
cnf(refute_1_2,plain,
B = B,
introduced(tautology,[refl,[$fot(B)]]) ).
cnf(refute_1_3,plain,
( unordered_pair(A,B) != unordered_pair(A,B)
| in(B,unordered_pair(A,B)) ),
inference(resolve,[$cnf( $equal(B,B) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
unordered_pair(A,B) = unordered_pair(A,B),
introduced(tautology,[refl,[$fot(unordered_pair(A,B))]]) ).
cnf(refute_1_5,plain,
in(B,unordered_pair(A,B)),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_1_5:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_7,plain,
subset(unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_8,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_9,plain,
( ~ in(X_41,unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))
| ~ subset(unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2)
| in(X_41,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))),bind(B,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(X_41))]]) ).
cnf(refute_1_10,plain,
( ~ in(X_41,unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))
| in(X_41,skolemFOFtoCNF_C_2) ),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2) )],[refute_1_7,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1))
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_1_10:[bind(X_41,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_12,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,unordered_pair(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)) )],[refute_1_6,refute_1_11]) ).
cnf(refute_1_13,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_14,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_2) )],[refute_1_12,refute_1_13]) ).
fof(negate_2_0,plain,
~ ! [A,B,C] :
( ( in(A,C)
& in(B,C) )
=> subset(unordered_pair(A,B),C) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_2_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
? [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
& in(A,C)
& in(B,C) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_5,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
& in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) ),
inference(skolemize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_8,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(canonicalize,[],[d2_tarski]) ).
fof(normalize_2_9,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(specialize,[],[normalize_2_8]) ).
fof(normalize_2_10,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_2_9]) ).
fof(normalize_2_11,plain,
! [A,B,C,D] :
( C != unordered_pair(A,B)
| ~ in(D,C)
| D = A
| D = B ),
inference(conjunct,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_2_5]) ).
fof(normalize_2_13,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_2_5]) ).
cnf(refute_2_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( ~ in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3)
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2))),bind(B,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_2,plain,
( ~ in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3)
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2))),bind(B,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_3,plain,
~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_4,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_5,plain,
( in(skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B),unordered_pair(X_68,X_69))
| subset(unordered_pair(X_68,X_69),B) ),
inference(subst,[],[refute_2_4:[bind(A,$fot(unordered_pair(X_68,X_69)))]]) ).
cnf(refute_2_6,plain,
( C != unordered_pair(A,B)
| ~ in(D,C)
| D = A
| D = B ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_7,plain,
( unordered_pair(A,B) != unordered_pair(A,B)
| ~ in(D,unordered_pair(A,B))
| D = A
| D = B ),
inference(subst,[],[refute_2_6:[bind(C,$fot(unordered_pair(A,B)))]]) ).
cnf(refute_2_8,plain,
unordered_pair(A,B) = unordered_pair(A,B),
introduced(tautology,[refl,[$fot(unordered_pair(A,B))]]) ).
cnf(refute_2_9,plain,
( ~ in(D,unordered_pair(A,B))
| D = A
| D = B ),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_2_8,refute_2_7]) ).
cnf(refute_2_10,plain,
( ~ in(skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B),unordered_pair(X_68,X_69))
| skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B) = X_68
| skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B) = X_69 ),
inference(subst,[],[refute_2_9:[bind(A,$fot(X_68)),bind(B,$fot(X_69)),bind(D,$fot(skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B)))]]) ).
cnf(refute_2_11,plain,
( skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B) = X_68
| skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B) = X_69
| subset(unordered_pair(X_68,X_69),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(unordered_pair(X_68,X_69),B),unordered_pair(X_68,X_69)) )],[refute_2_5,refute_2_10]) ).
cnf(refute_2_12,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_2_11:[bind(B,$fot(skolemFOFtoCNF_C_3)),bind(X_68,$fot(skolemFOFtoCNF_A_2)),bind(X_69,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_13,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) )],[refute_2_12,refute_2_3]) ).
cnf(refute_2_14,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_A_2
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_2_15,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2
| in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_A_2) )],[refute_2_13,refute_2_14]) ).
cnf(refute_2_16,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) )],[refute_2_15,refute_2_2]) ).
cnf(refute_2_17,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_18,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3) )],[refute_2_17,refute_2_16]) ).
cnf(refute_2_19,plain,
skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2,
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) )],[refute_2_18,refute_2_3]) ).
cnf(refute_2_20,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),[0],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_2_21,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2
| in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_B_2) )],[refute_2_13,refute_2_20]) ).
cnf(refute_2_22,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) )],[refute_2_21,refute_2_2]) ).
cnf(refute_2_23,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_A_2) ),[0],$fot(skolemFOFtoCNF_B_2)]]) ).
cnf(refute_2_24,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_B_2) )],[refute_2_19,refute_2_23]) ).
cnf(refute_2_25,plain,
( ~ in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_2
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_A_2) )],[refute_2_22,refute_2_24]) ).
cnf(refute_2_26,plain,
in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_27,plain,
( skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_2
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_3) )],[refute_2_26,refute_2_25]) ).
cnf(refute_2_28,plain,
skolemFOFtoCNF_B_2 = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) )],[refute_2_27,refute_2_3]) ).
cnf(refute_2_29,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2))]]) ).
cnf(refute_2_30,plain,
( skolemFOFtoCNF_B_2 != skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2)) ),[1,1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_2_31,plain,
( skolemFOFtoCNF_B_2 != skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2)) )],[refute_2_29,refute_2_30]) ).
cnf(refute_2_32,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_2) )],[refute_2_28,refute_2_31]) ).
cnf(refute_2_33,plain,
skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_34,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)) ),[1,0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2))]]) ).
cnf(refute_2_35,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)) )],[refute_2_33,refute_2_34]) ).
cnf(refute_2_36,plain,
skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)) )],[refute_2_32,refute_2_35]) ).
cnf(refute_2_37,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3)
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_B_2) ),[0],$fot(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3))]]) ).
cnf(refute_2_38,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_B_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3)) )],[refute_2_36,refute_2_37]) ).
cnf(refute_2_39,plain,
( skolemFOFtoCNF_B_2 != skolemFOFtoCNF_A_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_B_2) ),[1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_2_40,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_2) )],[refute_2_28,refute_2_39]) ).
cnf(refute_2_41,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_B_2
| skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_B_2) )],[refute_2_38,refute_2_40]) ).
cnf(refute_2_42,plain,
skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_B_2) )],[refute_2_19,refute_2_41]) ).
cnf(refute_2_43,plain,
( skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) != skolemFOFtoCNF_A_2
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_2_44,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_A_2) )],[refute_2_42,refute_2_43]) ).
cnf(refute_2_45,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3)
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),skolemFOFtoCNF_C_3) )],[refute_2_44,refute_2_1]) ).
cnf(refute_2_46,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C_3) )],[refute_2_17,refute_2_45]) ).
cnf(refute_2_47,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3)
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
introduced(tautology,[equality,[$cnf( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),[0],$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2))]]) ).
cnf(refute_2_48,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3)
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)) )],[refute_2_32,refute_2_47]) ).
cnf(refute_2_49,plain,
~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) )],[refute_2_48,refute_2_3]) ).
cnf(refute_2_50,plain,
$false,
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),skolemFOFtoCNF_C_3) )],[refute_2_46,refute_2_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.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 Jun 18 22:54:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------