%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET099-7 : 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 : n027.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 05:07:18 PM UTC 2026
% Result : Unsatisfiable 8.42s 5.99s
% Output : CNFRefutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 48 ( 23 unt; 8 nHn; 32 RR)
% Number of literals : 83 ( 25 equ; 32 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 : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_2_to_number_of_elements_in_class_1,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(null_class_is_unique,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
cnf(corollary_1_to_unordered_pair,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
cnf(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(number_of_elements_in_class,axiom,
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
| singleton(not_subclass_element(X1,null_class)) = X1
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_of_elements_in_class) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(prove_corollary_2_to_number_of_elements_in_class_2,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
cnf(prove_corollary_2_to_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
cnf(existence_of_null_class,axiom,
~ member(X1,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
cnf(singleton_in_unordered_pair1,axiom,
subclass(singleton(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(c_0_15,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
prove_corollary_2_to_number_of_elements_in_class_1 ).
cnf(c_0_16,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_17,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_18,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
null_class_is_unique ).
cnf(c_0_19,negated_conjecture,
not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_1_to_unordered_pair ).
cnf(c_0_21,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_17,c_0_16]),c_0_16]) ).
cnf(c_0_22,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_23,axiom,
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
| singleton(not_subclass_element(X1,null_class)) = X1
| X1 = null_class ),
number_of_elements_in_class ).
cnf(c_0_24,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_25,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
| member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
prove_corollary_2_to_number_of_elements_in_class_2 ).
cnf(c_0_27,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_29,plain,
( X1 = null_class
| unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)) = X1
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
| member(not_subclass_element(x,null_class),x) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_32,negated_conjecture,
x != null_class,
prove_corollary_2_to_number_of_elements_in_class_3 ).
cnf(c_0_33,axiom,
~ member(X1,null_class),
existence_of_null_class ).
cnf(c_0_34,axiom,
subclass(singleton(X1),unordered_pair(X1,X2)),
singleton_in_unordered_pair1 ).
cnf(c_0_35,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X2,X3)
| ~ member(X1,X4) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
member(not_subclass_element(x,null_class),x),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_37,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_38,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_39,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_40,negated_conjecture,
( member(X1,unordered_pair(X1,not_subclass_element(x,null_class)))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)) = X1
| X1 = null_class
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1),null_class),complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)))) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_42,plain,
( member(X1,unordered_pair(X2,X3))
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_44,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_45,negated_conjecture,
member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_19]),c_0_31]),c_0_32]) ).
cnf(c_0_46,negated_conjecture,
member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),X1)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET099-7 : 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
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:11:05 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 8.42/5.99 % Version : CSE_E---1.7
% 8.42/5.99 % Problem : theBenchmark.p
% 8.42/5.99 % SZS status Unsatisfiable for theBenchmark.p
% 8.42/5.99 % SZS output start CNFRefutation
% See solution above
% 8.42/6.02 % Total time : 4.373s
%------------------------------------------------------------------------------