%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET382-6 : 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 : n022.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 05:07:48 PM UTC 2026
% Result : Unsatisfiable 6.77s 4.81s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 43 ( 18 unt; 6 nHn; 26 RR)
% Number of literals : 75 ( 9 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 78 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
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_corollary_1_to_relation_property2_1,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_relation_property2_1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_corollary_1_to_relation_property2_2,negated_conjecture,
restrict(x,universal_class,universal_class) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_relation_property2_2) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(c_0_11,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_12,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
prove_corollary_1_to_relation_property2_1 ).
cnf(c_0_13,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_14,negated_conjecture,
( member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_16,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_17,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,negated_conjecture,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X1,cross_product(universal_class,universal_class)),x) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( subclass(X1,intersection(X2,X3))
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_22,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_23,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
subclass(intersection(x,X1),cross_product(universal_class,universal_class)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( subclass(intersection(X1,X2),intersection(X3,X1))
| ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_27,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,intersection(x,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_29,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_30,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( subclass(X1,intersection(X2,universal_class))
| ~ member(not_subclass_element(X1,intersection(X2,universal_class)),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( member(not_subclass_element(intersection(x,X1),X2),cross_product(universal_class,universal_class))
| subclass(intersection(x,X1),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_33,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30])]) ).
cnf(c_0_34,plain,
subclass(X1,intersection(X1,universal_class)),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_35,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_36,negated_conjecture,
subclass(intersection(x,X1),intersection(x,cross_product(universal_class,universal_class))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
intersection(X1,universal_class) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
restrict(x,universal_class,universal_class) != x,
prove_corollary_1_to_relation_property2_2 ).
cnf(c_0_39,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_40,negated_conjecture,
subclass(x,intersection(x,cross_product(universal_class,universal_class))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
intersection(x,cross_product(universal_class,universal_class)) != x,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_40]),c_0_35])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET382-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n022.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:20:51 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 6.77/4.81 % Version : CSE_E---1.7
% 6.77/4.81 % Problem : theBenchmark.p
% 6.77/4.81 % SZS status Unsatisfiable for theBenchmark.p
% 6.77/4.81 % SZS output start CNFRefutation
% See solution above
% 6.77/4.83 % Total time : 3.423s
%------------------------------------------------------------------------------