%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM060-1 : 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 : n011.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 04:52:47 PM UTC 2026
% Result : Unsatisfiable 4.68s 3.41s
% Output : CNFRefutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of clauses : 65 ( 33 unt; 6 nHn; 42 RR)
% Number of literals : 108 ( 22 equ; 49 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_segments_property4_1,negated_conjecture,
member(ordered_pair(u,z),intersection(xr,cross_product(y,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_segments_property4_1) ).
cnf(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(segment,axiom,
segment(X1,X2,X3) = domain_of(restrict(X1,X2,singleton(X3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',segment) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
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(prove_segments_property4_2,negated_conjecture,
~ member(u,segment(xr,y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_segments_property4_2) ).
cnf(domain2,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain2) ).
cnf(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
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(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
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,negated_conjecture,
member(ordered_pair(u,z),intersection(xr,cross_product(y,universal_class))),
prove_segments_property4_1 ).
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,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_24,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_25,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),intersection(xr,cross_product(y,universal_class))),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_27,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_28,axiom,
segment(X1,X2,X3) = domain_of(restrict(X1,X2,singleton(X3))),
segment ).
cnf(c_0_29,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_30,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_23,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,universal_class)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_33,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_34,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
~ member(u,segment(xr,y,z)),
prove_segments_property4_2 ).
cnf(c_0_36,plain,
segment(X1,X2,X3) = domain_of(intersection(X1,cross_product(X2,unordered_pair(X3,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_20]),c_0_29]) ).
cnf(c_0_37,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
domain2 ).
cnf(c_0_38,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_39,negated_conjecture,
member(u,y),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
~ member(u,domain_of(intersection(xr,cross_product(y,unordered_pair(z,z))))),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_20]),c_0_29]) ).
cnf(c_0_44,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_45,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_46,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_48,negated_conjecture,
intersection(cross_product(unordered_pair(u,u),universal_class),intersection(xr,cross_product(y,unordered_pair(z,z)))) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_49,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_46]),c_0_34]) ).
cnf(c_0_50,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
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,
( ~ member(X1,intersection(xr,cross_product(y,unordered_pair(z,z))))
| ~ member(X1,cross_product(unordered_pair(u,u),universal_class)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_53,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_50,c_0_22]) ).
cnf(c_0_54,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_55,negated_conjecture,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),intersection(xr,cross_product(y,unordered_pair(z,z))))
| ~ member(X1,unordered_pair(u,u))
| ~ member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
member(z,universal_class),
inference(spm,[status(thm)],[c_0_54,c_0_31]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(z,z))),intersection(xr,cross_product(y,unordered_pair(z,z))))
| ~ member(X1,unordered_pair(u,u)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_58,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_59,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_60,negated_conjecture,
~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),intersection(xr,cross_product(y,unordered_pair(z,z)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_45])]) ).
cnf(c_0_61,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),xr),
inference(spm,[status(thm)],[c_0_59,c_0_25]) ).
cnf(c_0_62,negated_conjecture,
~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_47]),c_0_61])]) ).
cnf(c_0_63,negated_conjecture,
~ member(z,unordered_pair(z,z)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_53]),c_0_39])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_58]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM060-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.09/0.14 % 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
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:07:17 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.19/0.35 % start to proof: theBenchmark
% 4.68/3.41 % Version : CSE_E---1.7
% 4.68/3.41 % Problem : theBenchmark.p
% 4.68/3.41 % SZS status Unsatisfiable for theBenchmark.p
% 4.68/3.41 % SZS output start CNFRefutation
% See solution above
% 4.68/3.43 % Total time : 2.368s
%------------------------------------------------------------------------------