%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM069-1 : 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 : 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 04:52:48 PM UTC 2026
% Result : Unsatisfiable 32.38s 23.92s
% Output : CNFRefutation 32.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of clauses : 80 ( 29 unt; 14 nHn; 55 RR)
% Number of literals : 151 ( 39 equ; 60 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 128 ( 35 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(prove_corollary_to_well_ordering_property3_2,negated_conjecture,
member(ordered_pair(u,v),cross_product(y,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_2) ).
cnf(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
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(prove_corollary_to_well_ordering_property3_4,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_4) ).
cnf(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(prove_corollary_to_well_ordering_property3_3,negated_conjecture,
member(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_3) ).
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(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(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(c_0_19,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_20,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_21,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(c_0_22,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_19,c_0_20]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
member(ordered_pair(u,v),cross_product(y,y)),
prove_corollary_to_well_ordering_property3_2 ).
cnf(c_0_24,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_25,plain,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(y,y)),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,plain,
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_30,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_31,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_32,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_34,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
member(v,u),
prove_corollary_to_well_ordering_property3_4 ).
cnf(c_0_36,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(v,X2)
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_38,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_40,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
member(u,v),
prove_corollary_to_well_ordering_property3_3 ).
cnf(c_0_42,negated_conjecture,
( ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(u,complement(X1)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_44,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_46,negated_conjecture,
( member(u,X1)
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_47,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_48,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_49,negated_conjecture,
member(u,unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_47])]) ).
cnf(c_0_50,negated_conjecture,
( first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u
| u = X1 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(c_0_52,negated_conjecture,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u,
inference(ef,[status(thm)],[c_0_50]) ).
cnf(c_0_53,plain,
( member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_54,negated_conjecture,
unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_52]),c_0_52]),c_0_52]) ).
cnf(c_0_55,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_56,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X2,X1)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_55]) ).
cnf(c_0_58,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(v,X1)
| ~ member(u,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_60,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X1,X2))
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X2)
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(v,X1))
| ~ member(u,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_37]),c_0_38])]) ).
cnf(c_0_63,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_64,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_65,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_60]),c_0_34]) ).
cnf(c_0_66,negated_conjecture,
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(v,X1))
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_67,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(v,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_37]),c_0_44])]) ).
cnf(c_0_68,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_69,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_48,c_0_55]) ).
cnf(c_0_70,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(v,unordered_pair(v,X1))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,plain,
( regular(unordered_pair(X1,X2)) = X1
| unordered_pair(X1,X2) = null_class
| ~ member(X3,unordered_pair(X1,X2))
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
member(v,unordered_pair(v,X1)),
inference(spm,[status(thm)],[c_0_53,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( regular(unordered_pair(v,X1)) = v
| unordered_pair(v,X1) = null_class
| ~ member(v,X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_74,negated_conjecture,
( regular(unordered_pair(v,u)) = v
| unordered_pair(v,u) = null_class ),
inference(spm,[status(thm)],[c_0_73,c_0_35]) ).
cnf(c_0_75,negated_conjecture,
( unordered_pair(v,u) = null_class
| ~ member(X1,unordered_pair(v,u))
| ~ member(X1,v) ),
inference(spm,[status(thm)],[c_0_68,c_0_74]) ).
cnf(c_0_76,negated_conjecture,
( unordered_pair(v,u) = null_class
| ~ member(u,unordered_pair(v,u)) ),
inference(spm,[status(thm)],[c_0_75,c_0_41]) ).
cnf(c_0_77,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_78,negated_conjecture,
unordered_pair(v,u) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_44])]) ).
cnf(c_0_79,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_78]),c_0_38])]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM069-1 : 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 : n026.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 00:12:23 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 32.38/23.92 % Version : CSE_E---1.7
% 32.38/23.92 % Problem : theBenchmark.p
% 32.38/23.92 % SZS status Unsatisfiable for theBenchmark.p
% 32.38/23.92 % SZS output start CNFRefutation
% See solution above
% 32.49/24.07 % Total time : 18.535s
%------------------------------------------------------------------------------