TSTP Solution File: SET625+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET625+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 03:36:07 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 100 ( 44 ~; 32 |; 14 &)
% ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ) ).
fof(prove_th101,conjecture,
! [B,C,D] :
( ( intersect(B,C)
& subset(C,D) )
=> intersect(B,D) ) ).
fof(subgoal_0,plain,
! [B,C,D] :
( ( intersect(B,C)
& subset(C,D) )
=> intersect(B,D) ),
inference(strip,[],[prove_th101]) ).
fof(negate_0_0,plain,
~ ! [B,C,D] :
( ( intersect(B,C)
& subset(C,D) )
=> intersect(B,D) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B,C,D] :
( ~ intersect(B,D)
& intersect(B,C)
& subset(C,D) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2)
& intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(canonicalize,[],[intersect_defn]) ).
fof(normalize_0_4,plain,
! [B,C] :
( ~ intersect(B,C)
<=> ! [D] :
( ~ member(D,B)
| ~ member(D,C) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B,C,D] :
( ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) )
& ( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) )
& ( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(canonicalize,[],[subset_defn]) ).
fof(normalize_0_11,plain,
! [B,C] :
( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& member(D,B) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D] :
( ( ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) )
& ( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) )
& ( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C,D] :
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_3,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ member(D,B)
| ~ member(D,C)
| intersect(B,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),X_18)
| ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B)
| intersect(skolemFOFtoCNF_B,X_18) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_18)),bind(D,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_6,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),X_18)
| intersect(skolemFOFtoCNF_B,X_18) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_B) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2)
| intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_6:[bind(X_18,$fot(skolemFOFtoCNF_D_2))]]) ).
cnf(refute_0_8,plain,
( ~ intersect(B,C)
| member(skolemFOFtoCNF_D(B,C),C) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_9,plain,
( ~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_10,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C),
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
( ~ member(X_34,skolemFOFtoCNF_C)
| ~ subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2)
| member(X_34,skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_C)),bind(C,$fot(skolemFOFtoCNF_D_2)),bind(D,$fot(X_34))]]) ).
cnf(refute_0_14,plain,
( ~ member(X_34,skolemFOFtoCNF_C)
| member(X_34,skolemFOFtoCNF_D_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,skolemFOFtoCNF_D_2) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) ),
inference(subst,[],[refute_0_14:[bind(X_34,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_16,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_C) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_B,skolemFOFtoCNF_C),skolemFOFtoCNF_D_2) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
~ intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( intersect(skolemFOFtoCNF_B,skolemFOFtoCNF_D_2) )],[refute_0_17,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET625+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 11:15:07 EDT 2022
% 0.13/0.33 % 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
%------------------------------------------------------------------------------