%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET098-7 : 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 : 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 05:07:18 PM UTC 2026
% Result : Unsatisfiable 1.92s 1.91s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 14 unt; 6 nHn; 14 RR)
% Number of literals : 33 ( 17 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_1_to_number_of_elements_in_class_1,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_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(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(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(prove_corollary_1_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_1_to_number_of_elements_in_class_2) ).
cnf(prove_corollary_1_to_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_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(c_0_8,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
prove_corollary_1_to_number_of_elements_in_class_1 ).
cnf(c_0_9,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_10,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_11,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
null_class_is_unique ).
cnf(c_0_12,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_13,negated_conjecture,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( intersection(X1,X2) = null_class
| member(not_subclass_element(intersection(X1,X2),null_class),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
prove_corollary_1_to_number_of_elements_in_class_2 ).
cnf(c_0_16,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_12,c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_17,negated_conjecture,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_19,negated_conjecture,
x != null_class,
prove_corollary_1_to_number_of_elements_in_class_3 ).
cnf(c_0_20,axiom,
~ member(X1,null_class),
existence_of_null_class ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET098-7 : 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
% 0.16/0.33 % Computer : n022.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 02:10:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.92/1.91 % Version : CSE_E---1.7
% 1.92/1.91 % Problem : theBenchmark.p
% 1.92/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.92/1.91 % SZS output start CNFRefutation
% See solution above
% 1.92/1.92 % Total time : 1.372s
%------------------------------------------------------------------------------