TSTP Solution File: SET664+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 : 300s
% DateTime : Wed May 31 12:34:58 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 11 unt; 0 def)
% Number of atoms : 154 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 162 ( 61 ~; 57 |; 17 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 74 (; 71 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( domain_of(B) = empty_set
| range_of(B) = empty_set )
=> B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ilf_type(D,relation_type(C,empty_set))
=> D = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ilf_type(D,relation_type(C,empty_set))
=> D = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ subset(B,empty_set)
| B = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f38,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| ( domain_of(B) != empty_set
& range_of(B) != empty_set )
| B = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| range_of(X0) != empty_set
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f42,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| subset(range_of(X2),X1) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f49,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f72,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f73,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ ilf_type(B,binary_relation_type)
| ( relation_like(B)
& ilf_type(B,set_type) ) )
& ( ilf_type(B,binary_relation_type)
| ~ relation_like(B)
| ~ ilf_type(B,set_type) ) ) ),
inference(NNF_transformation,[status(esa)],[f72]) ).
fof(f76,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f133,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f144,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,B))
& ilf_type(D,relation_type(C,empty_set))
& D != empty_set ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f145,plain,
( ilf_type(sk0_12,set_type)
& ilf_type(sk0_13,set_type)
& ilf_type(sk0_14,relation_type(sk0_13,sk0_12))
& ilf_type(sk0_14,relation_type(sk0_13,empty_set))
& sk0_14 != empty_set ),
inference(skolemization,[status(esa)],[f144]) ).
fof(f149,plain,
ilf_type(sk0_14,relation_type(sk0_13,empty_set)),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f150,plain,
sk0_14 != empty_set,
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f151,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f76]) ).
fof(f156,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f143]) ).
fof(f172,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f143]) ).
fof(f201,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| subset(range_of(X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f143]) ).
fof(f202,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(range_of(X0),X2) ),
inference(resolution,[status(thm)],[f201,f143]) ).
fof(f207,plain,
subset(range_of(sk0_14),empty_set),
inference(resolution,[status(thm)],[f202,f149]) ).
fof(f209,plain,
range_of(sk0_14) = empty_set,
inference(resolution,[status(thm)],[f207,f156]) ).
fof(f219,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(X1,subset_type(cross_product(X2,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f143]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f219,f143]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| relation_like(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f143]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(resolution,[status(thm)],[f251,f143]) ).
fof(f254,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f252,f220]) ).
fof(f258,plain,
relation_like(sk0_14),
inference(resolution,[status(thm)],[f254,f149]) ).
fof(f260,plain,
ilf_type(sk0_14,binary_relation_type),
inference(resolution,[status(thm)],[f258,f172]) ).
fof(f264,plain,
( spl0_8
<=> range_of(sk0_14) = empty_set ),
introduced(split_symbol_definition) ).
fof(f266,plain,
( range_of(sk0_14) != empty_set
| spl0_8 ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,plain,
( spl0_9
<=> sk0_14 = empty_set ),
introduced(split_symbol_definition) ).
fof(f268,plain,
( sk0_14 = empty_set
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( range_of(sk0_14) != empty_set
| sk0_14 = empty_set ),
inference(resolution,[status(thm)],[f260,f41]) ).
fof(f271,plain,
( ~ spl0_8
| spl0_9 ),
inference(split_clause,[status(thm)],[f270,f264,f267]) ).
fof(f277,plain,
( empty_set != empty_set
| spl0_8 ),
inference(forward_demodulation,[status(thm)],[f209,f266]) ).
fof(f278,plain,
( $false
| spl0_8 ),
inference(trivial_equality_resolution,[status(esa)],[f277]) ).
fof(f279,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f280,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f268,f150]) ).
fof(f281,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f282,plain,
$false,
inference(sat_refutation,[status(thm)],[f271,f279,f281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:12:10 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.013906 seconds
% 0.14/0.53 % CPU time: 0.014568 seconds
% 0.14/0.53 % Memory used: 3.055 MB
%------------------------------------------------------------------------------