%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 08:56:04 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 51 ( 30 unt; 10 nHn; 50 RR)
% Number of literals : 86 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 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 : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(element_substitution1,axiom,
( element(Z,Y)
| ~ element(Z,X)
| ~ set_equal(X,Y) ),
file('theBenchmark.p',element_substitution1) ).
cnf(element_substitution2,axiom,
( element(Z,X)
| ~ element(Z,Y)
| ~ set_equal(X,Y) ),
file('theBenchmark.p',element_substitution2) ).
cnf(clause_3,axiom,
( set_equal(X,Y)
| element(f(X,Y),Y)
| element(f(X,Y),X) ),
file('theBenchmark.p',clause_3) ).
cnf(clause_4,axiom,
( set_equal(X,Y)
| ~ element(f(X,Y),X)
| ~ element(f(X,Y),Y) ),
file('theBenchmark.p',clause_4) ).
cnf(prove_symmetry1,negated_conjecture,
( set_equal(b,a)
| set_equal(a,b) ),
file('theBenchmark.p',prove_symmetry1) ).
cnf(prove_symmetry2,negated_conjecture,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
file('theBenchmark.p',prove_symmetry2) ).
cnf(t1,plain,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
inference(start,[status(thm),parent(0:0)],[prove_symmetry2]) ).
cnf(t2,plain,
( ~ element(f(b,a),b)
| ~ element(f(b,a),a)
| set_equal(b,a) ),
inference(extension,[status(thm),parent(t1:1)],[clause_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( set_equal(b,a)
| element(f(b,a),b)
| element(f(b,a),a) ),
inference(extension,[status(thm),parent(t2:2)],[clause_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( element(f(b,a),a)
| ~ set_equal(a,b)
| ~ element(f(b,a),b) ),
inference(extension,[status(thm),parent(t4:2)],[element_substitution2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(extension,[status(thm),parent(t6:2)],[prove_symmetry1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
$false,
inference(reduction,[status(thm),parent(t6:3)],[t6:3,t2:2]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t4:3)],[t4:3,t1:1]) ).
cnf(t13,plain,
( element(f(b,a),a)
| set_equal(b,a)
| element(f(b,a),b) ),
inference(extension,[status(thm),parent(t2:3)],[clause_3]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t2:3]) ).
cnf(t15,plain,
$false,
inference(reduction,[status(thm),parent(t13:2)],[t13:2,t1:1]) ).
cnf(l9,lemma,
~ set_equal(b,a),
inference(lemma,[status(cth),parent(t13:2),below(t2:3)],[t13:2]) ).
cnf(t16,plain,
( element(f(b,a),b)
| ~ set_equal(a,b)
| ~ element(f(b,a),a) ),
inference(extension,[status(thm),parent(t13:3)],[element_substitution1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t13:3]) ).
cnf(t18,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(extension,[status(thm),parent(t16:2)],[prove_symmetry1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
~ set_equal(b,a),
inference(lemma_extension,[status(thm),parent(t18:2)],[l9:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
$false,
inference(reduction,[status(thm),parent(t16:3)],[t16:3,t2:3]) ).
cnf(t23,plain,
( ~ element(f(a,b),a)
| ~ element(f(a,b),b)
| set_equal(a,b) ),
inference(extension,[status(thm),parent(t1:2)],[clause_4]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t1:2]) ).
cnf(t25,plain,
( set_equal(a,b)
| element(f(a,b),a)
| element(f(a,b),b) ),
inference(extension,[status(thm),parent(t23:2)],[clause_3]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
( element(f(a,b),b)
| ~ set_equal(b,a)
| ~ element(f(a,b),a) ),
inference(extension,[status(thm),parent(t25:2)],[element_substitution2]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(t29,plain,
( set_equal(a,b)
| set_equal(b,a) ),
inference(extension,[status(thm),parent(t27:2)],[prove_symmetry1]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t27:2]) ).
cnf(t31,plain,
$false,
inference(reduction,[status(thm),parent(t29:2)],[t29:2,t1:2]) ).
cnf(t32,plain,
$false,
inference(reduction,[status(thm),parent(t27:3)],[t27:3,t23:2]) ).
cnf(t33,plain,
$false,
inference(reduction,[status(thm),parent(t25:3)],[t25:3,t1:2]) ).
cnf(t34,plain,
( element(f(a,b),b)
| set_equal(a,b)
| element(f(a,b),a) ),
inference(extension,[status(thm),parent(t23:3)],[clause_3]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t23:3]) ).
cnf(t36,plain,
$false,
inference(reduction,[status(thm),parent(t34:2)],[t34:2,t1:2]) ).
cnf(l21,lemma,
~ set_equal(a,b),
inference(lemma,[status(cth),parent(t34:2),below(t23:3)],[t34:2]) ).
cnf(t37,plain,
( element(f(a,b),a)
| ~ set_equal(b,a)
| ~ element(f(a,b),b) ),
inference(extension,[status(thm),parent(t34:3)],[element_substitution1]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t34:3]) ).
cnf(t39,plain,
( set_equal(a,b)
| set_equal(b,a) ),
inference(extension,[status(thm),parent(t37:2)],[prove_symmetry1]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t37:2]) ).
cnf(t41,plain,
~ set_equal(a,b),
inference(lemma_extension,[status(thm),parent(t39:2)],[l21:1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
$false,
inference(reduction,[status(thm),parent(t37:3)],[t37:3,t23:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 21:35:27 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------