%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET162+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 : n023.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 03:31:42 PM UTC 2025
% Result : Theorem 0.13s 0.32s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 45 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 17 ~; 17 |; 1 &)
% ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 2 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_union_empty_set,plain,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(prove_union_empty_set_negated,plain,
~ ! [B] : union(B,empty_set) = B,
inference(negate_conjecture,[status(cth)],[prove_union_empty_set]) ).
cnf(20,plain,
union(sK4,empty_set) != sK4,
inference(cnf,[status(esa)],[prove_union_empty_set_negated]) ).
cnf(l0,plain,
union(sK4,empty_set) != sK4,
inference(instantiation,[status(thm)],[20]) ).
fof(equal_defn,plain,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
cnf(6,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf,[status(esa)],[equal_defn]) ).
cnf(l1,plain,
( ~ subset(union(sK4,empty_set),sK4)
| ~ subset(sK4,union(sK4,empty_set))
| union(sK4,empty_set) = sK4 ),
inference(instantiation,[status(thm)],[6]) ).
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(10,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l3,plain,
( ~ member(sK1(sK4,union(sK4,empty_set)),union(sK4,empty_set))
| subset(sK4,union(sK4,empty_set)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(9,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l2,plain,
( subset(union(sK4,empty_set),sK4)
| member(sK1(union(sK4,empty_set),sK4),union(sK4,empty_set)) ),
inference(instantiation,[status(thm)],[9]) ).
fof(union_defn,plain,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
cnf(0,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l14,plain,
( ~ member(sK1(union(sK4,empty_set),sK4),union(sK4,empty_set))
| member(sK1(union(sK4,empty_set),sK4),sK4)
| member(sK1(union(sK4,empty_set),sK4),empty_set) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l18,plain,
( ~ member(sK1(union(sK4,empty_set),sK4),sK4)
| subset(union(sK4,empty_set),sK4) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l5,plain,
( ~ member(sK1(sK4,union(sK4,empty_set)),sK4)
| member(sK1(sK4,union(sK4,empty_set)),union(sK4,empty_set)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l10,plain,
( subset(sK4,union(sK4,empty_set))
| member(sK1(sK4,union(sK4,empty_set)),sK4) ),
inference(instantiation,[status(thm)],[9]) ).
fof(empty_set_defn,plain,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
cnf(3,plain,
~ member(X0,empty_set),
inference(cnf,[status(esa)],[empty_set_defn]) ).
cnf(l26,plain,
~ member(sK1(union(sK4,empty_set),sK4),empty_set),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l14,l18,l5,l10,l26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET162+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.29 % Computer : n023.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 21 20:14:19 EDT 2025
% 0.08/0.29 % CPUTime :
% 0.13/0.29 % launching worker at depth: 2
% 0.13/0.29 % launching worker at depth: 3
% 0.13/0.29 % launching worker at depth: 4
% 0.13/0.29 % launching worker at depth: 1
% 0.13/0.29 % launching worker at depth: 5
% 0.13/0.29 % launching worker at depth: 6
% 0.13/0.29 % launching worker at depth: 7
% 0.13/0.30 % launching worker at depth: 8
% 0.13/0.30 % launching worker at depth: 9
% 0.13/0.30 % launching worker at depth: 10
% 0.13/0.30 % launching worker at depth: 11
% 0.13/0.32 % SZS status Theorem for theBenchmark
% 0.13/0.32 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------