%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET595+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 : n022.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 03:32:18 PM UTC 2025
% Result : Theorem 4.81s 0.99s
% Output : CNFRefutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 72 ( 12 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 70 ( 28 ~; 33 |; 1 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th54,plain,
! [B,C] :
( subset(B,C)
=> C = union(B,difference(C,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th54) ).
fof(prove_th54_negated,plain,
~ ! [B,C] :
( subset(B,C)
=> C = union(B,difference(C,B)) ),
inference(negate_conjecture,[status(cth)],[prove_th54]) ).
cnf(23,plain,
sK5 != union(sK4,difference(sK5,sK4)),
inference(cnf,[status(esa)],[prove_th54_negated]) ).
cnf(l0,plain,
sK5 != union(sK4,difference(sK5,sK4)),
inference(instantiation,[status(thm)],[23]) ).
fof(member_equal,plain,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_equal) ).
cnf(0,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[member_equal]) ).
cnf(l1,plain,
( sK5 = union(sK4,difference(sK5,sK4))
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5)
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4))) ),
inference(instantiation,[status(thm)],[0]) ).
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(2,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l3,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4)))
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK4)
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
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(8,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l14,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK4)
| ~ subset(sK4,sK5)
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5) ),
inference(instantiation,[status(thm)],[8]) ).
fof(difference_defn,plain,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
cnf(7,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l2,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5)
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK4)
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(22,plain,
subset(sK4,sK5),
inference(cnf,[status(esa)],[prove_th54_negated]) ).
cnf(l15,plain,
subset(sK4,sK5),
inference(instantiation,[status(thm)],[22]) ).
cnf(5,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l7,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),difference(sK5,sK4))
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(1,plain,
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[member_equal]) ).
cnf(l10,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5)
| ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4)))
| sK5 = union(sK4,difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(4,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l24,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),difference(sK5,sK4))
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l17,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5)
| ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4)))
| sK5 = union(sK4,difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l33,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5)
| ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4)))
| sK5 = union(sK4,difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(3,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l21,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK4)
| member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l22,plain,
( ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),sK5)
| ~ member(sK1(sK5,union(sK4,difference(sK5,sK4))),union(sK4,difference(sK5,sK4)))
| sK5 = union(sK4,difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l14,l2,l15,l7,l10,l24,l17,l33,l21,l22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET595+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n022.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 22:04:49 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.14/0.41 % launching worker at depth: 11
% 4.81/0.99 % SZS status Theorem for theBenchmark
% 4.81/0.99 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------