%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET009+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 03:31:03 PM UTC 2025
% Result : Theorem 2.43s 0.66s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 49 ( 23 ~; 20 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_difference,plain,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_difference) ).
fof(prove_subset_difference_negated,plain,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
inference(negate_conjecture,[status(cth)],[prove_subset_difference]) ).
cnf(7,plain,
subset(sK2,sK3),
inference(cnf,[status(esa)],[prove_subset_difference_negated]) ).
cnf(l0,plain,
subset(sK2,sK3),
inference(instantiation,[status(thm)],[7]) ).
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(3,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l1,plain,
( ~ subset(sK2,sK3)
| ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK2)
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK3) ),
inference(instantiation,[status(thm)],[3]) ).
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(2,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l2,plain,
( ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK4)
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK2)
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK2)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l3,plain,
( ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK3)
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK3))
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK3,difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(5,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l50,plain,
( ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK2))
| subset(difference(sK4,sK3),difference(sK4,sK2)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(0,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l7,plain,
( ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK3))
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK4) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(4,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l16,plain,
( subset(difference(sK4,sK3),difference(sK4,sK2))
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(1,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l8,plain,
( ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),sK3)
| ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(8,plain,
~ subset(difference(sK4,sK3),difference(sK4,sK2)),
inference(cnf,[status(esa)],[prove_subset_difference_negated]) ).
cnf(l21,plain,
~ subset(difference(sK4,sK3),difference(sK4,sK2)),
inference(instantiation,[status(thm)],[8]) ).
cnf(l5,plain,
( ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK3))
| ~ member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK3,difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l33,plain,
( subset(difference(sK4,sK3),difference(sK4,sK2))
| member(sK1(difference(sK4,sK3),difference(sK4,sK2)),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l35,plain,
~ subset(difference(sK4,sK3),difference(sK4,sK2)),
inference(instantiation,[status(thm)],[8]) ).
cnf(l51,plain,
~ subset(difference(sK4,sK3),difference(sK4,sK2)),
inference(instantiation,[status(thm)],[8]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l50,l7,l16,l8,l21,l5,l33,l35,l51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET009+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 19:12:34 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: 5
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 4
% 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
% 0.12/0.34 % launching worker at depth: 11
% 0.12/0.38 % launching worker at depth: 12
% 2.43/0.66 % SZS status Theorem for theBenchmark
% 2.43/0.66 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------