%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:56:12 AM UTC 2026
% Result : Unsatisfiable 82.15s 82.41s
% Output : Proof 82.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 20 RR)
% Number of literals : 31 ( 20 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X),
file('theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(left_cancellation,axiom,
( Y = Z
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| unordered_pair(X,Y) != unordered_pair(X,Z) ),
file('theBenchmark.p',left_cancellation) ).
cnf(prove_right_cancellation_1,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('theBenchmark.p',prove_right_cancellation_1) ).
cnf(prove_right_cancellation_2,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_right_cancellation_2) ).
cnf(prove_right_cancellation_3,negated_conjecture,
x != y,
file('theBenchmark.p',prove_right_cancellation_3) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
x != y,
inference(start,[status(thm),parent(0:0)],[prove_right_cancellation_3]) ).
cnf(t2,plain,
( ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| unordered_pair(z,x) != unordered_pair(z,y)
| x = y ),
inference(extension,[status(thm),parent(t1:1)],[left_cancellation]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( unordered_pair(x,z) != unordered_pair(z,y)
| unordered_pair(z,x) != unordered_pair(x,z)
| unordered_pair(z,x) = unordered_pair(z,y) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
unordered_pair(z,x) = unordered_pair(x,z),
inference(extension,[status(thm),parent(t4:2)],[commutativity_of_unordered_pair]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( unordered_pair(y,z) != unordered_pair(z,y)
| unordered_pair(x,z) != unordered_pair(y,z)
| unordered_pair(x,z) = unordered_pair(z,y) ),
inference(extension,[status(thm),parent(t4:3)],[equality_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(extension,[status(thm),parent(t8:2)],[prove_right_cancellation_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
unordered_pair(y,z) = unordered_pair(z,y),
inference(extension,[status(thm),parent(t8:3)],[commutativity_of_unordered_pair]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(extension,[status(thm),parent(t2:3)],[prove_right_cancellation_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 21:38:01 UTC 2026
% 0.07/0.35 % CPUTime :
% 82.15/82.41 % SZS status Unsatisfiable for theBenchmark
% 82.15/82.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------