%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET260-6 : 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 : n006.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 05:07:40 PM UTC 2026
% Result : Unsatisfiable 10.01s 7.15s
% Output : CNFRefutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of clauses : 78 ( 24 unt; 20 nHn; 47 RR)
% Number of literals : 152 ( 31 equ; 59 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 160 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
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(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
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(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(domain2,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain2) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
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(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(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(prove_domain_alternate_defn3_2,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_alternate_defn3_2) ).
cnf(prove_domain_alternate_defn3_1,negated_conjecture,
member(ordered_pair(x,y),xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_alternate_defn3_1) ).
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(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(prove_domain_alternate_defn3_3,negated_conjecture,
~ member(x,domain_of(xr)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_alternate_defn3_3) ).
cnf(c_0_22,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_23,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_24,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_25,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_26,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_27,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_28,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_30,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_31,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_33,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_34,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_35,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_36,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_37,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_30,c_0_29]) ).
cnf(c_0_38,plain,
( intersection(complement(X1),X2) = null_class
| ~ member(regular(intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_39,plain,
( intersection(X1,intersection(X2,X3)) = null_class
| member(regular(intersection(X1,intersection(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_40,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_42,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_44,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_37])]) ).
cnf(c_0_45,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
domain2 ).
cnf(c_0_46,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_47,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_48,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_49,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_50,plain,
intersection(complement(X1),intersection(X1,X2)) = null_class,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_51,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_28]) ).
cnf(c_0_52,plain,
( intersection(X1,X2) = X2
| ~ subclass(X2,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,plain,
( member(X1,universal_class)
| subclass(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,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_45,c_0_46]),c_0_47]) ).
cnf(c_0_55,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_56,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_48,c_0_46]),c_0_46]) ).
cnf(c_0_57,plain,
( ~ member(X1,intersection(X2,X3))
| ~ member(X1,complement(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_58,plain,
( intersection(X1,unordered_pair(X2,X2)) = unordered_pair(X2,X2)
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
( member(X1,universal_class)
| member(X2,X3)
| ~ member(X2,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_60,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(c_0_61,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
prove_domain_alternate_defn3_2 ).
cnf(c_0_62,plain,
( member(X1,domain_of(X2))
| ~ member(X3,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| ~ member(X3,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_54]),c_0_51]) ).
cnf(c_0_63,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_55,c_0_56]) ).
cnf(c_0_64,plain,
( member(X1,universal_class)
| ~ member(X2,unordered_pair(X1,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_65,negated_conjecture,
member(ordered_pair(x,y),xr),
prove_domain_alternate_defn3_1 ).
cnf(c_0_66,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_60,c_0_56]) ).
cnf(c_0_67,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[c_0_61,c_0_56]) ).
cnf(c_0_68,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_69,plain,
( member(X1,domain_of(X2))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2)
| ~ member(X3,unordered_pair(X1,X1))
| ~ member(X4,universal_class) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_70,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),xr),
inference(rw,[status(thm)],[c_0_65,c_0_56]) ).
cnf(c_0_71,negated_conjecture,
member(y,universal_class),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,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_68,c_0_56]) ).
cnf(c_0_73,negated_conjecture,
( member(X1,domain_of(xr))
| ~ member(x,unordered_pair(X1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_74,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_75,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_72,c_0_67]) ).
cnf(c_0_76,negated_conjecture,
~ member(x,domain_of(xr)),
prove_domain_alternate_defn3_3 ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET260-6 : 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 : n006.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 02:17:01 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 10.01/7.15 % Version : CSE_E---1.7
% 10.01/7.15 % Problem : theBenchmark.p
% 10.01/7.15 % SZS status Unsatisfiable for theBenchmark.p
% 10.01/7.15 % SZS output start CNFRefutation
% See solution above
% 10.01/7.18 % Total time : 5.371s
%------------------------------------------------------------------------------