%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM172-1 : 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 : n025.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 04:52:55 PM UTC 2026
% Result : Unsatisfiable 27.40s 18.52s
% Output : CNFRefutation 27.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of clauses : 60 ( 21 unt; 18 nHn; 34 RR)
% Number of literals : 113 ( 34 equ; 37 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 : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(successor,axiom,
union(X1,singleton(X1)) = successor(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_successor_is_different_2,negated_conjecture,
successor(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_successor_is_different_2) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
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(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(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(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_successor_is_different_1,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_successor_is_different_1) ).
cnf(c_0_19,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(c_0_20,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_21,negated_conjecture,
successor(x) = x,
prove_successor_is_different_2 ).
cnf(c_0_22,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_24,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_25,negated_conjecture,
complement(intersection(complement(x),complement(unordered_pair(x,x)))) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_27,negated_conjecture,
( member(X1,intersection(complement(x),complement(unordered_pair(x,x))))
| member(X1,x)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_29,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_30,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_31,negated_conjecture,
( member(X1,complement(unordered_pair(x,x)))
| member(X1,x)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_34,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_35,negated_conjecture,
( member(X1,x)
| ~ member(X1,unordered_pair(x,x)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_37,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_38,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_39,plain,
( subclass(X1,intersection(X2,X3))
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( member(not_subclass_element(unordered_pair(x,x),X1),x)
| subclass(unordered_pair(x,x),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_42,plain,
( regular(unordered_pair(X1,X2)) = X1
| regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( subclass(unordered_pair(x,x),intersection(X1,x))
| ~ member(not_subclass_element(unordered_pair(x,x),intersection(X1,x)),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_45,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_46,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_42])]) ).
cnf(c_0_47,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_48,negated_conjecture,
subclass(unordered_pair(x,x),intersection(unordered_pair(x,x),x)),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_49,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_50,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_51,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_52,plain,
( intersection(unordered_pair(X1,X1),X1) = null_class
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
intersection(unordered_pair(x,x),x) = unordered_pair(x,x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_54,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_56,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
member(x,universal_class),
prove_successor_is_different_1 ).
cnf(c_0_58,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_54]),c_0_32]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : NUM172-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.03/0.21 % 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
% 0.11/0.42 % Computer : n025.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8042.1875MB
% 0.11/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Tue May 5 00:16:43 EDT 2026
% 0.11/0.43 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 27.40/18.52 % Version : CSE_E---1.7
% 27.40/18.52 % Problem : theBenchmark.p
% 27.40/18.52 % SZS status Unsatisfiable for theBenchmark.p
% 27.40/18.52 % SZS output start CNFRefutation
% See solution above
% 27.49/18.61 % Total time : 14.459s
%------------------------------------------------------------------------------