%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET762+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 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 03:32:37 PM UTC 2025
% Result : Theorem 27.37s 3.78s
% Output : CNFRefutation 27.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 9 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 24 ( 1 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIIa12,plain,
! [F,A,B] :
( maps(F,A,B)
=> equal_set(image2(F,empty_set),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa12) ).
fof(thIIa12_negated,plain,
~ ! [F,A,B] :
( maps(F,A,B)
=> equal_set(image2(F,empty_set),empty_set) ),
inference(negate_conjecture,[status(cth)],[thIIa12]) ).
cnf(137,plain,
~ equal_set(image2(sK51,empty_set),empty_set),
inference(cnf,[status(esa)],[thIIa12_negated]) ).
cnf(l0,plain,
~ equal_set(image2(sK51,empty_set),empty_set),
inference(instantiation,[status(thm)],[137]) ).
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(image2(sK51,empty_set),empty_set)
| ~ subset(empty_set,image2(sK51,empty_set))
| equal_set(image2(sK51,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(l2,plain,
( subset(empty_set,image2(sK51,empty_set))
| member(sK1(empty_set,image2(sK51,empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l160,plain,
( subset(image2(sK51,empty_set),empty_set)
| member(sK1(image2(sK51,empty_set),empty_set),image2(sK51,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(l12,plain,
~ member(sK1(empty_set,image2(sK51,empty_set)),empty_set),
inference(instantiation,[status(thm)],[14]) ).
fof(image2,plain,
! [F,A,Y] :
( member(Y,image2(F,A))
<=> ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
file('Axioms/SET006+1.ax',image2) ).
cnf(90,plain,
( ~ member(X0,image2(X1,X2))
| member(sK31(X1,X2,X0),X2) ),
inference(cnf,[status(esa)],[image2]) ).
cnf(l163,plain,
( ~ member(sK1(image2(sK51,empty_set),empty_set),image2(sK51,empty_set))
| member(sK31(sK51,empty_set,sK1(image2(sK51,empty_set),empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[90]) ).
cnf(l175,plain,
~ member(sK31(sK51,empty_set,sK1(image2(sK51,empty_set),empty_set)),empty_set),
inference(instantiation,[status(thm)],[14]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l160,l12,l163,l175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET762+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n023.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 22:36:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 6
% 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: 8
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.17/0.40 % launching worker at depth: 11
% 27.37/3.78 % SZS status Theorem for theBenchmark
% 27.37/3.78 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------