%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM071-1 : 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 : n021.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 04:52:48 PM UTC 2026
% Result : Unsatisfiable 165.82s 125.57s
% Output : CNFRefutation 166.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of clauses : 94 ( 23 unt; 33 nHn; 66 RR)
% Number of literals : 208 ( 58 equ; 82 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 143 ( 16 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(well_ordering3,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).
cnf(prove_well_ordering_is_irreflexive_1,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_ordering_is_irreflexive_1) ).
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(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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(prove_well_ordering_is_irreflexive_3,negated_conjecture,
member(u,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_ordering_is_irreflexive_3) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(well_ordering2,axiom,
( X3 = null_class
| member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering2) ).
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(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(well_ordering5,axiom,
( ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,least(X1,X3)),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering5) ).
cnf(prove_well_ordering_is_irreflexive_2,negated_conjecture,
member(ordered_pair(u,u),xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_well_ordering_is_irreflexive_2) ).
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(c_0_21,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_22,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_23,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
well_ordering3 ).
cnf(c_0_24,negated_conjecture,
well_ordering(xr,y),
prove_well_ordering_is_irreflexive_1 ).
cnf(c_0_25,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_26,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_28,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_29,negated_conjecture,
( member(least(xr,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_32,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( member(least(xr,intersection(y,X1)),intersection(y,X1))
| ~ member(X2,intersection(y,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_35,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_36,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_37,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_38,negated_conjecture,
( member(least(xr,intersection(y,X1)),intersection(y,X1))
| ~ member(X2,y)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
member(u,y),
prove_well_ordering_is_irreflexive_3 ).
cnf(c_0_40,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_35,c_0_36]),c_0_37]) ).
cnf(c_0_41,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_37]) ).
cnf(c_0_42,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_43,negated_conjecture,
( member(least(xr,intersection(y,X1)),intersection(y,X1))
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_45,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_46,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_47,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_48,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_49,negated_conjecture,
( member(least(xr,intersection(y,X1)),X1)
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( complement(complement(X1)) = X1
| ~ subclass(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_46,c_0_22]) ).
cnf(c_0_52,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_47,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(least(xr,intersection(y,complement(X1))),X1)
| ~ member(u,complement(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_54,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
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_52])]) ).
cnf(c_0_56,negated_conjecture,
( ~ member(least(xr,intersection(y,X1)),complement(X1))
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
( unordered_pair(u,u) = null_class
| ~ member(least(xr,intersection(y,unordered_pair(u,u))),complement(unordered_pair(u,u))) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_59,negated_conjecture,
( unordered_pair(u,u) = null_class
| member(least(xr,intersection(y,unordered_pair(u,u))),unordered_pair(u,u))
| ~ member(least(xr,intersection(y,unordered_pair(u,u))),universal_class) ),
inference(spm,[status(thm)],[c_0_58,c_0_36]) ).
cnf(c_0_60,negated_conjecture,
( least(xr,intersection(y,unordered_pair(u,u))) = u
| unordered_pair(u,u) = null_class
| ~ member(least(xr,intersection(y,unordered_pair(u,u))),universal_class) ),
inference(spm,[status(thm)],[c_0_47,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
( member(least(xr,intersection(y,X1)),universal_class)
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_62,negated_conjecture,
( least(xr,intersection(y,unordered_pair(u,u))) = u
| unordered_pair(u,u) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( unordered_pair(u,u) = null_class
| member(u,intersection(y,unordered_pair(u,u))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_62]),c_0_57]) ).
cnf(c_0_64,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_47,c_0_22]) ).
cnf(c_0_65,negated_conjecture,
( unordered_pair(u,u) = null_class
| member(least(xr,intersection(y,unordered_pair(u,u))),intersection(y,unordered_pair(u,u))) ),
inference(spm,[status(thm)],[c_0_33,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
( not_subclass_element(unordered_pair(X1,X2),y) = X2
| not_subclass_element(unordered_pair(X1,X2),y) = X1
| member(least(xr,unordered_pair(X1,X2)),unordered_pair(X1,X2))
| ~ member(X3,unordered_pair(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
( unordered_pair(u,u) = null_class
| member(least(xr,intersection(y,unordered_pair(u,u))),unordered_pair(u,u)) ),
inference(spm,[status(thm)],[c_0_42,c_0_65]) ).
cnf(c_0_68,axiom,
( X3 = null_class
| member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2) ),
well_ordering2 ).
cnf(c_0_69,negated_conjecture,
( not_subclass_element(unordered_pair(u,u),y) = u
| unordered_pair(u,u) = null_class
| member(least(xr,unordered_pair(u,u)),unordered_pair(u,u)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_71,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_72,negated_conjecture,
( X1 = null_class
| member(least(xr,X1),X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_68,c_0_24]) ).
cnf(c_0_73,negated_conjecture,
( not_subclass_element(unordered_pair(u,u),y) = u
| least(xr,unordered_pair(u,u)) = u
| unordered_pair(u,u) = null_class ),
inference(spm,[status(thm)],[c_0_47,c_0_69]) ).
cnf(c_0_74,axiom,
( ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,least(X1,X3)),X1) ),
well_ordering5 ).
cnf(c_0_75,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_70,c_0_71]),c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( least(xr,unordered_pair(X1,X2)) = X1
| least(xr,unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| ~ subclass(unordered_pair(X1,X2),y) ),
inference(spm,[status(thm)],[c_0_47,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( least(xr,unordered_pair(u,u)) = u
| unordered_pair(u,u) = null_class
| subclass(unordered_pair(u,u),y) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_73]),c_0_39])]) ).
cnf(c_0_78,plain,
( ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ well_ordering(X1,X2)
| ~ member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(least(X1,X3),least(X1,X3)))),X1) ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,negated_conjecture,
( least(xr,unordered_pair(u,u)) = u
| unordered_pair(u,u) = null_class ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,negated_conjecture,
( unordered_pair(u,u) = null_class
| ~ well_ordering(xr,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(u,u))),xr)
| ~ member(X2,unordered_pair(u,u))
| ~ subclass(unordered_pair(u,u),X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
member(ordered_pair(u,u),xr),
prove_well_ordering_is_irreflexive_2 ).
cnf(c_0_82,negated_conjecture,
( unordered_pair(u,u) = null_class
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(u,u))),xr)
| ~ member(X1,unordered_pair(u,u))
| ~ subclass(unordered_pair(u,u),y) ),
inference(spm,[status(thm)],[c_0_80,c_0_24]) ).
cnf(c_0_83,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(u,u))),xr),
inference(rw,[status(thm)],[c_0_81,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( unordered_pair(u,u) = null_class
| ~ subclass(unordered_pair(u,u),y) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_57]) ).
cnf(c_0_85,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_48]) ).
cnf(c_0_86,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_87,negated_conjecture,
( not_subclass_element(unordered_pair(u,u),y) = u
| unordered_pair(u,u) = null_class ),
inference(spm,[status(thm)],[c_0_84,c_0_64]) ).
cnf(c_0_88,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_90,negated_conjecture,
unordered_pair(u,u) = null_class,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_87]),c_0_39])]),c_0_84]) ).
cnf(c_0_91,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_92,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_88]),c_0_32]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91])]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM071-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue May 5 00:10:25 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 165.82/125.57 % Version : CSE_E---1.7
% 165.82/125.57 % Problem : theBenchmark.p
% 165.82/125.57 % SZS status Unsatisfiable for theBenchmark.p
% 165.82/125.57 % SZS output start CNFRefutation
% See solution above
% 166.72/126.48 % Total time : 91.716s
%------------------------------------------------------------------------------