%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET025-3 : 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 : n019.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 08:55:59 AM UTC 2026
% Result : Unsatisfiable 120.94s 126.29s
% Output : Proof 120.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 20 ( 8 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X,Y)),
file('SET003-0.ax',non_ordered_pair4) ).
cnf(ordered_pair,axiom,
ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
file('SET003-0.ax',ordered_pair) ).
cnf(prove_ordered_pairs_are_small,negated_conjecture,
~ little_set(ordered_pair(a,b)),
file('theBenchmark.p',prove_ordered_pairs_are_small) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_58,axiom,
( little_set(Eq_y_0)
| ~ little_set(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ little_set(ordered_pair(a,b)),
inference(start,[status(thm),parent(0:0)],[prove_ordered_pairs_are_small]) ).
cnf(t2,plain,
( ~ little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)))
| non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)) != ordered_pair(a,b)
| little_set(ordered_pair(a,b)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_58]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ordered_pair(a,b) != non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))
| non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)) = ordered_pair(a,b) ),
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,
ordered_pair(a,b) = non_ordered_pair(singleton_set(a),non_ordered_pair(a,b)),
inference(extension,[status(thm),parent(t4:2)],[ordered_pair]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))),
inference(extension,[status(thm),parent(t2:3)],[non_ordered_pair4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET025-3 : 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
% 0.08/5.36 % Computer : n019.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 19 21:28:27 UTC 2026
% 0.08/5.36 % CPUTime :
% 120.94/126.29 % SZS status Unsatisfiable for theBenchmark
% 120.94/126.29 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------