TSTP Solution File: SET689+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET689+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 03:36:39 EDT 2022
% Result : Theorem 1.15s 1.34s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 113 ( 45 ~; 39 |; 19 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 36 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(thI05,conjecture,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C)
& subset(C,A) )
=> equal_set(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C)
& subset(C,A) )
=> equal_set(A,C) ),
inference(strip,[],[thI05]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( subset(A,B)
& subset(B,C)
& subset(C,A) )
=> equal_set(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,X] :
( ( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) )
& ( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) )
& ( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( ~ equal_set(A,C)
& subset(A,B)
& subset(B,C)
& subset(C,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,X] :
( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[equal_set]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| subset(A,B) )
& ( ~ equal_set(A,B)
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,skolemFOFtoCNF_C),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ member(X_3145,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_3145,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C)),bind(X,$fot(X_3145))]]) ).
cnf(refute_0_5,plain,
( ~ member(X_3145,skolemFOFtoCNF_B)
| member(X_3145,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,X_3151),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,X_3151),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_5:[bind(X_3145,$fot(skolemFOFtoCNF_X(skolemFOFtoCNF_A,X_3151)))]]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,B),skolemFOFtoCNF_A)
| subset(skolemFOFtoCNF_A,B) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_9,plain,
subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ member(X_3145,skolemFOFtoCNF_A)
| ~ subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| member(X_3145,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(X,$fot(X_3145))]]) ).
cnf(refute_0_11,plain,
( ~ member(X_3145,skolemFOFtoCNF_A)
| member(X_3145,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,B),skolemFOFtoCNF_A)
| member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,B),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_11:[bind(X_3145,$fot(skolemFOFtoCNF_X(skolemFOFtoCNF_A,B)))]]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,B),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A,B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,B),skolemFOFtoCNF_A) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,X_3151),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_A,X_3151) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(X_3151))]]) ).
cnf(refute_0_15,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,X_3151),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_A,X_3151) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,X_3151),skolemFOFtoCNF_B) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,skolemFOFtoCNF_C),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_15:[bind(X_3151,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_17,plain,
subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_A,skolemFOFtoCNF_C),skolemFOFtoCNF_C) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( ~ subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
| ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A)
| equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_21,plain,
( ~ subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
| equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_23,plain,
~ subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(resolve,[$cnf( equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A,skolemFOFtoCNF_C) )],[refute_0_17,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET689+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n025.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 : Sat Jul 9 23:40:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.15/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.15/1.34
% 1.15/1.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.15/1.34
%------------------------------------------------------------------------------