%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET065-7 : 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 : n011.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 08:56:10 AM UTC 2026
% Result : Unsatisfiable 31.46s 31.79s
% Output : Proof 31.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 15 unt; 0 nHn; 23 RR)
% Number of literals : 35 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cartesian_product3,axiom,
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('SET004-0.ax',cartesian_product3) ).
cnf(inductive1,axiom,
( member(null_class,X)
| ~ inductive(X) ),
file('SET004-0.ax',inductive1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('SET004-0.ax',omega_is_inductive1) ).
cnf(omega_in_universal,axiom,
member(omega,universal_class),
file('SET004-0.ax',omega_in_universal) ).
cnf(replacement,axiom,
( member(image(Xf,X),universal_class)
| ~ member(X,universal_class)
| ~ function(Xf) ),
file('SET004-0.ax',replacement) ).
cnf(choice1,axiom,
function(choice),
file('SET004-0.ax',choice1) ).
cnf(corollary_2_to_cartesian_product,axiom,
( member(V,universal_class)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(prove_null_class_is_a_set_1,negated_conjecture,
~ member(null_class,universal_class),
file('theBenchmark.p',prove_null_class_is_a_set_1) ).
cnf(t1,plain,
~ member(null_class,universal_class),
inference(start,[status(thm),parent(0:0)],[prove_null_class_is_a_set_1]) ).
cnf(t2,plain,
( ~ member(ordered_pair(image(choice,omega),null_class),cross_product(universal_class,omega))
| member(null_class,universal_class) ),
inference(extension,[status(thm),parent(t1:1)],[corollary_2_to_cartesian_product]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(null_class,omega)
| ~ member(image(choice,omega),universal_class)
| member(ordered_pair(image(choice,omega),null_class),cross_product(universal_class,omega)) ),
inference(extension,[status(thm),parent(t2:2)],[cartesian_product3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(omega,universal_class)
| ~ function(choice)
| member(image(choice,omega),universal_class) ),
inference(extension,[status(thm),parent(t4:2)],[replacement]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
function(choice),
inference(extension,[status(thm),parent(t6:2)],[choice1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
member(omega,universal_class),
inference(extension,[status(thm),parent(t6:3)],[omega_in_universal]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( ~ inductive(omega)
| member(null_class,omega) ),
inference(extension,[status(thm),parent(t4:3)],[inductive1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
inductive(omega),
inference(extension,[status(thm),parent(t12:2)],[omega_is_inductive1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 21:36:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 31.46/31.79 % SZS status Unsatisfiable for theBenchmark
% 31.46/31.79 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------