%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET519-6 : 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 : n026.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 05:07:57 PM UTC 2026
% Result : Unsatisfiable 104.59s 56.12s
% Output : CNFRefutation 104.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of clauses : 91 ( 25 unt; 36 nHn; 39 RR)
% Number of literals : 183 ( 52 equ; 62 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 161 ( 40 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
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(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(domain1,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
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(prove_corollary_1_no_cycles_length_2_1,negated_conjecture,
ordered_pair(x,y) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_no_cycles_length_2_1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
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(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(c_0_18,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_19,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_20,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_21,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_24,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_25,plain,
( X1 = null_class
| subclass(null_class,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_27,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(c_0_28,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_29,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_30,plain,
( X1 = null_class
| ~ subclass(X1,null_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,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_26,c_0_19]) ).
cnf(c_0_32,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_33,plain,
( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,plain,
intersection(null_class,X1) = null_class,
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_35,plain,
( not_subclass_element(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
ordered_pair(x,y) = x,
prove_corollary_1_no_cycles_length_2_1 ).
cnf(c_0_37,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_32,c_0_28]),c_0_28]) ).
cnf(c_0_38,plain,
~ member(X1,domain_of(null_class)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_40,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_31])]) ).
cnf(c_0_41,plain,
( member(X1,unordered_pair(X1,X2))
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_42,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_43,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_44,negated_conjecture,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) = x,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_47,plain,
( member(X1,unordered_pair(X1,X2))
| subclass(unordered_pair(X1,X2),unordered_pair(X2,X3))
| ~ member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_50,plain,
~ member(X1,null_class),
inference(rw,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_51,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_26,c_0_39]) ).
cnf(c_0_52,plain,
( X1 = unordered_pair(X2,X2)
| ~ member(X2,X1)
| ~ subclass(X1,unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( member(X1,unordered_pair(X1,x))
| subclass(unordered_pair(X1,x),unordered_pair(x,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_23]),c_0_50]) ).
cnf(c_0_55,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_51])]) ).
cnf(c_0_56,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_57,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_58,negated_conjecture,
( unordered_pair(X1,x) = unordered_pair(x,x)
| member(X1,unordered_pair(X1,x))
| ~ member(x,unordered_pair(X1,x)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_60,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_39,c_0_55]) ).
cnf(c_0_62,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( unordered_pair(X1,x) = unordered_pair(x,x)
| member(X1,unordered_pair(X1,x)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_48])]) ).
cnf(c_0_64,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( member(X1,universal_class)
| subclass(unordered_pair(X1,x),unordered_pair(x,X2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_66,negated_conjecture,
( unordered_pair(X1,x) = unordered_pair(x,x)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
( member(X1,unordered_pair(X1,X2))
| subclass(unordered_pair(X1,X2),unordered_pair(X3,X2))
| ~ member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_41,c_0_59]) ).
cnf(c_0_68,plain,
~ member(X1,X1),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_64]),c_0_50]),c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( member(X1,unordered_pair(x,X2))
| member(X3,universal_class)
| ~ member(X1,unordered_pair(X3,x)) ),
inference(spm,[status(thm)],[c_0_56,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( member(x,unordered_pair(X1,x))
| member(X1,universal_class) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_66]),c_0_48])]) ).
cnf(c_0_71,negated_conjecture,
( member(X1,unordered_pair(X1,x))
| subclass(unordered_pair(X1,x),unordered_pair(X2,x)) ),
inference(spm,[status(thm)],[c_0_67,c_0_48]) ).
cnf(c_0_72,plain,
( ~ member(intersection(X1,X2),X2)
| ~ member(intersection(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_49]) ).
cnf(c_0_73,negated_conjecture,
( member(x,unordered_pair(x,X1))
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( member(X1,universal_class)
| subclass(unordered_pair(X1,x),unordered_pair(X2,x)) ),
inference(spm,[status(thm)],[c_0_62,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( member(x,unordered_pair(x,X1))
| ~ member(intersection(X2,universal_class),X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
( member(X1,universal_class)
| subclass(unordered_pair(x,x),unordered_pair(X2,x)) ),
inference(spm,[status(thm)],[c_0_74,c_0_66]) ).
cnf(c_0_77,negated_conjecture,
( member(x,unordered_pair(x,X1))
| member(x,unordered_pair(x,X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( member(X1,unordered_pair(X2,x))
| member(X3,universal_class)
| ~ member(X1,unordered_pair(x,x)) ),
inference(spm,[status(thm)],[c_0_56,c_0_76]) ).
cnf(c_0_79,negated_conjecture,
member(x,unordered_pair(x,X1)),
inference(ef,[status(thm)],[c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( member(x,unordered_pair(X1,x))
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
( member(x,unordered_pair(X1,x))
| ~ member(intersection(X2,universal_class),X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( member(x,unordered_pair(X1,x))
| member(x,unordered_pair(X2,x)) ),
inference(spm,[status(thm)],[c_0_81,c_0_80]) ).
cnf(c_0_83,plain,
( regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| ~ member(X3,unordered_pair(X1,X2))
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_84,negated_conjecture,
member(x,unordered_pair(X1,x)),
inference(ef,[status(thm)],[c_0_82]) ).
cnf(c_0_85,negated_conjecture,
( regular(unordered_pair(X1,x)) = x
| unordered_pair(X1,x) = null_class
| ~ member(x,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_86,negated_conjecture,
( unordered_pair(X1,x) = null_class
| ~ member(X2,unordered_pair(X1,x))
| ~ member(X2,x)
| ~ member(x,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_85]) ).
cnf(c_0_87,negated_conjecture,
( unordered_pair(X1,x) = null_class
| ~ member(X1,x)
| ~ member(x,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_42]),c_0_62]) ).
cnf(c_0_88,negated_conjecture,
( ~ member(X1,x)
| ~ member(x,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_87]),c_0_48])]),c_0_50]) ).
cnf(c_0_89,negated_conjecture,
member(unordered_pair(x,unordered_pair(y,y)),x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_44]),c_0_43])]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_79])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET519-6 : 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
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:25:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 104.59/56.12 % Version : CSE_E---1.7
% 104.59/56.12 % Problem : theBenchmark.p
% 104.59/56.12 % SZS status Unsatisfiable for theBenchmark.p
% 104.59/56.12 % SZS output start CNFRefutation
% See solution above
% 104.98/56.49 % Total time : 38.450s
%------------------------------------------------------------------------------