%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET002+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 : 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 03:31:02 PM UTC 2025
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 18 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 4 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_idempotency_of_union,plain,
! [B] : union(B,B) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
fof(prove_idempotency_of_union_negated,plain,
~ ! [B] : union(B,B) = B,
inference(negate_conjecture,[status(cth)],[prove_idempotency_of_union]) ).
cnf(18,plain,
union(sK3,sK3) != sK3,
inference(cnf,[status(esa)],[prove_idempotency_of_union_negated]) ).
cnf(l0,plain,
union(sK3,sK3) != sK3,
inference(instantiation,[status(thm)],[18]) ).
fof(subset_union,plain,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
cnf(0,plain,
( ~ subset(X0,X1)
| union(X0,X1) = X1 ),
inference(cnf,[status(esa)],[subset_union]) ).
cnf(l1,plain,
( ~ subset(sK3,sK3)
| union(sK3,sK3) = sK3 ),
inference(instantiation,[status(thm)],[0]) ).
fof(equal_defn,plain,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
cnf(5,plain,
( X0 != X1
| subset(X1,X0) ),
inference(cnf,[status(esa)],[equal_defn]) ).
cnf(l2,plain,
( sK3 != sK3
| subset(sK3,sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET002+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 19:11:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % SZS status Theorem for theBenchmark
% 0.13/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------