%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM154-1 : 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 : n004.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 04:52:54 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of clauses : 58 ( 26 unt; 8 nHn; 39 RR)
% Number of literals : 96 ( 25 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(successor,axiom,
union(X1,singleton(X1)) = successor(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',successor) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_corollary_5_to_successor_property1_1,negated_conjecture,
successor(x) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_5_to_successor_property1_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
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(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
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(c_0_17,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_20,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_21,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(c_0_23,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_24,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_27,negated_conjecture,
successor(x) = null_class,
prove_corollary_5_to_successor_property1_1 ).
cnf(c_0_28,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_30,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( universal_class = X1
| ~ subclass(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_32,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_33,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_34,negated_conjecture,
complement(intersection(complement(x),complement(unordered_pair(x,x)))) = null_class,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30]),c_0_21]) ).
cnf(c_0_36,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_37,plain,
( universal_class = X1
| ~ member(not_subclass_element(universal_class,X1),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( member(X1,intersection(complement(x),complement(unordered_pair(x,x))))
| ~ member(X1,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
( universal_class = X1
| member(not_subclass_element(universal_class,X1),universal_class) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_40,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_41,negated_conjecture,
intersection(complement(x),complement(unordered_pair(x,x))) = universal_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( member(X1,complement(x))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
~ member(X1,x),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_42]),c_0_21]) ).
cnf(c_0_44,negated_conjecture,
x = null_class,
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_45,negated_conjecture,
( member(X1,complement(null_class))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
intersection(complement(null_class),complement(unordered_pair(null_class,null_class))) = universal_class,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_44]),c_0_44]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
complement(null_class) = universal_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_39]) ).
cnf(c_0_48,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_49,negated_conjecture,
intersection(universal_class,complement(unordered_pair(null_class,null_class))) = universal_class,
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1 ).
cnf(c_0_51,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_52,negated_conjecture,
( member(X1,complement(unordered_pair(null_class,null_class)))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
member(null_class,omega),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
~ member(X1,unordered_pair(null_class,null_class)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_52]),c_0_21]) ).
cnf(c_0_55,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_56,plain,
member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM154-1 : 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 : n004.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 00:15:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------