%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET108-6 : 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 : n026.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 08:56:21 AM UTC 2026
% Result : Unsatisfiable 94.46s 94.70s
% Output : Proof 94.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of clauses : 55 ( 36 unt; 2 nHn; 51 RR)
% Number of literals : 88 ( 33 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X,Y),universal_class),
file('SET004-0.ax',unordered_pairs_in_universal) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('SET004-0.ax',ordered_pair) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('SET004-0.ax',cartesian_product4) ).
cnf(intersection2,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('SET004-0.ax',intersection2) ).
cnf(intersection3,axiom,
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('SET004-0.ax',intersection3) ).
cnf(complement1,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('SET004-0.ax',complement1) ).
cnf(complement2,axiom,
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('SET004-0.ax',complement2) ).
cnf(prove_existence_of_1st_and_2nd_1_1,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
cnf(prove_existence_of_1st_and_2nd_1_2,negated_conjecture,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_8,axiom,
( cross_product(Eq_x_0,Eq_x_1) = cross_product(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( intersection(Eq_x_0,Eq_x_1) = intersection(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( complement(Eq_x_0) = complement(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,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(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(start,[status(thm),parent(0:0)],[prove_existence_of_1st_and_2nd_1_2]) ).
cnf(t2,plain,
( member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),complement(cross_product(universal_class,universal_class)))
| ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),universal_class)
| member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)) ),
inference(extension,[status(thm),parent(t1:1)],[complement2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),intersection(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),universal_class) ),
inference(extension,[status(thm),parent(t2:2)],[intersection2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( intersection(universal_class,universal_class) != intersection(universal_class,universal_class)
| ~ member(unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))),intersection(universal_class,universal_class))
| unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))) != ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z)))
| member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),intersection(universal_class,universal_class)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_35]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))) = ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),
inference(extension,[status(thm),parent(t6:2)],[ordered_pair]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ member(unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))),universal_class)
| ~ member(unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))),universal_class)
| member(unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))),intersection(universal_class,universal_class)) ),
inference(extension,[status(thm),parent(t6:3)],[intersection3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
member(unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))),universal_class),
inference(extension,[status(thm),parent(t10:2)],[unordered_pairs_in_universal]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
member(unordered_pair(singleton(first(ordered_pair(y,z))),unordered_pair(first(ordered_pair(y,z)),singleton(second(ordered_pair(y,z))))),universal_class),
inference(extension,[status(thm),parent(t10:3)],[unordered_pairs_in_universal]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( universal_class != universal_class
| universal_class != universal_class
| intersection(universal_class,universal_class) = intersection(universal_class,universal_class) ),
inference(extension,[status(thm),parent(t6:4)],[equality_11]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:4]) ).
cnf(t18,plain,
universal_class = universal_class,
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(l9,lemma,
universal_class = universal_class,
inference(lemma,[status(cth),parent(t16:2),below(t6:4)],[t16:2]) ).
cnf(t20,plain,
universal_class = universal_class,
inference(lemma_extension,[status(thm),parent(t16:3)],[l9:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( complement(cross_product(universal_class,universal_class)) != complement(cross_product(universal_class,universal_class))
| member(ordered_pair(y,z),complement(cross_product(universal_class,universal_class)))
| ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) != ordered_pair(y,z)
| ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),complement(cross_product(universal_class,universal_class))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_35]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
cnf(t24,plain,
( ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) = ordered_pair(y,z) ),
inference(extension,[status(thm),parent(t22:2)],[cartesian_product4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(extension,[status(thm),parent(t24:2)],[prove_existence_of_1st_and_2nd_1_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| ~ member(ordered_pair(y,z),complement(cross_product(universal_class,universal_class))) ),
inference(extension,[status(thm),parent(t22:3)],[complement1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t22:3]) ).
cnf(t30,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(extension,[status(thm),parent(t28:2)],[prove_existence_of_1st_and_2nd_1_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( cross_product(universal_class,universal_class) != cross_product(universal_class,universal_class)
| complement(cross_product(universal_class,universal_class)) = complement(cross_product(universal_class,universal_class)) ),
inference(extension,[status(thm),parent(t22:4)],[equality_12]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t22:4]) ).
cnf(t34,plain,
( universal_class != universal_class
| universal_class != universal_class
| cross_product(universal_class,universal_class) = cross_product(universal_class,universal_class) ),
inference(extension,[status(thm),parent(t32:2)],[equality_8]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
universal_class = universal_class,
inference(extension,[status(thm),parent(t34:2)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(l17,lemma,
universal_class = universal_class,
inference(lemma,[status(cth),parent(t34:2),below(t32:2)],[t34:2]) ).
cnf(t38,plain,
universal_class = universal_class,
inference(lemma_extension,[status(thm),parent(t34:3)],[l17:1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 21:47:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 94.46/94.70 % SZS status Unsatisfiable for theBenchmark
% 94.46/94.70 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------