%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET143+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 : n026.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 03:31:39 PM UTC 2025
% Result : Theorem 221.51s 28.14s
% Output : CNFRefutation 221.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 9 unt; 0 def)
% Number of atoms : 88 ( 15 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 86 ( 39 ~; 39 |; 2 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 39 ( 2 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_associativity_of_intersection,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
fof(prove_associativity_of_intersection_negated,plain,
~ ! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(negate_conjecture,[status(cth)],[prove_associativity_of_intersection]) ).
cnf(17,plain,
intersection(intersection(sK3,sK4),sK5) != intersection(sK3,intersection(sK4,sK5)),
inference(cnf,[status(esa)],[prove_associativity_of_intersection_negated]) ).
cnf(l0,plain,
intersection(intersection(sK3,sK4),sK5) != intersection(sK3,intersection(sK4,sK5)),
inference(instantiation,[status(thm)],[17]) ).
fof(equal_defn,plain,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
cnf(5,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf,[status(esa)],[equal_defn]) ).
cnf(l1,plain,
( ~ subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5)))
| ~ subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5))
| intersection(intersection(sK3,sK4),sK5) = intersection(sK3,intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
cnf(8,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l3,plain,
( subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[8]) ).
fof(intersection_defn,plain,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
cnf(1,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l230,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l2,plain,
( subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5)))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(0,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l118,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l232,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK5) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(2,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l120,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5)))
| ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,intersection(sK4,sK5)),intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[2]) ).
fof(equal_member_defn,plain,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
cnf(12,plain,
( X0 != X1
| ~ member(X2,X1)
| member(X2,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l644,plain,
( intersection(intersection(sK3,intersection(sK4,sK5)),intersection(sK4,sK3)) != intersection(intersection(sK3,intersection(sK4,sK5)),intersection(sK3,sK4))
| ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,intersection(sK4,sK5)),intersection(sK3,sK4)))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,intersection(sK4,sK5)),intersection(sK4,sK3))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l866,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,intersection(sK4,sK5)),intersection(sK4,sK3)))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(9,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l867,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5)))
| subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l238,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK5)
| ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,sK4))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK5,intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l273,plain,
( intersection(intersection(sK3,sK4),sK5) != intersection(sK5,intersection(sK3,sK4))
| ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK5,intersection(sK3,sK4)))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[12]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(6,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l304,plain,
intersection(intersection(sK3,sK4),sK5) = intersection(sK5,intersection(sK3,sK4)),
inference(instantiation,[status(thm)],[6]) ).
cnf(l650,plain,
intersection(sK4,sK3) = intersection(sK3,sK4),
inference(instantiation,[status(thm)],[6]) ).
cnf(l394,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(intersection(sK3,sK4),sK5))
| subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l265,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3)
| ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4)
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l338,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l124,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK3)
| ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK4,sK5))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l266,plain,
( ~ member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5))
| member(sK1(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l125,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK4)
| ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5)
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l178,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK4) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l212,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l135,plain,
( ~ member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK1(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l230,l2,l118,l232,l120,l644,l866,l867,l238,l273,l304,l650,l394,l265,l338,l124,l266,l125,l178,l212,l135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET143+3 : TPTP v9.0.0. Released v2.2.0.
% 0.02/0.10 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Jul 21 20:09:19 EDT 2025
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % launching worker at depth: 1
% 0.10/0.30 % launching worker at depth: 2
% 0.10/0.30 % launching worker at depth: 3
% 0.10/0.30 % launching worker at depth: 4
% 0.10/0.30 % launching worker at depth: 5
% 0.10/0.30 % launching worker at depth: 6
% 0.10/0.30 % launching worker at depth: 7
% 0.10/0.30 % launching worker at depth: 8
% 0.10/0.30 % launching worker at depth: 9
% 0.10/0.30 % launching worker at depth: 10
% 0.15/0.32 % launching worker at depth: 11
% 3.32/0.71 % launching worker at depth: 12
% 221.51/28.14 % SZS status Theorem for theBenchmark
% 221.51/28.14 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------