%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 : Unsatisfiable 4.02s 16.33s
% Output : Proof 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 4 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 41 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 46 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( set_equal(X,Y)
| element(f(X,Y),Y)
| element(f(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
! [X,Y] :
( set_equal(X,Y)
| element(f(X,Y),Y)
| element(f(X,Y),X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( set_equal(X,Y)
| element(f(X,Y),Y)
| element(f(X,Y),X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( set_equal(X0,X1)
| element(f(X0,X1),X1)
| element(f(X0,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f0,axiom,
( element(Z,Y)
| ~ element(Z,X)
| ~ set_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitution1) ).
fof(f0_nnf,plain,
! [X,Y,Z] :
( element(Z,Y)
| ~ element(Z,X)
| ~ set_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] :
( element(Z,Y)
| ~ element(Z,X)
| ~ set_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( element(X2,X1)
| ~ element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f4,negated_conjecture,
( set_equal(b,a)
| set_equal(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry1) ).
fof(f4_nnf,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p6,plain,
( set_equal(a,b)
| element(X0,a)
| ~ element(X0,b) ),
inference(resolution,[status(thm)],[c0,c4]) ).
cnf(p10,plain,
( set_equal(a,b)
| element(f(X0,b),a)
| set_equal(X0,b)
| element(f(X0,b),X0) ),
inference(resolution,[status(thm)],[c2,p6]) ).
cnf(p14,plain,
( set_equal(a,b)
| set_equal(a,b)
| element(f(a,b),a) ),
inference(factoring,[status(thm)],[p10]) ).
cnf(p17,plain,
( set_equal(a,b)
| element(f(a,b),a) ),
inference(factoring,[status(thm)],[p14]) ).
cnf(f1,axiom,
( element(Z,X)
| ~ element(Z,Y)
| ~ set_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitution2) ).
fof(f1_nnf,plain,
! [X,Y,Z] :
( element(Z,X)
| ~ element(Z,Y)
| ~ set_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] :
( element(Z,X)
| ~ element(Z,Y)
| ~ set_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( element(X2,X0)
| ~ element(X2,X1)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p7,plain,
( set_equal(a,b)
| element(X0,b)
| ~ element(X0,a) ),
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(p18,plain,
( set_equal(a,b)
| element(f(a,b),b)
| set_equal(a,b) ),
inference(resolution,[status(thm)],[p17,p7]) ).
cnf(p19,plain,
( element(f(a,b),b)
| set_equal(a,b) ),
inference(factoring,[status(thm)],[p18]) ).
cnf(f3,axiom,
( set_equal(X,Y)
| ~ element(f(X,Y),X)
| ~ element(f(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
! [X,Y] :
( set_equal(X,Y)
| ~ element(f(X,Y),X)
| ~ element(f(X,Y),Y) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( set_equal(X,Y)
| ~ element(f(X,Y),X)
| ~ element(f(X,Y),Y) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( set_equal(X0,X1)
| ~ element(f(X0,X1),X0)
| ~ element(f(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p20,plain,
( set_equal(a,b)
| ~ element(f(a,b),a)
| set_equal(a,b) ),
inference(resolution,[status(thm)],[p19,c3]) ).
cnf(p23,plain,
( ~ element(f(a,b),a)
| set_equal(a,b) ),
inference(factoring,[status(thm)],[p20]) ).
cnf(p24,plain,
( set_equal(a,b)
| set_equal(a,b) ),
inference(resolution,[status(thm)],[p23,p17]) ).
cnf(p25,plain,
set_equal(a,b),
inference(factoring,[status(thm)],[p24]) ).
cnf(p26,plain,
( element(X0,b)
| ~ element(X0,a) ),
inference(resolution,[status(thm)],[p25,c0]) ).
cnf(p30,plain,
( set_equal(X0,a)
| element(f(X0,a),X0)
| element(f(X0,a),b) ),
inference(resolution,[status(thm)],[p26,c2]) ).
cnf(p36,plain,
( set_equal(b,a)
| element(f(b,a),b) ),
inference(factoring,[status(thm)],[p30]) ).
cnf(p27,plain,
( element(X0,a)
| ~ element(X0,b) ),
inference(resolution,[status(thm)],[p25,c1]) ).
cnf(p37,plain,
( element(f(b,a),a)
| set_equal(b,a) ),
inference(resolution,[status(thm)],[p36,p27]) ).
cnf(p38,plain,
( set_equal(b,a)
| ~ element(f(b,a),b)
| set_equal(b,a) ),
inference(resolution,[status(thm)],[p37,c3]) ).
cnf(p39,plain,
( ~ element(f(b,a),b)
| set_equal(b,a) ),
inference(factoring,[status(thm)],[p38]) ).
cnf(p40,plain,
( set_equal(b,a)
| set_equal(b,a) ),
inference(resolution,[status(thm)],[p39,p36]) ).
cnf(p41,plain,
set_equal(b,a),
inference(factoring,[status(thm)],[p40]) ).
cnf(f5,negated_conjecture,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry2) ).
fof(f5_nnf,plain,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p42,plain,
~ set_equal(a,b),
inference(resolution,[status(thm)],[p41,c5]) ).
cnf(p43,plain,
$false,
inference(resolution,[status(thm)],[p42,p25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.60 % CPULimit : 300
% 0.07/15.60 % WCLimit : 300
% 0.07/15.60 % DateTime : Thu Sep 24 09:26:49 UTC 2026
% 0.07/15.60 % CPUTime :
% 0.07/15.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.02/16.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/16.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------