TSTP Solution File: SET890+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET890+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 03:38:08 EDT 2022
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 18 unt; 0 def)
% Number of atoms : 165 ( 87 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 171 ( 67 ~; 81 |; 11 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ) ).
fof(t31_zfmisc_1,conjecture,
! [A] : union(singleton(A)) = A ).
fof(subgoal_0,plain,
! [A] : union(singleton(A)) = A,
inference(strip,[],[t31_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A] : union(singleton(A)) = A,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : union(singleton(A)) != A,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
union(singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(canonicalize,[],[d4_tarski]) ).
fof(normalize_0_3,plain,
! [A,B] :
( B != union(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C,D] :
( ( B != union(A)
| ~ in(C,B)
| in(C,skolemFOFtoCNF_D_1(A,C)) )
& ( B != union(A)
| ~ in(C,B)
| in(skolemFOFtoCNF_D_1(A,C),A) )
& ( B = union(A)
| in(skolemFOFtoCNF_C_2(A,B),B)
| in(skolemFOFtoCNF_C_2(A,B),skolemFOFtoCNF_D(A,B)) )
& ( B = union(A)
| in(skolemFOFtoCNF_C_2(A,B),B)
| in(skolemFOFtoCNF_D(A,B),A) )
& ( B != union(A)
| ~ in(C,D)
| ~ in(D,A)
| in(C,B) )
& ( ~ in(D,A)
| ~ in(skolemFOFtoCNF_C_2(A,B),B)
| ~ in(skolemFOFtoCNF_C_2(A,B),D)
| B = union(A) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,D] :
( ~ in(D,A)
| ~ in(skolemFOFtoCNF_C_2(A,B),B)
| ~ in(skolemFOFtoCNF_C_2(A,B),D)
| B = union(A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B = union(A)
| in(skolemFOFtoCNF_C_2(A,B),B)
| in(skolemFOFtoCNF_C_2(A,B),skolemFOFtoCNF_D(A,B)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_7,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_8,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_12,plain,
! [A,B] :
( B = union(A)
| in(skolemFOFtoCNF_C_2(A,B),B)
| in(skolemFOFtoCNF_D(A,B),A) ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
union(singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ in(D,A)
| ~ in(skolemFOFtoCNF_C_2(A,B),B)
| ~ in(skolemFOFtoCNF_C_2(A,B),D)
| B = union(A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ in(X_320,singleton(X_320))
| ~ in(skolemFOFtoCNF_C_2(singleton(X_320),X_320),X_320)
| X_320 = union(singleton(X_320)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(singleton(X_320))),bind(B,$fot(X_320)),bind(D,$fot(X_320))]]) ).
cnf(refute_0_3,plain,
( B = union(A)
| in(skolemFOFtoCNF_C_2(A,B),B)
| in(skolemFOFtoCNF_C_2(A,B),skolemFOFtoCNF_D(A,B)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( B = union(singleton(B))
| in(skolemFOFtoCNF_C_2(singleton(B),B),B)
| in(skolemFOFtoCNF_C_2(singleton(B),B),skolemFOFtoCNF_D(singleton(B),B)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(singleton(B)))]]) ).
cnf(refute_0_5,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_5:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_7,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_8,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ in(skolemFOFtoCNF_D(singleton(X_318),X_318),singleton(X_318))
| skolemFOFtoCNF_D(singleton(X_318),X_318) = X_318 ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_318)),bind(C,$fot(skolemFOFtoCNF_D(singleton(X_318),X_318)))]]) ).
cnf(refute_0_10,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_10:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_12,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_13,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
in(X_317,singleton(X_317)),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_317))]]) ).
cnf(refute_0_16,plain,
( B = union(A)
| in(skolemFOFtoCNF_C_2(A,B),B)
| in(skolemFOFtoCNF_D(A,B),A) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_17,plain,
( X_315 = union(X_314)
| in(skolemFOFtoCNF_C_2(X_314,X_315),X_315)
| in(skolemFOFtoCNF_D(X_314,X_315),X_314) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_314)),bind(B,$fot(X_315))]]) ).
cnf(refute_0_18,plain,
( ~ in(X_315,X_314)
| ~ in(skolemFOFtoCNF_C_2(X_314,X_315),X_315)
| X_315 = union(X_314) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_314)),bind(B,$fot(X_315)),bind(D,$fot(X_315))]]) ).
