TSTP Solution File: SET658+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET658+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 03:36:24 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 56 ( 26 ~; 21 |; 2 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 17 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ) ).
fof(p28,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_20,conjecture,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
inference(strip,[],[prove_relset_1_20]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ~ ilf_type(B,relation_type(domain_of(B),range_of(B)))
& ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ ilf_type(skolemFOFtoCNF_B_1,relation_type(domain_of(skolemFOFtoCNF_B_1),range_of(skolemFOFtoCNF_B_1)))
& ilf_type(skolemFOFtoCNF_B_1,binary_relation_type) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
ilf_type(skolemFOFtoCNF_B_1,binary_relation_type),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B] :
( ~ ilf_type(B,set_type)
| subset(B,B) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_0_4,plain,
! [B] :
( ~ ilf_type(B,set_type)
| subset(B,B) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p28]) ).
fof(normalize_0_6,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ~ subset(domain_of(C),B)
| ilf_type(C,relation_type(B,range_of(C))) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_8,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ~ subset(domain_of(C),B)
| ilf_type(C,relation_type(B,range_of(C))) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ subset(domain_of(C),B)
| ilf_type(C,relation_type(B,range_of(C))) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ ilf_type(skolemFOFtoCNF_B_1,relation_type(domain_of(skolemFOFtoCNF_B_1),range_of(skolemFOFtoCNF_B_1))),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
ilf_type(skolemFOFtoCNF_B_1,binary_relation_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ ilf_type(B,set_type)
| subset(B,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
subset(B,B),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
subset(domain_of(X_643),domain_of(X_643)),
inference(subst,[],[refute_0_3:[bind(B,$fot(domain_of(X_643)))]]) ).
cnf(refute_0_5,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ subset(domain_of(C),B)
| ilf_type(C,relation_type(B,range_of(C))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(C,binary_relation_type)
| ~ subset(domain_of(C),B)
| ilf_type(C,relation_type(B,range_of(C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(X_643,binary_relation_type)
| ~ subset(domain_of(X_643),domain_of(X_643))
| ilf_type(X_643,relation_type(domain_of(X_643),range_of(X_643))) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(domain_of(X_643))),bind(C,$fot(X_643))]]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(X_643,binary_relation_type)
| ilf_type(X_643,relation_type(domain_of(X_643),range_of(X_643))) ),
inference(resolve,[$cnf( subset(domain_of(X_643),domain_of(X_643)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(skolemFOFtoCNF_B_1,binary_relation_type)
| ilf_type(skolemFOFtoCNF_B_1,relation_type(domain_of(skolemFOFtoCNF_B_1),range_of(skolemFOFtoCNF_B_1))) ),
inference(subst,[],[refute_0_8:[bind(X_643,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_10,plain,
ilf_type(skolemFOFtoCNF_B_1,relation_type(domain_of(skolemFOFtoCNF_B_1),range_of(skolemFOFtoCNF_B_1))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_B_1,binary_relation_type) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
~ ilf_type(skolemFOFtoCNF_B_1,relation_type(domain_of(skolemFOFtoCNF_B_1),range_of(skolemFOFtoCNF_B_1))),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_B_1,relation_type(domain_of(skolemFOFtoCNF_B_1),range_of(skolemFOFtoCNF_B_1))) )],[refute_0_10,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET658+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.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 : Sat Jul 9 20:55:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.48
%------------------------------------------------------------------------------