%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET079-6 : 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 : n024.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 05:07:12 PM UTC 2026
% Result : Unsatisfiable 1.16s 1.65s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of clauses : 58 ( 33 unt; 8 nHn; 35 RR)
% Number of literals : 91 ( 32 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 64 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_to_set_in_its_singleton_2,negated_conjecture,
singleton(x) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_set_in_its_singleton_2) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
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(prove_corollary_to_set_in_its_singleton_1,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_set_in_its_singleton_1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(image,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
cnf(range_of,axiom,
domain_of(inverse(X1)) = range_of(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
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(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(inductive3,axiom,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive3) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(omega_in_universal,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
cnf(c_0_19,negated_conjecture,
singleton(x) = null_class,
prove_corollary_to_set_in_its_singleton_2 ).
cnf(c_0_20,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_21,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_22,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_23,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_24,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
member(x,universal_class),
prove_corollary_to_set_in_its_singleton_1 ).
cnf(c_0_26,plain,
( X1 = null_class
| member(X2,X1)
| ~ member(X2,null_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
member(x,null_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_29,negated_conjecture,
( X1 = null_class
| member(x,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( complement(X1) = null_class
| ~ member(x,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(c_0_32,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(c_0_33,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_34,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_35,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_36,negated_conjecture,
complement(null_class) = null_class,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_37,axiom,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1) ),
inductive3 ).
cnf(c_0_38,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_39,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_40,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_41,negated_conjecture,
( X1 = x
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_42,negated_conjecture,
( member(X1,null_class)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class)))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_45,negated_conjecture,
member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( X1 = x
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1 ).
cnf(c_0_48,plain,
inductive(universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_49,axiom,
member(omega,universal_class),
omega_in_universal ).
cnf(c_0_50,negated_conjecture,
null_class = x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_51,negated_conjecture,
x = omega,
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_52,plain,
( ~ inductive(complement(X1))
| ~ member(null_class,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( complement(X1) = omega
| ~ member(omega,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_50]),c_0_51]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
~ inductive(complement(universal_class)),
inference(spm,[status(thm)],[c_0_52,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
complement(universal_class) = omega,
inference(spm,[status(thm)],[c_0_53,c_0_49]) ).
cnf(c_0_56,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET079-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.08 % 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
% 0.07/0.27 % Computer : n024.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon May 4 21:08:56 EDT 2026
% 0.07/0.27 % CPUTime :
% 0.07/0.27 % start to proof: theBenchmark
% 1.16/1.65 % Version : CSE_E---1.7
% 1.16/1.65 % Problem : theBenchmark.p
% 1.16/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 1.16/1.65 % SZS output start CNFRefutation
% See solution above
% 1.16/1.65 % Total time : 1.361s
%------------------------------------------------------------------------------