%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET630+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 : n031.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 21.89s 3.12s
% Output : CNFRefutation 21.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 22 unt; 0 def)
% Number of atoms : 43 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 10 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_symmetric_difference_disjoint,plain,
! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(prove_intersection_and_symmetric_difference_disjoint_negated,plain,
~ ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(negate_conjecture,[status(cth)],[prove_intersection_and_symmetric_difference_disjoint]) ).
cnf(23,plain,
~ disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(cnf,[status(esa)],[prove_intersection_and_symmetric_difference_disjoint_negated]) ).
cnf(l0,plain,
~ disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(instantiation,[status(thm)],[23]) ).
fof(disjoint_defn,plain,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
cnf(12,plain,
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf,[status(esa)],[disjoint_defn]) ).
cnf(l1,plain,
( disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5))
| intersect(intersection(sK4,sK5),symmetric_difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[12]) ).
fof(intersect_with_union,plain,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,C)
| intersect(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_with_union) ).
cnf(1,plain,
( ~ intersect(X0,union(X1,X2))
| intersect(X0,X1)
| intersect(X0,X2) ),
inference(cnf,[status(esa)],[intersect_with_union]) ).
cnf(l80,plain,
( ~ intersect(intersection(sK5,sK4),union(difference(sK4,sK5),difference(sK5,sK4)))
| intersect(intersection(sK5,sK4),difference(sK4,sK5))
| intersect(intersection(sK5,sK4),difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
fof(commutativity_of_symmetric_difference,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
cnf(15,plain,
symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_symmetric_difference]) ).
cnf(l4,plain,
symmetric_difference(sK4,sK5) = symmetric_difference(sK5,sK4),
inference(instantiation,[status(thm)],[15]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(14,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l112,plain,
intersection(sK5,sK4) = intersection(sK4,sK5),
inference(instantiation,[status(thm)],[14]) ).
cnf(11,plain,
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf,[status(esa)],[disjoint_defn]) ).
cnf(l124,plain,
( ~ disjoint(intersection(sK4,sK5),difference(sK4,sK5))
| ~ intersect(intersection(sK4,sK5),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l380,plain,
( ~ disjoint(intersection(sK5,sK4),difference(sK5,sK4))
| ~ intersect(intersection(sK5,sK4),difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[11]) ).
fof(intersection_and_union_disjoint,plain,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
cnf(4,plain,
disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf,[status(esa)],[intersection_and_union_disjoint]) ).
cnf(l126,plain,
disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(instantiation,[status(thm)],[4]) ).
fof(symmetric_difference_defn,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
cnf(0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf,[status(esa)],[symmetric_difference_defn]) ).
cnf(l11,plain,
symmetric_difference(sK5,sK4) = union(difference(sK5,sK4),difference(sK4,sK5)),
inference(instantiation,[status(thm)],[0]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(13,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l18,plain,
union(difference(sK4,sK5),difference(sK5,sK4)) = union(difference(sK5,sK4),difference(sK4,sK5)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l79,plain,
intersection(sK5,sK4) = intersection(sK4,sK5),
inference(instantiation,[status(thm)],[14]) ).
cnf(l381,plain,
disjoint(intersection(sK5,sK4),difference(sK5,sK4)),
inference(instantiation,[status(thm)],[4]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l80,l4,l112,l124,l380,l126,l11,l18,l79,l381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET630+3 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 22:10:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.36 % launching worker at depth: 11
% 0.19/0.47 % launching worker at depth: 12
% 21.89/3.12 % SZS status Theorem for theBenchmark
% 21.89/3.12 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------