%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET581+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 : 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 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 50 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 19 ~; 14 |; 3 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th24,plain,
! [B,C,D] :
( ( member(B,C)
& member(B,D) )
=> not_equal(intersection(C,D),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th24) ).
fof(prove_th24_negated,plain,
~ ! [B,C,D] :
( ( member(B,C)
& member(B,D) )
=> not_equal(intersection(C,D),empty_set) ),
inference(negate_conjecture,[status(cth)],[prove_th24]) ).
cnf(15,plain,
member(sK3,sK4),
inference(cnf,[status(esa)],[prove_th24_negated]) ).
cnf(l0,plain,
member(sK3,sK4),
inference(instantiation,[status(thm)],[15]) ).
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(2,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l1,plain,
( ~ member(sK3,empty_set)
| ~ member(sK3,sK4)
| member(sK3,intersection(empty_set,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(4,plain,
( X0 != X1
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l3,plain,
( intersection(empty_set,sK4) != intersection(sK4,empty_set)
| ~ member(sK3,intersection(empty_set,sK4))
| member(sK3,intersection(sK4,empty_set)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(12,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l16,plain,
intersection(sK4,empty_set) = intersection(empty_set,sK4),
inference(instantiation,[status(thm)],[12]) ).
cnf(1,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l28,plain,
( ~ member(sK3,intersection(sK4,empty_set))
| member(sK3,empty_set) ),
inference(instantiation,[status(thm)],[1]) ).
fof(not_equal_defn,plain,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
cnf(11,plain,
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf,[status(esa)],[not_equal_defn]) ).
cnf(l7,plain,
( intersection(sK4,sK5) = empty_set
| not_equal(intersection(sK4,sK5),empty_set) ),
inference(instantiation,[status(thm)],[11]) ).
fof(empty_set_defn,plain,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
cnf(3,plain,
~ member(X0,empty_set),
inference(cnf,[status(esa)],[empty_set_defn]) ).
cnf(l31,plain,
~ member(sK3,empty_set),
inference(instantiation,[status(thm)],[3]) ).
cnf(17,plain,
~ not_equal(intersection(sK4,sK5),empty_set),
inference(cnf,[status(esa)],[prove_th24_negated]) ).
cnf(l23,plain,
~ not_equal(intersection(sK4,sK5),empty_set),
inference(instantiation,[status(thm)],[17]) ).
cnf(l4,plain,
( ~ member(sK3,sK4)
| ~ member(sK3,sK5)
| member(sK3,intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(16,plain,
member(sK3,sK5),
inference(cnf,[status(esa)],[prove_th24_negated]) ).
cnf(l33,plain,
member(sK3,sK5),
inference(instantiation,[status(thm)],[16]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l16,l28,l7,l31,l23,l4,l33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET581+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n024.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 22:02:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.13/0.37 % launching worker at depth: 11
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------