%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET347+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 : n027.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 03:31:58 PM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 13 ~; 9 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI38,plain,
equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI38) ).
fof(thI38_negated,plain,
~ equal_set(sum(empty_set),empty_set),
inference(negate_conjecture,[status(cth)],[thI38]) ).
cnf(29,plain,
~ equal_set(sum(empty_set),empty_set),
inference(cnf,[status(esa)],[thI38_negated]) ).
cnf(l0,plain,
~ equal_set(sum(empty_set),empty_set),
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(sum(empty_set),empty_set)
| ~ subset(empty_set,sum(empty_set))
| equal_set(sum(empty_set),empty_set) ),
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(empty_set,sum(empty_set))
| member(sK1(empty_set,sum(empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l2,plain,
( subset(sum(empty_set),empty_set)
| member(sK1(sum(empty_set),empty_set),sum(empty_set)) ),
inference(instantiation,[status(thm)],[1]) ).
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(l31,plain,
~ member(sK1(empty_set,sum(empty_set)),empty_set),
inference(instantiation,[status(thm)],[14]) ).
fof(sum,plain,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
file('Axioms/SET006+0.ax',sum) ).
cnf(23,plain,
( ~ member(X0,sum(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf,[status(esa)],[sum]) ).
cnf(l20,plain,
( ~ member(sK1(sum(empty_set),empty_set),sum(empty_set))
| member(sK2(sK1(sum(empty_set),empty_set),empty_set),empty_set) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(l34,plain,
~ member(sK2(sK1(sum(empty_set),empty_set),empty_set),empty_set),
inference(instantiation,[status(thm)],[14]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l31,l20,l34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET347+4 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n027.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 21:00:34 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.14/0.35 % launching worker at depth: 11
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------