%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET584+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 : 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 03:32:16 PM UTC 2025
% Result : Theorem 16.61s 2.43s
% Output : CNFRefutation 16.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 59 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 22 ~; 22 |; 0 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 38 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th33,plain,
! [B,C,D] :
( subset(B,C)
=> subset(union(B,D),union(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th33) ).
fof(prove_th33_negated,plain,
~ ! [B,C,D] :
( subset(B,C)
=> subset(union(B,D),union(C,D)) ),
inference(negate_conjecture,[status(cth)],[prove_th33]) ).
cnf(14,plain,
subset(sK3,sK4),
inference(cnf,[status(esa)],[prove_th33_negated]) ).
cnf(l0,plain,
subset(sK3,sK4),
inference(instantiation,[status(thm)],[14]) ).
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(3,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l1,plain,
( ~ subset(sK3,sK4)
| ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),sK3)
| member(sK1(union(sK3,sK5),union(sK4,sK5)),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
fof(union_defn,plain,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
cnf(1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l142,plain,
( ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),sK4)
| member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK4,sK5)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(0,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l3,plain,
( ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK5,sK3))
| member(sK1(union(sK3,sK5),union(sK4,sK5)),sK5)
| member(sK1(union(sK3,sK5),union(sK4,sK5)),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(5,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l147,plain,
( ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK4,sK5))
| subset(union(sK3,sK5),union(sK4,sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
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(9,plain,
( ~ member(X0,X1)
| X2 != X1
| member(X0,X2) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l5,plain,
( ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK3,sK5))
| union(sK5,sK3) != union(sK3,sK5)
| member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK5,sK3)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(4,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l23,plain,
( subset(union(sK3,sK5),union(sK4,sK5))
| member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK3,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(2,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l46,plain,
( ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),sK5)
| member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK4,sK5)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(15,plain,
~ subset(union(sK3,sK5),union(sK4,sK5)),
inference(cnf,[status(esa)],[prove_th33_negated]) ).
cnf(l157,plain,
~ subset(union(sK3,sK5),union(sK4,sK5)),
inference(instantiation,[status(thm)],[15]) ).
cnf(l38,plain,
~ subset(union(sK3,sK5),union(sK4,sK5)),
inference(instantiation,[status(thm)],[15]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(6,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l34,plain,
union(sK5,sK3) = union(sK3,sK5),
inference(instantiation,[status(thm)],[6]) ).
cnf(l67,plain,
( ~ member(sK1(union(sK3,sK5),union(sK4,sK5)),union(sK4,sK5))
| subset(union(sK3,sK5),union(sK4,sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l69,plain,
~ subset(union(sK3,sK5),union(sK4,sK5)),
inference(instantiation,[status(thm)],[15]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l142,l3,l147,l5,l23,l46,l157,l38,l34,l67,l69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET584+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n025.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 22:03:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.38 % launching worker at depth: 11
% 3.07/0.77 % launching worker at depth: 12
% 16.61/2.43 % SZS status Theorem for theBenchmark
% 16.61/2.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------