TSTP Solution File: SET676+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:36:33 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 38 ~; 29 |; 2 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ) ).
fof(p19,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_41,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
inference(strip,[],[prove_relset_1_41]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ~ ilf_type(cross_product(B,B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p19]) ).
fof(normalize_0_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [B] : ~ ilf_type(cross_product(B,B),identity_relation_of_type(B)),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
~ ilf_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_B),identity_relation_of_type(skolemFOFtoCNF_B)),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_6,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(cross_product(B,C),relation_type(B,C)) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,identity_relation_of_type(B))
<=> ~ ilf_type(C,relation_type(B,B)) ) ) ),
inference(canonicalize,[],[p4]) ).
fof(normalize_0_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,identity_relation_of_type(B))
<=> ~ ilf_type(C,relation_type(B,B)) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,identity_relation_of_type(B))
| ~ ilf_type(C,set_type)
| ilf_type(C,relation_type(B,B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
~ ilf_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_B),identity_relation_of_type(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(cross_product(B,C),relation_type(B,C)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
( ~ ilf_type(C,set_type)
| ilf_type(cross_product(B,C),relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(C))]]) ).
cnf(refute_0_5,plain,
ilf_type(cross_product(B,C),relation_type(B,C)),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
ilf_type(cross_product(X_18,X_18),relation_type(X_18,X_18)),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_18)),bind(C,$fot(X_18))]]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(cross_product(X_18,X_18),relation_type(X_18,X_18))
| ilf_type(cross_product(X_18,X_18),identity_relation_of_type(X_18)) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_18)),bind(C,$fot(cross_product(X_18,X_18)))]]) ).
cnf(refute_0_11,plain,
ilf_type(cross_product(X_18,X_18),identity_relation_of_type(X_18)),
inference(resolve,[$cnf( ilf_type(cross_product(X_18,X_18),relation_type(X_18,X_18)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
ilf_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_B),identity_relation_of_type(skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_11:[bind(X_18,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( ilf_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_B),identity_relation_of_type(skolemFOFtoCNF_B)) )],[refute_0_12,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.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 : Sun Jul 10 12:31:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------