%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET235-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 05:07:38 PM UTC 2026
% Result : Unsatisfiable 3.65s 3.18s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 14 unt; 2 nHn; 16 RR)
% Number of literals : 34 ( 9 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 29 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(prove_cross_product_property10_1,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_1) ).
cnf(prove_cross_product_property10_2,negated_conjecture,
~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_2) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(prove_cross_product_property10_3,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property10_3) ).
cnf(c_0_8,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_9,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_10,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(c_0_11,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_8,c_0_9]),c_0_9]) ).
cnf(c_0_12,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_13,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
prove_cross_product_property10_1 ).
cnf(c_0_14,negated_conjecture,
~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
prove_cross_product_property10_2 ).
cnf(c_0_15,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_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ member(unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))),x),
inference(rw,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ member(not_subclass_element(x,y),x),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_21,negated_conjecture,
~ subclass(x,y),
prove_cross_product_property10_3 ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET235-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:16:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.65/3.18 % Version : CSE_E---1.7
% 3.65/3.18 % Problem : theBenchmark.p
% 3.65/3.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.65/3.18 % SZS output start CNFRefutation
% See solution above
% 3.65/3.19 % Total time : 2.370s
%------------------------------------------------------------------------------