%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET585+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:43:30 PM UTC 2026
% Result : Theorem 3.02s 0.84s
% Output : Proof 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 15 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 7 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 5 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subset) ).
fof(f0_nnf,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f2,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f2_nnf,plain,
! [B,C] : subset(intersection(B,C),B),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] : subset(intersection(B,C),B),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p23,plain,
( subset(intersection(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[c0,c2]) ).
fof(f1,axiom,
! [B,C] : subset(B,union(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(f1_nnf,plain,
! [B,C] : subset(B,union(B,C)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] : subset(B,union(B,C)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
subset(X0,union(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p52,plain,
subset(intersection(X0,X1),union(X0,X2)),
inference(resolution,[status(thm)],[p23,c1]) ).
fof(f10,conjecture,
! [B,C,D] : subset(intersection(B,C),union(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_subset_of_union) ).
fof(f10_neg,negated_conjecture,
~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [B,C,D] : ~ subset(intersection(B,C),union(B,D)),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
~ subset(intersection(sk2,sk3),union(sk2,sk4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f10_nnf]) ).
cnf(c21,plain,
~ subset(intersection(sk2,sk3),union(sk2,sk4)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p62,plain,
$false,
inference(resolution,[status(thm)],[p52,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET585+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.41 % Computer : n003.cluster.edu
% 0.07/0.41 % Model : x86_64 x86_64
% 0.07/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.41 % Memory : 8046.5625MB
% 0.07/0.41 % OS : Linux 6.8.0-71-generic
% 0.07/0.41 % CPULimit : 300
% 0.07/0.41 % WCLimit : 300
% 0.07/0.41 % DateTime : Thu Sep 24 11:23:08 UTC 2026
% 0.07/0.41 % CPUTime :
% 0.07/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.02/0.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.02/0.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------