%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET629+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 : n025.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 03:32:25 PM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 47 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 15 |; 3 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_difference_disjoint,plain,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).
fof(prove_intersection_and_difference_disjoint_negated,plain,
~ ! [B,C] : disjoint(intersection(B,C),difference(B,C)),
inference(negate_conjecture,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
cnf(19,plain,
~ disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(cnf,[status(esa)],[prove_intersection_and_difference_disjoint_negated]) ).
cnf(l0,plain,
~ disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(instantiation,[status(thm)],[19]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(11,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l2,plain,
intersection(sK5,sK4) = intersection(sK4,sK5),
inference(instantiation,[status(thm)],[11]) ).
fof(disjoint_defn,plain,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
cnf(10,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf,[status(esa)],[disjoint_defn]) ).
cnf(l3,plain,
( intersect(intersection(sK5,sK4),difference(sK4,sK5))
| disjoint(intersection(sK5,sK4),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(intersect_defn,plain,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
cnf(6,plain,
( ~ intersect(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[intersect_defn]) ).
cnf(l5,plain,
( ~ intersect(intersection(sK5,sK4),difference(sK4,sK5))
| member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),intersection(sK5,sK4)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(difference_defn,plain,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
cnf(5,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l8,plain,
( ~ member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),intersection(sK5,sK4))
| member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),sK5)
| member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),difference(intersection(sK5,sK4),sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(4,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l12,plain,
( ~ member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),sK5)
| ~ member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(7,plain,
( ~ intersect(X0,X1)
| member(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[intersect_defn]) ).
cnf(l14,plain,
( ~ intersect(intersection(sK5,sK4),difference(sK4,sK5))
| member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l20,plain,
( ~ member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),sK5)
| ~ member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),difference(intersection(sK5,sK4),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(l21,plain,
( ~ member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),intersection(sK5,sK4))
| member(sK1(intersection(sK5,sK4),difference(sK4,sK5)),sK5) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l3,l5,l8,l12,l14,l20,l21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET629+3 : TPTP v9.0.0. Released v2.2.0.
% 0.13/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 22:09:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.20/0.34 % launching worker at depth: 2
% 0.20/0.34 % launching worker at depth: 3
% 0.20/0.34 % launching worker at depth: 4
% 0.20/0.34 % launching worker at depth: 5
% 0.20/0.34 % launching worker at depth: 6
% 0.20/0.34 % launching worker at depth: 7
% 0.20/0.34 % launching worker at depth: 8
% 0.20/0.34 % launching worker at depth: 9
% 0.20/0.34 % launching worker at depth: 10
% 0.20/0.34 % launching worker at depth: 11
% 0.20/0.37 % launching worker at depth: 12
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------