cnf(refute_0_19,plain,
( ~ in(X_315,X_314)
| X_315 = union(X_314)
| in(skolemFOFtoCNF_D(X_314,X_315),X_314) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_2(X_314,X_315),X_315) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ in(X_317,singleton(X_317))
| X_317 = union(singleton(X_317))
| in(skolemFOFtoCNF_D(singleton(X_317),X_317),singleton(X_317)) ),
inference(subst,[],[refute_0_19:[bind(X_314,$fot(singleton(X_317))),bind(X_315,$fot(X_317))]]) ).
cnf(refute_0_21,plain,
( X_317 = union(singleton(X_317))
| in(skolemFOFtoCNF_D(singleton(X_317),X_317),singleton(X_317)) ),
inference(resolve,[$cnf( in(X_317,singleton(X_317)) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
( X_318 = union(singleton(X_318))
| in(skolemFOFtoCNF_D(singleton(X_318),X_318),singleton(X_318)) ),
inference(subst,[],[refute_0_21:[bind(X_317,$fot(X_318))]]) ).
cnf(refute_0_23,plain,
( X_318 = union(singleton(X_318))
| skolemFOFtoCNF_D(singleton(X_318),X_318) = X_318 ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(singleton(X_318),X_318),singleton(X_318)) )],[refute_0_22,refute_0_9]) ).
cnf(refute_0_24,plain,
( B = union(singleton(B))
| skolemFOFtoCNF_D(singleton(B),B) = B ),
inference(subst,[],[refute_0_23:[bind(X_318,$fot(B))]]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_D(singleton(B),B) != B
| ~ in(skolemFOFtoCNF_C_2(singleton(B),B),skolemFOFtoCNF_D(singleton(B),B))
| in(skolemFOFtoCNF_C_2(singleton(B),B),B) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_C_2(singleton(B),B),skolemFOFtoCNF_D(singleton(B),B)) ),[1],$fot(B)]]) ).
cnf(refute_0_26,plain,
( ~ in(skolemFOFtoCNF_C_2(singleton(B),B),skolemFOFtoCNF_D(singleton(B),B))
| B = union(singleton(B))
| in(skolemFOFtoCNF_C_2(singleton(B),B),B) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(singleton(B),B),B) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( B = union(singleton(B))
| in(skolemFOFtoCNF_C_2(singleton(B),B),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_2(singleton(B),B),skolemFOFtoCNF_D(singleton(B),B)) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
( X_320 = union(singleton(X_320))
| in(skolemFOFtoCNF_C_2(singleton(X_320),X_320),X_320) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_320))]]) ).
cnf(refute_0_29,plain,
( ~ in(X_320,singleton(X_320))
| X_320 = union(singleton(X_320)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_2(singleton(X_320),X_320),X_320) )],[refute_0_28,refute_0_2]) ).
cnf(refute_0_30,plain,
in(X_320,singleton(X_320)),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_320))]]) ).
cnf(refute_0_31,plain,
X_320 = union(singleton(X_320)),
inference(resolve,[$cnf( in(X_320,singleton(X_320)) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_33,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_34,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( X_320 != union(singleton(X_320))
| union(singleton(X_320)) = X_320 ),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_320)),bind(Y,$fot(union(singleton(X_320))))]]) ).
cnf(refute_0_36,plain,
union(singleton(X_320)) = X_320,
inference(resolve,[$cnf( $equal(X_320,union(singleton(X_320))) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
union(singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2,
inference(subst,[],[refute_0_36:[bind(X_320,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_38,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| union(singleton(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| union(singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
introduced(tautology,[equality,[$cnf( $equal(union(singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) ),[0,0,0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2
| union(singleton(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
inference(resolve,[$cnf( $equal(union(singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
skolemFOFtoCNF_A_2 != skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( $equal(union(singleton(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_39,refute_0_0]) ).
cnf(refute_0_41,plain,
skolemFOFtoCNF_A_2 = skolemFOFtoCNF_A_2,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,skolemFOFtoCNF_A_2) )],[refute_0_41,refute_0_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET890+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % 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 : Mon Jul 11 09:34:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.57
% 0.20/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.57
%------------------------------------------------------------------------------