%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET509-6 : 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 : n018.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 05:07:56 PM UTC 2026
% Result : Unsatisfiable 3.77s 3.20s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 58 ( 12 unt; 25 nHn; 29 RR)
% Number of literals : 123 ( 40 equ; 43 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 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 : 94 ( 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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
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(prove_corollary_2_to_singleton_in_unordered_pair_1,negated_conjecture,
unordered_pair(universal_class,x) != singleton(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_singleton_in_unordered_pair_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(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_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_14,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_15,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_16,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_17,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_18,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_21,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_23,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_24,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_25,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_18]) ).
cnf(c_0_26,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_22,c_0_17]) ).
cnf(c_0_27,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_28,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_26])]) ).
cnf(c_0_30,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
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_22,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
unordered_pair(universal_class,x) != singleton(x),
prove_corollary_2_to_singleton_in_unordered_pair_1 ).
cnf(c_0_33,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_34,plain,
( regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_35,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_37,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_30,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
unordered_pair(x,x) != unordered_pair(universal_class,x),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_40,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_41,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_42,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( member(X1,unordered_pair(X1,X2))
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( member(x,universal_class)
| member(universal_class,universal_class) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
~ member(X1,X1),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_25]),c_0_18]) ).
cnf(c_0_46,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_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_43,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
member(x,universal_class),
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_50,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_51,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_52,plain,
( X1 = unordered_pair(X2,X2)
| ~ member(X2,X1)
| ~ subclass(X1,unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( member(X1,universal_class)
| subclass(unordered_pair(X1,x),unordered_pair(x,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( unordered_pair(X1,x) = unordered_pair(x,x)
| member(X1,universal_class)
| ~ member(x,unordered_pair(X1,x)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_56,negated_conjecture,
( unordered_pair(X1,x) = unordered_pair(x,x)
| member(X1,universal_class) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_48])]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_56]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET509-6 : 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
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:25:47 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.77/3.20 % Version : CSE_E---1.7
% 3.77/3.20 % Problem : theBenchmark.p
% 3.77/3.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.77/3.20 % SZS output start CNFRefutation
% See solution above
% 3.77/3.21 % Total time : 2.373s
%------------------------------------------------------------------------------