%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET097-6 : 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 : 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 05:07:17 PM UTC 2026
% Result : Unsatisfiable 23.86s 14.86s
% Output : CNFRefutation 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 86 ( 33 unt; 24 nHn; 50 RR)
% Number of literals : 156 ( 38 equ; 56 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 131 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(prove_number_of_elements_in_class_1,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_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(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).
cnf(prove_number_of_elements_in_class_2,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).
cnf(c_0_16,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_17,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_18,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_19,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_20,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_22,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_23,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_24,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_26,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2))
| ~ member(not_subclass_element(X1,complement(X2)),universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_28,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_29,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_30,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_31,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
prove_number_of_elements_in_class_1 ).
cnf(c_0_32,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_33,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,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_21,c_0_28]) ).
cnf(c_0_36,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_37,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_38,plain,
( not_subclass_element(unordered_pair(X1,X2),X3) = X1
| not_subclass_element(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_39,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),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_40,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_33]),c_0_20]) ).
cnf(c_0_41,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_42,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_43,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_35,c_0_36]) ).
cnf(c_0_44,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_45,plain,
( not_subclass_element(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_38])]) ).
cnf(c_0_46,plain,
( regular(unordered_pair(X1,X2)) = X1
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_47,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_48,negated_conjecture,
subclass(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_39,c_0_23]) ).
cnf(c_0_49,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_50,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_51,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_22]),c_0_27]) ).
cnf(c_0_52,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
( member(X1,X2)
| subclass(unordered_pair(X1,X1),complement(X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_54,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_46])]) ).
cnf(c_0_55,plain,
( subclass(X1,intersection(X2,universal_class))
| ~ member(not_subclass_element(X1,intersection(X2,universal_class)),X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_56,negated_conjecture,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_57,plain,
( complement(complement(X1)) = X1
| ~ subclass(complement(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_50]) ).
cnf(c_0_58,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_21,c_0_51]) ).
cnf(c_0_59,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_52])]) ).
cnf(c_0_60,plain,
( member(X1,complement(X2))
| member(X3,X2)
| ~ member(X1,unordered_pair(X3,X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_53]) ).
cnf(c_0_61,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_54]) ).
cnf(c_0_62,plain,
( universal_class = X1
| ~ subclass(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_17]) ).
cnf(c_0_63,plain,
subclass(X1,complement(null_class)),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_64,plain,
subclass(X1,intersection(X1,universal_class)),
inference(spm,[status(thm)],[c_0_55,c_0_23]) ).
cnf(c_0_65,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_66,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_67,negated_conjecture,
( ~ member(X1,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ member(X1,x) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_56]),c_0_40]) ).
cnf(c_0_68,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_69,negated_conjecture,
intersection(x,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) = null_class,
inference(rw,[status(thm)],[c_0_56,c_0_59]) ).
cnf(c_0_70,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,complement(X2))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
complement(null_class) = universal_class,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
intersection(X1,universal_class) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_64]),c_0_65])]) ).
cnf(c_0_73,negated_conjecture,
x != null_class,
prove_number_of_elements_in_class_3 ).
cnf(c_0_74,plain,
( intersection(X1,X2) = X2
| ~ subclass(X2,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_66]) ).
cnf(c_0_75,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_76,negated_conjecture,
( subclass(X1,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(X1,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_34]),c_0_68]),c_0_68]) ).
cnf(c_0_77,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),complement(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( member(not_subclass_element(x,null_class),complement(X1))
| member(not_subclass_element(x,null_class),X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72]),c_0_73]) ).
cnf(c_0_79,negated_conjecture,
~ subclass(x,null_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_56]),c_0_73]) ).
cnf(c_0_80,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
prove_number_of_elements_in_class_2 ).
cnf(c_0_81,plain,
( X1 = unordered_pair(X2,X2)
| ~ member(X2,X1)
| ~ subclass(X1,unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_75]) ).
cnf(c_0_82,negated_conjecture,
subclass(x,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
inference(spm,[status(thm)],[c_0_76,c_0_23]) ).
cnf(c_0_83,negated_conjecture,
member(not_subclass_element(x,null_class),x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_84,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_80,c_0_32]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET097-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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 : n015.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 02:11:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 23.86/14.86 % Version : CSE_E---1.7
% 23.86/14.86 % Problem : theBenchmark.p
% 23.86/14.86 % SZS status Unsatisfiable for theBenchmark.p
% 23.86/14.86 % SZS output start CNFRefutation
% See solution above
% 23.97/14.96 % Total time : 10.384s
%------------------------------------------------------------------------------