%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET233-6 : 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 : n006.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 05:07:37 PM UTC 2026
% Result : Unsatisfiable 28.97s 17.60s
% Output : CNFRefutation 29.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 10 unt; 5 nHn; 12 RR)
% Number of literals : 33 ( 9 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 12 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(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(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(prove_cross_product_property8_2,negated_conjecture,
~ member(second(not_subclass_element(cross_product(x,y),z)),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property8_2) ).
cnf(prove_cross_product_property8_1,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property8_1) ).
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,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
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,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(c_0_12,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_9,c_0_10]) ).
cnf(c_0_13,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_14,plain,
( member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,plain,
( unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X1,X2),X3)),first(not_subclass_element(cross_product(X1,X2),X3))),unordered_pair(first(not_subclass_element(cross_product(X1,X2),X3)),unordered_pair(second(not_subclass_element(cross_product(X1,X2),X3)),second(not_subclass_element(cross_product(X1,X2),X3))))) = not_subclass_element(cross_product(X1,X2),X3)
| subclass(cross_product(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( member(second(not_subclass_element(cross_product(X1,X2),X3)),X4)
| subclass(cross_product(X1,X2),X3)
| ~ member(not_subclass_element(cross_product(X1,X2),X3),cross_product(X5,X4)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
~ member(second(not_subclass_element(cross_product(x,y),z)),y),
prove_cross_product_property8_2 ).
cnf(c_0_18,plain,
( member(second(not_subclass_element(cross_product(X1,X2),X3)),X2)
| subclass(cross_product(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
~ subclass(cross_product(x,y),z),
prove_cross_product_property8_1 ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET233-6 : 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
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:16:01 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 28.97/17.60 % Version : CSE_E---1.7
% 28.97/17.60 % Problem : theBenchmark.p
% 28.97/17.60 % SZS status Unsatisfiable for theBenchmark.p
% 28.97/17.60 % SZS output start CNFRefutation
% See solution above
% 29.07/17.72 % Total time : 12.392s
%------------------------------------------------------------------------------