%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n015.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 08:56:35 AM UTC 2026
% Result : Unsatisfiable 6.65s 12.02s
% Output : Proof 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 10 unt; 0 nHn; 16 RR)
% Number of literals : 24 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cartesian_product1,axiom,
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('SET004-0.ax',cartesian_product1) ).
cnf(cartesian_product2,axiom,
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('SET004-0.ax',cartesian_product2) ).
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(prove_cross_product_property2_1,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('theBenchmark.p',prove_cross_product_property2_1) ).
cnf(prove_cross_product_property2_2,negated_conjecture,
~ member(ordered_pair(v,u),cross_product(y,x)),
file('theBenchmark.p',prove_cross_product_property2_2) ).
cnf(t1,plain,
~ member(ordered_pair(v,u),cross_product(y,x)),
inference(start,[status(thm),parent(0:0)],[prove_cross_product_property2_2]) ).
cnf(t2,plain,
( ~ member(u,x)
| ~ member(v,y)
| member(ordered_pair(v,u),cross_product(y,x)) ),
inference(extension,[status(thm),parent(t1:1)],[cartesian_product3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(ordered_pair(u,v),cross_product(x,y))
| member(v,y) ),
inference(extension,[status(thm),parent(t2:2)],[cartesian_product2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(extension,[status(thm),parent(t4:2)],[prove_cross_product_property2_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ member(ordered_pair(u,v),cross_product(x,y))
| member(u,x) ),
inference(extension,[status(thm),parent(t2:3)],[cartesian_product1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(extension,[status(thm),parent(t8:2)],[prove_cross_product_property2_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET204-6 : 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/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 : n015.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
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 19 22:00:10 UTC 2026
% 0.08/5.37 % CPUTime :
% 6.65/12.02 % SZS status Unsatisfiable for theBenchmark
% 6.65/12.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------