%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET599+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 03:32:19 PM UTC 2025
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 37 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 12 |; 0 &)
% ( 3 <=>; 1 =>; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th58,plain,
! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th58) ).
fof(prove_th58_negated,plain,
~ ! [B,C] : subset(difference(B,C),symmetric_difference(B,C)),
inference(negate_conjecture,[status(cth)],[prove_th58]) ).
cnf(17,plain,
~ subset(difference(sK3,sK4),symmetric_difference(sK3,sK4)),
inference(cnf,[status(esa)],[prove_th58_negated]) ).
cnf(l0,plain,
~ subset(difference(sK3,sK4),symmetric_difference(sK3,sK4)),
inference(instantiation,[status(thm)],[17]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
cnf(6,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l1,plain,
( member(sK1(difference(sK3,sK4),symmetric_difference(sK3,sK4)),difference(sK3,sK4))
| subset(difference(sK3,sK4),symmetric_difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(5,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l2,plain,
( ~ member(sK1(difference(sK3,sK4),symmetric_difference(sK3,sK4)),difference(sK3,sK4))
| ~ subset(difference(sK3,sK4),union(difference(sK3,sK4),difference(sK4,sK3)))
| member(sK1(difference(sK3,sK4),symmetric_difference(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[5]) ).
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(11,plain,
( X0 != X1
| ~ member(X2,X1)
| member(X2,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l4,plain,
( symmetric_difference(sK3,sK4) != union(difference(sK3,sK4),difference(sK4,sK3))
| ~ member(sK1(difference(sK3,sK4),symmetric_difference(sK3,sK4)),union(difference(sK3,sK4),difference(sK4,sK3)))
| member(sK1(difference(sK3,sK4),symmetric_difference(sK3,sK4)),symmetric_difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[11]) ).
fof(subset_of_union,plain,
! [B,C] : subset(B,union(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
cnf(1,plain,
subset(X0,union(X0,X1)),
inference(cnf,[status(esa)],[subset_of_union]) ).
cnf(l3,plain,
subset(difference(sK3,sK4),union(difference(sK3,sK4),difference(sK4,sK3))),
inference(instantiation,[status(thm)],[1]) ).
cnf(7,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l6,plain,
( ~ member(sK1(difference(sK3,sK4),symmetric_difference(sK3,sK4)),symmetric_difference(sK3,sK4))
| subset(difference(sK3,sK4),symmetric_difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[7]) ).
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(l7,plain,
symmetric_difference(sK3,sK4) = union(difference(sK3,sK4),difference(sK4,sK3)),
inference(instantiation,[status(thm)],[0]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l3,l6,l7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET599+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 22:05:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.14/0.35 % SZS status Theorem for theBenchmark
% 0.14/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------