%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET242-6 : 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 : n001.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 08:56:38 AM UTC 2026
% Result : Unsatisfiable 97.65s 97.94s
% Output : Proof 97.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 17
% Syntax : Number of clauses : 64 ( 43 unt; 3 nHn; 58 RR)
% Number of literals : 101 ( 22 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X,universal_class),
file('SET004-0.ax',class_elements_are_sets) ).
cnf(equal_implies_subclass2,axiom,
( subclass(Y,X)
| X != Y ),
file('SET004-0.ax',equal_implies_subclass2) ).
cnf(subclass_implies_equal,axiom,
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('SET004-0.ax',subclass_implies_equal) ).
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(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(restriction2,axiom,
intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('SET004-0.ax',restriction2) ).
cnf(prove_restriction_alternate_defn5_1,negated_conjecture,
member(z,xr),
file('theBenchmark.p',prove_restriction_alternate_defn5_1) ).
cnf(prove_restriction_alternate_defn5_2,negated_conjecture,
member(z,cross_product(x,y)),
file('theBenchmark.p',prove_restriction_alternate_defn5_2) ).
cnf(prove_restriction_alternate_defn5_3,negated_conjecture,
~ member(z,restrict(xr,x,y)),
file('theBenchmark.p',prove_restriction_alternate_defn5_3) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_12,axiom,
( complement(Eq_x_0) = complement(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,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(z,restrict(xr,x,y)),
inference(start,[status(thm),parent(0:0)],[prove_restriction_alternate_defn5_3]) ).
cnf(t2,plain,
( member(z,complement(restrict(xr,x,y)))
| ~ member(z,universal_class)
| member(z,restrict(xr,x,y)) ),
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,
( universal_class != universal_class
| ~ member(ordered_pair(first(z),second(z)),universal_class)
| ordered_pair(first(z),second(z)) != z
| member(z,universal_class) ),
inference(extension,[status(thm),parent(t2:2)],[equality_39]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(z,cross_product(x,y))
| ordered_pair(first(z),second(z)) = z ),
inference(extension,[status(thm),parent(t4:2)],[cartesian_product4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
member(z,cross_product(x,y)),
inference(extension,[status(thm),parent(t6:2)],[prove_restriction_alternate_defn5_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( member(ordered_pair(first(z),second(z)),complement(universal_class))
| ~ member(ordered_pair(first(z),second(z)),universal_class)
| member(ordered_pair(first(z),second(z)),universal_class) ),
inference(extension,[status(thm),parent(t4:3)],[complement2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
( universal_class != universal_class
| ~ member(unordered_pair(singleton(first(z)),unordered_pair(first(z),singleton(second(z)))),universal_class)
| unordered_pair(singleton(first(z)),unordered_pair(first(z),singleton(second(z)))) != ordered_pair(first(z),second(z))
| member(ordered_pair(first(z),second(z)),universal_class) ),
inference(extension,[status(thm),parent(t10:2)],[equality_39]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
unordered_pair(singleton(first(z)),unordered_pair(first(z),singleton(second(z)))) = ordered_pair(first(z),second(z)),
inference(extension,[status(thm),parent(t12:2)],[ordered_pair]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
member(unordered_pair(singleton(first(z)),unordered_pair(first(z),singleton(second(z)))),universal_class),
inference(extension,[status(thm),parent(t12:3)],[unordered_pairs_in_universal]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
universal_class = universal_class,
inference(extension,[status(thm),parent(t12:4)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
( member(ordered_pair(first(z),second(z)),universal_class)
| ~ subclass(complement(universal_class),universal_class)
| ~ member(ordered_pair(first(z),second(z)),complement(universal_class)) ),
inference(extension,[status(thm),parent(t10:3)],[subclass_members]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t10:3]) ).
cnf(t22,plain,
subclass(complement(universal_class),universal_class),
inference(extension,[status(thm),parent(t20:2)],[class_elements_are_sets]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
$false,
inference(reduction,[status(thm),parent(t20:3)],[t20:3,t4:3]) ).
cnf(t25,plain,
( ~ subclass(universal_class,universal_class)
| ~ subclass(universal_class,universal_class)
| universal_class = universal_class ),
inference(extension,[status(thm),parent(t4:4)],[subclass_implies_equal]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t4:4]) ).
cnf(t27,plain,
subclass(universal_class,universal_class),
inference(extension,[status(thm),parent(t25:2)],[class_elements_are_sets]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(l14,lemma,
subclass(universal_class,universal_class),
inference(lemma,[status(cth),parent(t25:2),below(t4:4)],[t25:2]) ).
cnf(t29,plain,
subclass(universal_class,universal_class),
inference(lemma_extension,[status(thm),parent(t25:3)],[l14:1]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t25:3]) ).
cnf(t31,plain,
( member(z,complement(intersection(cross_product(x,y),xr)))
| ~ subclass(complement(restrict(xr,x,y)),complement(intersection(cross_product(x,y),xr)))
| ~ member(z,complement(restrict(xr,x,y))) ),
inference(extension,[status(thm),parent(t2:3)],[subclass_members]) ).
cnf(t32,plain,
$false,
inference(connection,[status(thm),parent(t31:1)],[t31:1,t2:3]) ).
cnf(t33,plain,
( complement(intersection(cross_product(x,y),xr)) != complement(restrict(xr,x,y))
| subclass(complement(restrict(xr,x,y)),complement(intersection(cross_product(x,y),xr))) ),
inference(extension,[status(thm),parent(t31:2)],[equal_implies_subclass2]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t31:2]) ).
cnf(t35,plain,
( intersection(cross_product(x,y),xr) != restrict(xr,x,y)
| complement(intersection(cross_product(x,y),xr)) = complement(restrict(xr,x,y)) ),
inference(extension,[status(thm),parent(t33:2)],[equality_12]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
intersection(cross_product(x,y),xr) = restrict(xr,x,y),
inference(extension,[status(thm),parent(t35:2)],[restriction2]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t35:2]) ).
cnf(t39,plain,
( ~ member(z,intersection(cross_product(x,y),xr))
| ~ member(z,complement(intersection(cross_product(x,y),xr))) ),
inference(extension,[status(thm),parent(t31:3)],[complement1]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t31:3]) ).
cnf(t41,plain,
( ~ member(z,xr)
| ~ member(z,cross_product(x,y))
| member(z,intersection(cross_product(x,y),xr)) ),
inference(extension,[status(thm),parent(t39:2)],[intersection3]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(t43,plain,
member(z,cross_product(x,y)),
inference(extension,[status(thm),parent(t41:2)],[prove_restriction_alternate_defn5_2]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t41:2]) ).
cnf(t45,plain,
member(z,xr),
inference(extension,[status(thm),parent(t41:3)],[prove_restriction_alternate_defn5_1]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t41:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET242-6 : 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
% 0.07/0.36 % Computer : n001.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 22:05:55 UTC 2026
% 0.07/0.36 % CPUTime :
% 97.65/97.94 % SZS status Unsatisfiable for theBenchmark
% 97.65/97.94 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------