%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:41:43 PM UTC 2026
% Result : Theorem 3.30s 1.08s
% Output : Proof 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 4 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 97 ( 32 ~; 49 |; 12 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X,Y] :
( set_equal(X,Y)
<=> ! [Z] :
( element(Z,X)
<=> element(Z,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43_1) ).
fof(f0_nnf,plain,
! [X,Y] :
( ( ? [Z] :
( ( element(Z,Y)
& ~ element(Z,X) )
| ( ~ element(Z,Y)
& element(Z,X) ) )
| set_equal(X,Y) )
& ( ! [Z] :
( ( ~ element(Z,Y)
| element(Z,X) )
& ( element(Z,Y)
| ~ element(Z,X) ) )
| ~ set_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] :
( ( ( element(sk0(X,Y),Y)
& ~ element(sk0(X,Y),X) )
| ( ~ element(sk0(X,Y),Y)
& element(sk0(X,Y),X) )
| set_equal(X,Y) )
& ( ( ( ~ element(Z,Y)
| element(Z,X) )
& ( element(Z,Y)
| ~ element(Z,X) ) )
| ~ set_equal(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c4,plain,
( ~ element(sk0(X0,X1),X0)
| ~ element(sk0(X0,X1),X1)
| set_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
( element(sk0(X0,X1),X1)
| element(sk0(X0,X1),X0)
| set_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( element(X2,X1)
| ~ element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,conjecture,
! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel43) ).
fof(f1_neg,negated_conjecture,
~ ! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
? [X,Y] :
( ( set_equal(Y,X)
& ~ set_equal(X,Y) )
| ( ~ set_equal(Y,X)
& set_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
( ( set_equal(sk2,sk1)
& ~ set_equal(sk1,sk2) )
| ( ~ set_equal(sk2,sk1)
& set_equal(sk1,sk2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f1_nnf]) ).
cnf(c7,plain,
( set_equal(sk2,sk1)
| set_equal(sk1,sk2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p10,plain,
( set_equal(sk1,sk2)
| element(X0,sk1)
| ~ element(X0,sk2) ),
inference(resolution,[status(thm)],[c0,c7]) ).
cnf(p14,plain,
( set_equal(sk1,sk2)
| element(sk0(X0,sk2),sk1)
| element(sk0(X0,sk2),X0)
| set_equal(X0,sk2) ),
inference(resolution,[status(thm)],[c3,p10]) ).
cnf(p19,plain,
( set_equal(sk1,sk2)
| element(sk0(sk1,sk2),sk1)
| set_equal(sk1,sk2) ),
inference(factoring,[status(thm)],[p14]) ).
cnf(p20,plain,
( element(sk0(sk1,sk2),sk1)
| set_equal(sk1,sk2) ),
inference(factoring,[status(thm)],[p19]) ).
cnf(c1,plain,
( ~ element(X2,X1)
| element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( set_equal(sk1,sk2)
| ~ element(X0,sk1)
| element(X0,sk2) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(p21,plain,
( set_equal(sk1,sk2)
| element(sk0(sk1,sk2),sk2)
| set_equal(sk1,sk2) ),
inference(resolution,[status(thm)],[p20,p11]) ).
cnf(p22,plain,
( element(sk0(sk1,sk2),sk2)
| set_equal(sk1,sk2) ),
inference(factoring,[status(thm)],[p21]) ).
cnf(p31,plain,
( set_equal(sk1,sk2)
| ~ element(sk0(sk1,sk2),sk1)
| set_equal(sk1,sk2) ),
inference(resolution,[status(thm)],[c4,p22]) ).
cnf(p32,plain,
( ~ element(sk0(sk1,sk2),sk1)
| set_equal(sk1,sk2) ),
inference(factoring,[status(thm)],[p31]) ).
cnf(p33,plain,
( set_equal(sk1,sk2)
| set_equal(sk1,sk2) ),
inference(resolution,[status(thm)],[p32,p20]) ).
cnf(p34,plain,
set_equal(sk1,sk2),
inference(factoring,[status(thm)],[p33]) ).
cnf(p35,plain,
( element(X0,sk2)
| ~ element(X0,sk1) ),
inference(resolution,[status(thm)],[p34,c0]) ).
cnf(p38,plain,
( element(sk0(X0,sk1),X0)
| set_equal(X0,sk1)
| element(sk0(X0,sk1),sk2) ),
inference(resolution,[status(thm)],[p35,c3]) ).
cnf(p43,plain,
( set_equal(sk2,sk1)
| element(sk0(sk2,sk1),sk2) ),
inference(factoring,[status(thm)],[p38]) ).
cnf(p36,plain,
( ~ element(X0,sk2)
| element(X0,sk1) ),
inference(resolution,[status(thm)],[p34,c1]) ).
cnf(p44,plain,
( element(sk0(sk2,sk1),sk1)
| set_equal(sk2,sk1) ),
inference(resolution,[status(thm)],[p43,p36]) ).
cnf(p45,plain,
( ~ element(sk0(sk2,sk1),sk2)
| set_equal(sk2,sk1)
| set_equal(sk2,sk1) ),
inference(resolution,[status(thm)],[p44,c4]) ).
cnf(p46,plain,
( ~ element(sk0(sk2,sk1),sk2)
| set_equal(sk2,sk1) ),
inference(factoring,[status(thm)],[p45]) ).
cnf(p47,plain,
( set_equal(sk2,sk1)
| set_equal(sk2,sk1) ),
inference(resolution,[status(thm)],[p46,p43]) ).
cnf(p48,plain,
set_equal(sk2,sk1),
inference(factoring,[status(thm)],[p47]) ).
cnf(c8,plain,
( ~ set_equal(sk1,sk2)
| ~ set_equal(sk2,sk1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p49,plain,
~ set_equal(sk1,sk2),
inference(resolution,[status(thm)],[p48,c8]) ).
cnf(p50,plain,
$false,
inference(resolution,[status(thm)],[p49,p34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:26:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.30/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------