%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM011-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n022.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 04:52:43 PM UTC 2026
% Result : Unsatisfiable 1.98s 1.90s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 19 unt; 2 nHn; 24 RR)
% Number of literals : 59 ( 12 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(successor,axiom,
successor(X1) = union(X1,singleton_set(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',successor) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(prove_zero_is_first,negated_conjecture,
empty_set = successor(f75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_first) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',union) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection3) ).
cnf(a_natural_number,hypothesis,
member(f75,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_natural_number) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(c_0_13,axiom,
successor(X1) = union(X1,singleton_set(X1)),
successor ).
cnf(c_0_14,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_15,negated_conjecture,
empty_set = successor(f75),
prove_zero_is_first ).
cnf(c_0_16,plain,
successor(X1) = union(X1,non_ordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_18,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_19,hypothesis,
member(f75,natural_numbers),
a_natural_number ).
cnf(c_0_20,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_21,negated_conjecture,
empty_set = complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_22,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_23,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_24,hypothesis,
( member(f75,intersection(X1,natural_numbers))
| ~ member(f75,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,intersection(complement(f75),complement(non_ordered_pair(f75,f75))))
| ~ little_set(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,hypothesis,
little_set(f75),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_27,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_28,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_29,hypothesis,
member(f75,intersection(intersection(complement(f75),complement(non_ordered_pair(f75,f75))),natural_numbers)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_31,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_33,hypothesis,
member(f75,intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
~ member(X1,complement(non_ordered_pair(X1,X2))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_23]) ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM011-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n022.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 00:05:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.98/1.90 % Version : CSE_E---1.7
% 1.98/1.90 % Problem : theBenchmark.p
% 1.98/1.90 % SZS status Unsatisfiable for theBenchmark.p
% 1.98/1.90 % SZS output start CNFRefutation
% See solution above
% 1.98/1.90 % Total time : 1.375s
%------------------------------------------------------------------------------