%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET162+4 : 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 : n018.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 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 45 ( 0 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 ( 3 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(thI18,plain,
! [A] : equal_set(union(A,empty_set),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI18) ).
fof(thI18_negated,plain,
~ ! [A] : equal_set(union(A,empty_set),A),
inference(negate_conjecture,[status(cth)],[thI18]) ).
cnf(29,plain,
~ equal_set(union(sK5,empty_set),sK5),
inference(cnf,[status(esa)],[thI18_negated]) ).
cnf(l0,plain,
~ equal_set(union(sK5,empty_set),sK5),
inference(instantiation,[status(thm)],[29]) ).
fof(equal_set,plain,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('Axioms/SET006+0.ax',equal_set) ).
cnf(5,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf,[status(esa)],[equal_set]) ).
cnf(l1,plain,
( ~ subset(union(sK5,empty_set),sK5)
| ~ subset(sK5,union(sK5,empty_set))
| equal_set(union(sK5,empty_set),sK5) ),
inference(instantiation,[status(thm)],[5]) ).
fof(subset,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('Axioms/SET006+0.ax',subset) ).
cnf(1,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset]) ).
cnf(l3,plain,
( subset(sK5,union(sK5,empty_set))
| member(sK1(sK5,union(sK5,empty_set)),sK5) ),
inference(instantiation,[status(thm)],[1]) ).
fof(union,plain,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('Axioms/SET006+0.ax',union) ).
cnf(12,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union]) ).
cnf(l32,plain,
( ~ member(sK1(sK5,union(sK5,empty_set)),sK5)
| member(sK1(sK5,union(sK5,empty_set)),union(sK5,empty_set)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l2,plain,
( subset(union(sK5,empty_set),sK5)
| member(sK1(union(sK5,empty_set),sK5),union(sK5,empty_set)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(2,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset]) ).
cnf(l39,plain,
( ~ member(sK1(sK5,union(sK5,empty_set)),union(sK5,empty_set))
| subset(sK5,union(sK5,empty_set)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(11,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf,[status(esa)],[union]) ).
cnf(l20,plain,
( ~ member(sK1(union(sK5,empty_set),sK5),union(sK5,empty_set))
| member(sK1(union(sK5,empty_set),sK5),sK5)
| member(sK1(union(sK5,empty_set),sK5),empty_set) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l21,plain,
( ~ member(sK1(union(sK5,empty_set),sK5),sK5)
| subset(union(sK5,empty_set),sK5) ),
inference(instantiation,[status(thm)],[2]) ).
fof(empty_set,plain,
! [X] : ~ member(X,empty_set),
file('Axioms/SET006+0.ax',empty_set) ).
cnf(14,plain,
~ member(X0,empty_set),
inference(cnf,[status(esa)],[empty_set]) ).
cnf(l22,plain,
~ member(sK1(union(sK5,empty_set),sK5),empty_set),
inference(instantiation,[status(thm)],[14]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l32,l2,l39,l20,l21,l22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET162+4 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.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 20:14:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.34 % launching worker at depth: 11
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------