TSTP Solution File: SET688+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET688+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 1.44s 1.66s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 134 ( 58 ~; 42 |; 24 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 64 ( 0 sgn 38 !; 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(thI04,conjecture,
! [A,B,C] :
( ( subset(A,B)
& ~ equal_set(A,B)
& subset(B,C)
& ~ equal_set(B,C) )
=> ~ equal_set(A,C) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( subset(A,B)
& ~ equal_set(A,B)
& subset(B,C)
& ~ equal_set(B,C) )
=> ~ equal_set(A,C) ),
inference(strip,[],[thI04]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( subset(A,B)
& ~ equal_set(A,B)
& subset(B,C)
& ~ equal_set(B,C) )
=> ~ equal_set(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[equal_set]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A,B,C] :
( ~ equal_set(A,B)
& ~ equal_set(B,C)
& equal_set(A,C)
& subset(A,B)
& subset(B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
& ~ equal_set(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
& subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ equal_set(A,B)
| subset(B,A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [A,B,X] :
( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_14,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_15,plain,
subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,plain,
~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_4,plain,
equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( ~ equal_set(A,B)
| subset(B,A) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_7,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A),
inference(resolve,[$cnf( equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_C) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ member(X_3168,skolemFOFtoCNF_C)
| ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A)
| member(X_3168,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_A)),bind(X,$fot(X_3168))]]) ).
cnf(refute_0_10,plain,
( ~ member(X_3168,skolemFOFtoCNF_C)
| member(X_3168,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_A) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,X_3574),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,X_3574),skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_10:[bind(X_3168,$fot(skolemFOFtoCNF_X(skolemFOFtoCNF_B,X_3574)))]]) ).
cnf(refute_0_12,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,B),skolemFOFtoCNF_B)
| subset(skolemFOFtoCNF_B,B) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_14,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
( ~ member(X_3168,skolemFOFtoCNF_B)
| ~ subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(X_3168,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C)),bind(X,$fot(X_3168))]]) ).
cnf(refute_0_16,plain,
( ~ member(X_3168,skolemFOFtoCNF_B)
| member(X_3168,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,B),skolemFOFtoCNF_B)
| member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,B),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_16:[bind(X_3168,$fot(skolemFOFtoCNF_X(skolemFOFtoCNF_B,B)))]]) ).
cnf(refute_0_18,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,B),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,B),skolemFOFtoCNF_B) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,X_3574),skolemFOFtoCNF_C)
| subset(skolemFOFtoCNF_B,X_3574) ),
inference(subst,[],[refute_0_18:[bind(B,$fot(X_3574))]]) ).
cnf(refute_0_20,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,X_3574),skolemFOFtoCNF_A)
| subset(skolemFOFtoCNF_B,X_3574) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,X_3574),skolemFOFtoCNF_C) )],[refute_0_19,refute_0_11]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A)
| subset(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_20:[bind(X_3574,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_22,plain,
subset(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_A) )],[refute_0_21,refute_0_3]) ).
cnf(refute_0_23,plain,
( ~ subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_25,plain,
equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
~ equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( equal_set(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_25,refute_0_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET688+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 21:18:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.44/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.44/1.66
% 1.44/1.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.44/1.66
%------------------------------------------------------------------------------