TSTP Solution File: SET886+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 29 unt; 0 def)
% Number of atoms : 105 ( 80 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 87 ( 44 ~; 37 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 3 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
fof(t26_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ) ).
fof(t27_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A) ).
fof(subgoal_0,plain,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(strip,[],[t27_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( unordered_pair(A,B) != singleton(C)
& subset(unordered_pair(A,B),singleton(C)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_C)
& subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
inference(canonicalize,[],[t26_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(canonicalize,[],[t69_enumset1]) ).
fof(normalize_0_7,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[commutativity_k2_tarski]) ).
fof(normalize_0_9,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C))
| skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_4,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_C,
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_C
| skolemFOFtoCNF_C = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_A_2)),bind(Y,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_C = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
singleton(skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_11,plain,
( singleton(skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_C)
| skolemFOFtoCNF_C != skolemFOFtoCNF_A_2
| singleton(skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_C)) ),[1,0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_12,plain,
( skolemFOFtoCNF_C != skolemFOFtoCNF_A_2
| singleton(skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_C)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
singleton(skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,skolemFOFtoCNF_A_2) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( singleton(skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_15,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
unordered_pair(A,A) = singleton(A),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_18,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_19,plain,
( singleton(skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C))
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_20,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C))
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_C)) )],[refute_0_1,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ subset(unordered_pair(X_4,X_5),singleton(X_6))
| X_4 = X_6 ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(X_6))]]) ).
cnf(refute_0_23,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_24,plain,
unordered_pair(X_5,X_4) = unordered_pair(X_4,X_5),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_5)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_25,plain,
( unordered_pair(X_5,X_4) != unordered_pair(X_4,X_5)
| unordered_pair(X_4,X_5) = unordered_pair(X_5,X_4) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(unordered_pair(X_5,X_4))),bind(Y,$fot(unordered_pair(X_4,X_5)))]]) ).
cnf(refute_0_26,plain,
unordered_pair(X_4,X_5) = unordered_pair(X_5,X_4),
inference(resolve,[$cnf( $equal(unordered_pair(X_5,X_4),unordered_pair(X_4,X_5)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( unordered_pair(X_4,X_5) != unordered_pair(X_5,X_4)
| ~ subset(unordered_pair(X_5,X_4),singleton(X_6))
| subset(unordered_pair(X_4,X_5),singleton(X_6)) ),
introduced(tautology,[equality,[$cnf( ~ subset(unordered_pair(X_4,X_5),singleton(X_6)) ),[0],$fot(unordered_pair(X_5,X_4))]]) ).
cnf(refute_0_28,plain,
( ~ subset(unordered_pair(X_5,X_4),singleton(X_6))
| subset(unordered_pair(X_4,X_5),singleton(X_6)) ),
inference(resolve,[$cnf( $equal(unordered_pair(X_4,X_5),unordered_pair(X_5,X_4)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ subset(unordered_pair(X_5,X_4),singleton(X_6))
| X_4 = X_6 ),
inference(resolve,[$cnf( subset(unordered_pair(X_4,X_5),singleton(X_6)) )],[refute_0_28,refute_0_22]) ).
cnf(refute_0_30,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_B = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_29:[bind(X_4,$fot(skolemFOFtoCNF_B)),bind(X_5,$fot(skolemFOFtoCNF_A_2)),bind(X_6,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_31,plain,
skolemFOFtoCNF_B = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_21,refute_0_30]) ).
cnf(refute_0_32,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
introduced(tautology,[refl,[$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))]]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) ),[1,1],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_B != skolemFOFtoCNF_A_2
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_37,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_36]) ).
cnf(refute_0_38,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),bind(Y,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2))),bind(Z,$fot(singleton(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_39,plain,
( unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_18,refute_0_39]) ).
cnf(refute_0_41,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_42,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_42,refute_0_16]) ).
cnf(refute_0_44,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_45,plain,
$false,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_44,refute_0_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 08:44:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------