%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:38:01 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 130 ( 59 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 141 ( 57 ~; 56 |; 12 &)
% ( 15 <=>; 1 =>; 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 : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 90 ( 2 sgn 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
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(t12_zfmisc_1,conjecture,
! [A,B] : subset(singleton(A),unordered_pair(A,B)) ).
fof(subgoal_0,plain,
! [A,B] : subset(singleton(A),unordered_pair(A,B)),
inference(strip,[],[t12_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] : subset(singleton(A),unordered_pair(A,B)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] : ~ subset(singleton(A),unordered_pair(A,B)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
~ subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_7,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(canonicalize,[],[d2_tarski]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( C != unordered_pair(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( D = A
| D = B ) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,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_12]) ).
fof(normalize_0_14,plain,
! [A,B,C,D] :
( C != unordered_pair(A,B)
| D != A
| in(D,C) ),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(singleton(skolemFOFtoCNF_A_2))),bind(B,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
~ subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_3:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_5,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_6,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ in(skolemFOFtoCNF_C_1(singleton(A),X_16),singleton(A))
| skolemFOFtoCNF_C_1(singleton(A),X_16) = A ),
inference(subst,[],[refute_0_6:[bind(C,$fot(skolemFOFtoCNF_C_1(singleton(A),X_16)))]]) ).
cnf(refute_0_8,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( in(skolemFOFtoCNF_C_1(singleton(A),X_16),singleton(A))
| subset(singleton(A),X_16) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(singleton(A))),bind(B,$fot(X_16))]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_C_1(singleton(A),X_16) = A
| subset(singleton(A),X_16) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(singleton(A),X_16),singleton(A)) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
( skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2
| subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(X_16,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_11,refute_0_2]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) != skolemFOFtoCNF_A_2
| ~ in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_14,plain,
( ~ in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),skolemFOFtoCNF_A_2) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))
| subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_14,refute_0_1]) ).
cnf(refute_0_16,plain,
( C != unordered_pair(A,B)
| D != A
| in(D,C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_17,plain,
( A != A
| unordered_pair(A,B) != unordered_pair(A,B)
| in(A,unordered_pair(A,B)) ),
inference(subst,[],[refute_0_16:[bind(C,$fot(unordered_pair(A,B))),bind(D,$fot(A))]]) ).
cnf(refute_0_18,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_19,plain,
( unordered_pair(A,B) != unordered_pair(A,B)
| in(A,unordered_pair(A,B)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
unordered_pair(A,B) = unordered_pair(A,B),
introduced(tautology,[refl,[$fot(unordered_pair(A,B))]]) ).
cnf(refute_0_21,plain,
in(A,unordered_pair(A,B)),
inference(resolve,[$cnf( $equal(unordered_pair(A,B),unordered_pair(A,B)) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_23,plain,
subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_22,refute_0_15]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_2),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_23,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 14:14:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------