%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET586+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.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 15.13s 2.24s
% Output : CNFRefutation 15.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 63 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 24 ~; 23 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_of_subset,plain,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_of_subset) ).
fof(prove_intersection_of_subset_negated,plain,
~ ! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
inference(negate_conjecture,[status(cth)],[prove_intersection_of_subset]) ).
cnf(14,plain,
subset(sK3,sK4),
inference(cnf,[status(esa)],[prove_intersection_of_subset_negated]) ).
cnf(l0,plain,
subset(sK3,sK4),
inference(instantiation,[status(thm)],[14]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
cnf(3,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l1,plain,
( ~ subset(sK3,sK4)
| ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),sK3)
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l3,plain,
( ~ subset(intersection(sK3,sK5),sK3)
| ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK3,sK5))
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(4,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l5,plain,
( subset(intersection(sK3,sK5),sK3)
| member(sK1(intersection(sK3,sK5),sK3),intersection(sK3,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(intersection_defn,plain,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
cnf(0,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l49,plain,
( ~ member(sK1(intersection(sK3,sK5),sK3),intersection(sK3,sK5))
| member(sK1(intersection(sK3,sK5),sK3),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(2,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l138,plain,
( ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),sK5)
| ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),sK4)
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK5,sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l139,plain,
( ~ subset(intersection(sK5,sK4),intersection(sK4,sK5))
| ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK5,sK4))
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l130,plain,
( subset(intersection(sK3,sK5),intersection(sK4,sK5))
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK3,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(5,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l150,plain,
( ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK4,sK5))
| subset(intersection(sK3,sK5),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l56,plain,
( ~ member(sK1(intersection(sK3,sK5),sK3),sK3)
| subset(intersection(sK3,sK5),sK3) ),
inference(instantiation,[status(thm)],[5]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(6,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l175,plain,
intersection(sK5,sK4) = intersection(sK4,sK5),
inference(instantiation,[status(thm)],[6]) ).
fof(reflexivity_of_subset,plain,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
cnf(7,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_of_subset]) ).
cnf(l176,plain,
subset(intersection(sK5,sK4),intersection(sK5,sK4)),
inference(instantiation,[status(thm)],[7]) ).
cnf(1,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l187,plain,
( ~ member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK3,sK5))
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),sK5) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(15,plain,
~ subset(intersection(sK3,sK5),intersection(sK4,sK5)),
inference(cnf,[status(esa)],[prove_intersection_of_subset_negated]) ).
cnf(l131,plain,
~ subset(intersection(sK3,sK5),intersection(sK4,sK5)),
inference(instantiation,[status(thm)],[15]) ).
cnf(l166,plain,
~ subset(intersection(sK3,sK5),intersection(sK4,sK5)),
inference(instantiation,[status(thm)],[15]) ).
cnf(l190,plain,
( subset(intersection(sK3,sK5),intersection(sK4,sK5))
| member(sK1(intersection(sK3,sK5),intersection(sK4,sK5)),intersection(sK3,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l198,plain,
~ subset(intersection(sK3,sK5),intersection(sK4,sK5)),
inference(instantiation,[status(thm)],[15]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l5,l49,l138,l139,l130,l150,l56,l175,l176,l187,l131,l166,l190,l198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET586+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.31 % Computer : n024.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Jul 21 22:03:19 EDT 2025
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % launching worker at depth: 4
% 0.12/0.32 % launching worker at depth: 1
% 0.12/0.32 % launching worker at depth: 2
% 0.12/0.32 % launching worker at depth: 5
% 0.12/0.32 % launching worker at depth: 3
% 0.12/0.32 % launching worker at depth: 7
% 0.12/0.32 % launching worker at depth: 6
% 0.12/0.32 % launching worker at depth: 8
% 0.12/0.32 % launching worker at depth: 9
% 0.12/0.32 % launching worker at depth: 10
% 0.17/0.36 % launching worker at depth: 11
% 3.23/0.74 % launching worker at depth: 12
% 15.13/2.24 % SZS status Theorem for theBenchmark
% 15.13/2.24 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------