%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET120-7 : TPTP v9.2.1. Bugfixed v7.3.0.
% 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 : n027.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 05:07:23 PM UTC 2026
% Result : Unsatisfiable 4.74s 3.42s
% Output : CNFRefutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of clauses : 72 ( 34 unt; 24 nHn; 30 RR)
% Number of literals : 114 ( 66 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_corollary_2_to_OP_determines_components1_1,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components1_1) ).
cnf(only_member_in_singleton,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_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(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(existence_of_null_class,axiom,
~ member(X1,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(singleton_is_null_class,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(unordered_pairs_and_singletons,axiom,
unordered_pair(X1,X2) = union(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
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(prove_corollary_2_to_OP_determines_components1_2,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components1_2) ).
cnf(corollary_1_to_cartesian_product,axiom,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
cnf(corollary_to_unordered_pair_axiom2,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X2,X1) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
cnf(unordered_pair_equals_singleton2,axiom,
( member(X1,universal_class)
| unordered_pair(X1,X2) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
cnf(existence_of_1st_and_2nd_3,axiom,
( member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class))
| second(X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
cnf(existence_of_1st_and_2nd_5,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| second(X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
cnf(c_0_19,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(c_0_20,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_21,negated_conjecture,
~ member(x,universal_class),
prove_corollary_2_to_OP_determines_components1_1 ).
cnf(c_0_22,plain,
( unordered_pair(X2,X1) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
only_member_in_singleton ).
cnf(c_0_24,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_25,negated_conjecture,
unordered_pair(X1,x) = unordered_pair(X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( X1 = X2
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
unordered_pair(X1,X1) = unordered_pair(x,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_29,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_30,axiom,
~ member(X1,null_class),
existence_of_null_class ).
cnf(c_0_31,negated_conjecture,
( X1 = X2
| ~ member(X1,unordered_pair(x,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_33,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( regular(unordered_pair(x,X1)) = X1
| unordered_pair(x,X1) = null_class ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
singleton_is_null_class ).
cnf(c_0_36,negated_conjecture,
( unordered_pair(x,X1) = null_class
| ~ member(X2,unordered_pair(x,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(x,X1) = null_class
| member(X1,unordered_pair(x,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_38,axiom,
unordered_pair(X1,X2) = union(singleton(X1),singleton(X2)),
unordered_pairs_and_singletons ).
cnf(c_0_39,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_40,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_35,c_0_20]) ).
cnf(c_0_41,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_42,negated_conjecture,
( unordered_pair(x,X1) = null_class
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
unordered_pair(X1,X2) = complement(intersection(complement(unordered_pair(X1,X1)),complement(unordered_pair(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_20]),c_0_20]),c_0_39]) ).
cnf(c_0_44,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
prove_corollary_2_to_OP_determines_components1_2 ).
cnf(c_0_46,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_41,c_0_20]),c_0_20]) ).
cnf(c_0_47,axiom,
( member(X1,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_1_to_cartesian_product ).
cnf(c_0_48,negated_conjecture,
unordered_pair(universal_class,universal_class) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_27])]) ).
cnf(c_0_49,negated_conjecture,
complement(intersection(complement(null_class),complement(unordered_pair(X1,X1)))) = unordered_pair(x,X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X2,X1) != null_class ),
corollary_to_unordered_pair_axiom2 ).
cnf(c_0_51,axiom,
( member(X1,universal_class)
| unordered_pair(X1,X2) = singleton(X2) ),
unordered_pair_equals_singleton2 ).
cnf(c_0_52,axiom,
( member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class))
| second(X1) = X1 ),
existence_of_1st_and_2nd_3 ).
cnf(c_0_53,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| second(X1) = X1 ),
existence_of_1st_and_2nd_5 ).
cnf(c_0_54,negated_conjecture,
second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46]) ).
cnf(c_0_55,plain,
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
unordered_pair(x,X1) = unordered_pair(universal_class,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_49]) ).
cnf(c_0_57,negated_conjecture,
~ member(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_58,plain,
( unordered_pair(X1,X2) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_51,c_0_20]) ).
cnf(c_0_59,plain,
( second(X1) = X1
| member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_60,plain,
( second(X1) = X1
| unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1 ),
inference(rw,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_61,negated_conjecture,
second(unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_44]),c_0_44]) ).
cnf(c_0_62,negated_conjecture,
~ member(unordered_pair(null_class,unordered_pair(universal_class,unordered_pair(X1,X1))),cross_product(X2,X3)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56]),c_0_25]),c_0_48]),c_0_21]) ).
cnf(c_0_63,negated_conjecture,
unordered_pair(universal_class,X1) = unordered_pair(X1,X1),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( second(X1) = X1
| member(unordered_pair(unordered_pair(x,first(X1)),unordered_pair(first(X1),unordered_pair(x,second(X1)))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_27]),c_0_27]) ).
cnf(c_0_65,plain,
( unordered_pair(unordered_pair(x,first(X1)),unordered_pair(first(X1),unordered_pair(x,second(X1)))) = X1
| second(X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_27]),c_0_27]) ).
cnf(c_0_66,negated_conjecture,
second(unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y)))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_25]),c_0_24]),c_0_25]),c_0_24]) ).
cnf(c_0_67,negated_conjecture,
~ member(unordered_pair(null_class,unordered_pair(universal_class,unordered_pair(universal_class,X1))),cross_product(X2,X3)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
( second(X1) = X1
| member(X1,cross_product(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,negated_conjecture,
second(unordered_pair(null_class,unordered_pair(universal_class,unordered_pair(universal_class,y)))) != unordered_pair(null_class,unordered_pair(universal_class,unordered_pair(universal_class,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_56]),c_0_56]),c_0_56]),c_0_56]) ).
cnf(c_0_70,negated_conjecture,
second(unordered_pair(null_class,unordered_pair(universal_class,unordered_pair(universal_class,X1)))) = unordered_pair(null_class,unordered_pair(universal_class,unordered_pair(universal_class,X1))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET120-7 : TPTP v9.2.1. Bugfixed v7.3.0.
% 0.00/0.12 % 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 : n027.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 02:11:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.74/3.42 % Version : CSE_E---1.7
% 4.74/3.42 % Problem : theBenchmark.p
% 4.74/3.42 % SZS status Unsatisfiable for theBenchmark.p
% 4.74/3.42 % SZS output start CNFRefutation
% See solution above
% 4.74/3.44 % Total time : 2.372s
%------------------------------------------------------------------------------