%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET024-4 : 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 : n014.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 08:55:58 AM UTC 2026
% Result : Unsatisfiable 122.04s 122.31s
% Output : Proof 122.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 17 unt; 0 nHn; 21 RR)
% Number of literals : 37 ( 17 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(non_ordered_pair3,axiom,
( U != Y
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
file('SET003-0.ax',non_ordered_pair3) ).
cnf(singleton_set,axiom,
singleton_set(X) = non_ordered_pair(X,X),
file('SET003-0.ax',singleton_set) ).
cnf(a_little_set,hypothesis,
little_set(a),
file('theBenchmark.p',a_little_set) ).
cnf(prove_membership_of_singleton_set,negated_conjecture,
~ member(a,singleton_set(a)),
file('theBenchmark.p',prove_membership_of_singleton_set) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_57,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ member(a,singleton_set(a)),
inference(start,[status(thm),parent(0:0)],[prove_membership_of_singleton_set]) ).
cnf(t2,plain,
( non_ordered_pair(a,a) != singleton_set(a)
| ~ member(a,non_ordered_pair(a,a))
| a != a
| member(a,singleton_set(a)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_57]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( a != a
| a = a ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
a = a,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ little_set(a)
| a != a
| member(a,non_ordered_pair(a,a)) ),
inference(extension,[status(thm),parent(t2:3)],[non_ordered_pair3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
a = a,
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
little_set(a),
inference(extension,[status(thm),parent(t8:3)],[a_little_set]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( singleton_set(a) != non_ordered_pair(a,a)
| non_ordered_pair(a,a) = singleton_set(a) ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
singleton_set(a) = non_ordered_pair(a,a),
inference(extension,[status(thm),parent(t14:2)],[singleton_set]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET024-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_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
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 21:27:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 122.04/122.31 % SZS status Unsatisfiable for theBenchmark
% 122.04/122.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------