%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET021-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:54 PM UTC 2026
% Result : Unsatisfiable 16.82s 10.33s
% Output : CNFRefutation 16.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 15 unt; 0 nHn; 20 RR)
% Number of literals : 38 ( 21 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(corollary_2_to_cartesian_product,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets2_1,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_1) ).
cnf(ordered_pair_determines_components2,axiom,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| ~ member(X2,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets2_2,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
cnf(c_0_7,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_8,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_9,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_2_to_cartesian_product ).
cnf(c_0_10,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
prove_unique_1st_and_2nd_in_pair_of_sets2_1 ).
cnf(c_0_12,axiom,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| ~ member(X2,universal_class) ),
ordered_pair_determines_components2 ).
cnf(c_0_13,plain,
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(c_0_16,plain,
( X2 = X4
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) != unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))
| ~ member(X2,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10]),c_0_10]) ).
cnf(c_0_17,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(rw,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_19,negated_conjecture,
second(ordered_pair(u,v)) != v,
prove_unique_1st_and_2nd_in_pair_of_sets2_2 ).
cnf(c_0_20,negated_conjecture,
( v = X1
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(v,v))) != unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X1,X1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) != v,
inference(rw,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(v,v))) != unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET021-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:05:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 16.82/10.33 % Version : CSE_E---1.7
% 16.82/10.33 % Problem : theBenchmark.p
% 16.82/10.33 % SZS status Unsatisfiable for theBenchmark.p
% 16.82/10.33 % SZS output start CNFRefutation
% See solution above
% 16.82/10.39 % Total time : 7.383s
%------------------------------------------------------------------------------