%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM142-1 : 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 : n009.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 04:52:53 PM UTC 2026
% Result : Unsatisfiable 1.18s 1.89s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 18 unt; 4 nHn; 18 RR)
% Number of literals : 48 ( 7 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 5 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_of_set_is_set3_1,negated_conjecture,
~ subclass(x,successor(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_successor_of_set_is_set3_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
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(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(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(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(c_0_11,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(c_0_12,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_13,negated_conjecture,
~ subclass(x,successor(x)),
prove_successor_of_set_is_set3_1 ).
cnf(c_0_14,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_16,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_17,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_18,negated_conjecture,
~ subclass(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_20,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_21,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
member(not_subclass_element(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),x),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
~ member(not_subclass_element(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),complement(intersection(complement(x),complement(unordered_pair(x,x))))),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_25,negated_conjecture,
member(not_subclass_element(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),universal_class),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_27,negated_conjecture,
member(not_subclass_element(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),intersection(complement(x),complement(unordered_pair(x,x)))),
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,
member(not_subclass_element(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),complement(x)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.23 % Problem : NUM142-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.03/0.23 % 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
% 0.10/0.46 % Computer : n009.cluster.edu
% 0.10/0.46 % Model : x86_64 x86_64
% 0.10/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.46 % Memory : 8042.1875MB
% 0.10/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.46 % CPULimit : 300
% 0.10/0.46 % WCLimit : 300
% 0.10/0.46 % DateTime : Tue May 5 00:14:56 EDT 2026
% 0.10/0.46 % CPUTime :
% 0.10/0.47 % start to proof: theBenchmark
% 1.18/1.89 % Version : CSE_E---1.7
% 1.18/1.89 % Problem : theBenchmark.p
% 1.18/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 1.18/1.89 % SZS output start CNFRefutation
% See solution above
% 1.18/1.89 % Total time : 1.399s
%------------------------------------------------------------------------------