%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET585+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.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 : Fri Jul 25 03:32:16 PM UTC 2025
% Result : Theorem 0.20s 0.35s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 4 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 20 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_subset_of_union,plain,
! [B,C,D] : subset(intersection(B,C),union(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_subset_of_union) ).
fof(prove_intersection_subset_of_union_negated,plain,
~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
inference(negate_conjecture,[status(cth)],[prove_intersection_subset_of_union]) ).
cnf(21,plain,
~ subset(intersection(sK3,sK4),union(sK3,sK5)),
inference(cnf,[status(esa)],[prove_intersection_subset_of_union_negated]) ).
cnf(l0,plain,
~ subset(intersection(sK3,sK4),union(sK3,sK5)),
inference(instantiation,[status(thm)],[21]) ).
fof(transitivity_of_subset,plain,
! [B,C,D] :
( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subset) ).
cnf(0,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(cnf,[status(esa)],[transitivity_of_subset]) ).
cnf(l1,plain,
( ~ subset(intersection(sK3,sK4),sK3)
| ~ subset(sK3,union(sK3,sK5))
| subset(intersection(sK3,sK4),union(sK3,sK5)) ),
inference(instantiation,[status(thm)],[0]) ).
fof(subset_of_union,plain,
! [B,C] : subset(B,union(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
cnf(1,plain,
subset(X0,union(X0,X1)),
inference(cnf,[status(esa)],[subset_of_union]) ).
cnf(l3,plain,
subset(sK3,union(sK3,sK5)),
inference(instantiation,[status(thm)],[1]) ).
fof(intersection_is_subset,plain,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
cnf(2,plain,
subset(intersection(X0,X1),X0),
inference(cnf,[status(esa)],[intersection_is_subset]) ).
cnf(l2,plain,
subset(intersection(sK3,sK4),sK3),
inference(instantiation,[status(thm)],[2]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET585+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 22:03:19 EDT 2025
% 0.20/0.34 % CPUTime :
% 0.20/0.35 % launching worker at depth: 1
% 0.20/0.35 % launching worker at depth: 6
% 0.20/0.35 % launching worker at depth: 5
% 0.20/0.35 % launching worker at depth: 4
% 0.20/0.35 % launching worker at depth: 7
% 0.20/0.35 % launching worker at depth: 2
% 0.20/0.35 % launching worker at depth: 3
% 0.20/0.35 % launching worker at depth: 8
% 0.20/0.35 % launching worker at depth: 9
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------