%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET123-6 : 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 : n018.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 05:07:24 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 20 unt; 4 nHn; 22 RR)
% Number of literals : 54 ( 13 equ; 26 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_set_builder_alternate_defn1_1,negated_conjecture,
member(x,set_builder(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(prove_set_builder_alternate_defn1_2,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_2) ).
cnf(prove_set_builder_alternate_defn1_3,negated_conjecture,
~ member(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_alternate_defn1_3) ).
cnf(c_0_12,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_13,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_14,negated_conjecture,
member(x,set_builder(y,z)),
prove_set_builder_alternate_defn1_1 ).
cnf(c_0_15,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_17,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_18,negated_conjecture,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_20,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_21,negated_conjecture,
~ member(x,intersection(complement(unordered_pair(y,y)),complement(z))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_23,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(x,complement(unordered_pair(y,y)))
| ~ member(x,complement(z)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_26,negated_conjecture,
member(x,universal_class),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_27,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_28,negated_conjecture,
( member(x,unordered_pair(y,y))
| ~ member(x,complement(z)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
x != y,
prove_set_builder_alternate_defn1_2 ).
cnf(c_0_30,negated_conjecture,
~ member(x,complement(z)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
~ member(x,z),
prove_set_builder_alternate_defn1_3 ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_26])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET123-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:13:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------