TSTP Solution File: SYN966+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN966+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 : Thu Jul 21 09:12:30 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 111 ( 41 ~; 45 |; 7 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 34 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ) ).
fof(subgoal_0,plain,
( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
inference(strip,[],[prove_this]) ).
fof(negate_0_0,plain,
~ ( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ~ eq(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ eq(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ eq(X,Y)
<=> ? [Z] :
( ~ a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ( ~ a_member_of(Z,X)
| ~ eq(X,Y)
| a_member_of(Z,Y) )
& ( ~ a_member_of(Z,Y)
| ~ eq(X,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| eq(X,Y) )
& ( a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| eq(X,Y) ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| eq(X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [A,B] :
( ~ eq(B,A)
& eq(A,B) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
( ~ eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
& eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ a_member_of(Z,X)
| ~ eq(X,Y)
| a_member_of(Z,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| eq(X,Y) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
~ eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ a_member_of(Z,Y)
| ~ eq(X,Y)
| a_member_of(Z,X) ),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| ~ a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| eq(X,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_B)
| eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_2,plain,
eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ a_member_of(Z,X)
| ~ eq(X,Y)
| a_member_of(Z,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ a_member_of(X_5,skolemFOFtoCNF_A)
| ~ eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| a_member_of(X_5,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_B)),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_5,plain,
( ~ a_member_of(X_5,skolemFOFtoCNF_A)
| a_member_of(X_5,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_5:[bind(X_5,$fot(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_7,plain,
( a_member_of(skolemFOFtoCNF_Z(X,Y),X)
| a_member_of(skolemFOFtoCNF_Z(X,Y),Y)
| eq(X,Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),X_13)
| a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| eq(X_13,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_13)),bind(Y,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_9,plain,
( a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),X_13)
| a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),skolemFOFtoCNF_B)
| eq(X_13,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(X_13,skolemFOFtoCNF_A),skolemFOFtoCNF_A) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_B)
| eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_9:[bind(X_13,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_11,plain,
~ eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_12,plain,
a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_B),
inference(resolve,[$cnf( eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_B) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
( ~ a_member_of(Z,Y)
| ~ eq(X,Y)
| a_member_of(Z,X) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
( ~ a_member_of(X_9,skolemFOFtoCNF_B)
| ~ eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| a_member_of(X_9,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_B)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_16,plain,
( ~ a_member_of(X_9,skolemFOFtoCNF_B)
| a_member_of(X_9,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( eq(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),skolemFOFtoCNF_B)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(X_9,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14)))]]) ).
cnf(refute_0_18,plain,
( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),X_14)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),skolemFOFtoCNF_B)
| eq(skolemFOFtoCNF_B,X_14) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_B)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_19,plain,
( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),X_14)
| a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),skolemFOFtoCNF_A)
| eq(skolemFOFtoCNF_B,X_14) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,X_14),skolemFOFtoCNF_B) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_19:[bind(X_14,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_21,plain,
a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A),
inference(resolve,[$cnf( eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_20,refute_0_11]) ).
cnf(refute_0_22,plain,
eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_Z(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A) )],[refute_0_21,refute_0_13]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( eq(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_22,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN966+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n010.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 19:36:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------