%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET008+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 : n018.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 03:31:03 PM UTC 2025
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 39 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 12 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_difference_empty_set,plain,
! [B,C] : intersection(difference(B,C),C) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(prove_intersection_difference_empty_set_negated,plain,
~ ! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(negate_conjecture,[status(cth)],[prove_intersection_difference_empty_set]) ).
cnf(23,plain,
intersection(difference(sK4,sK5),sK5) != empty_set,
inference(cnf,[status(esa)],[prove_intersection_difference_empty_set_negated]) ).
cnf(l0,plain,
intersection(difference(sK4,sK5),sK5) != empty_set,
inference(instantiation,[status(thm)],[23]) ).
fof(equal_member_defn,plain,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
cnf(19,plain,
( member(sK3(X0,X1),X0)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l1,plain,
( member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),intersection(difference(sK4,sK5),sK5))
| intersection(difference(sK4,sK5),sK5) = empty_set
| sP0(empty_set,intersection(difference(sK4,sK5),sK5)) ),
inference(instantiation,[status(thm)],[19]) ).
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(l2,plain,
( ~ member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),intersection(difference(sK4,sK5),sK5))
| member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(22,plain,
( member(sK3(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l3,plain,
( member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),empty_set)
| ~ sP0(empty_set,intersection(difference(sK4,sK5),sK5)) ),
inference(instantiation,[status(thm)],[22]) ).
fof(empty_set_defn,plain,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
cnf(6,plain,
~ member(X0,empty_set),
inference(cnf,[status(esa)],[empty_set_defn]) ).
cnf(l5,plain,
~ member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),empty_set),
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(4,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l8,plain,
( ~ member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),sK5)
| ~ member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(1,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l11,plain,
( ~ member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),intersection(difference(sK4,sK5),sK5))
| member(sK3(intersection(difference(sK4,sK5),sK5),empty_set),sK5) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l5,l8,l11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET008+3 : TPTP v9.0.0. Released v2.2.0.
% 0.06/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Jul 21 19:11:49 EDT 2025
% 0.13/0.32 % CPUTime :
% 0.13/0.32 % launching worker at depth: 2
% 0.13/0.32 % launching worker at depth: 7
% 0.13/0.32 % launching worker at depth: 6
% 0.13/0.32 % launching worker at depth: 3
% 0.13/0.32 % launching worker at depth: 4
% 0.13/0.32 % launching worker at depth: 8
% 0.13/0.32 % launching worker at depth: 1
% 0.13/0.32 % launching worker at depth: 5
% 0.13/0.32 % launching worker at depth: 9
% 0.13/0.33 % launching worker at depth: 10
% 0.13/0.34 % launching worker at depth: 11
% 0.13/0.36 % SZS status Theorem for theBenchmark
% 0.13/0.36 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------