%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET090-7 : 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 : n020.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 05:07:15 PM UTC 2026
% Result : Unsatisfiable 1.86s 1.90s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 11 unt; 4 nHn; 17 RR)
% Number of literals : 37 ( 28 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(singleton_identified_by_element2,axiom,
( X1 = X2
| singleton(X1) != singleton(X2)
| ~ member(X2,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_member_of_singleton_is_unique_1,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_1) ).
cnf(member_exists4,axiom,
( singleton(member_of(X1)) = X1
| member_of(X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists4) ).
cnf(prove_member_of_singleton_is_unique_2,negated_conjecture,
member_of(singleton(u)) != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_2) ).
cnf(member_exists2,axiom,
( singleton(member_of(singleton(X1))) = singleton(X1)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists2) ).
cnf(c_0_6,axiom,
( X1 = X2
| singleton(X1) != singleton(X2)
| ~ member(X2,universal_class) ),
singleton_identified_by_element2 ).
cnf(c_0_7,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_8,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X2)
| ~ member(X2,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_9,negated_conjecture,
member(u,universal_class),
prove_member_of_singleton_is_unique_1 ).
cnf(c_0_10,axiom,
( singleton(member_of(X1)) = X1
| member_of(X1) = X1 ),
member_exists4 ).
cnf(c_0_11,negated_conjecture,
( X1 = u
| unordered_pair(X1,X1) != unordered_pair(u,u) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( member_of(X1) = X1
| unordered_pair(member_of(X1),member_of(X1)) = X1 ),
inference(rw,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_13,negated_conjecture,
member_of(singleton(u)) != u,
prove_member_of_singleton_is_unique_2 ).
cnf(c_0_14,axiom,
( singleton(member_of(singleton(X1))) = singleton(X1)
| ~ member(X1,universal_class) ),
member_exists2 ).
cnf(c_0_15,negated_conjecture,
( member_of(X1) = u
| member_of(X1) = X1
| X1 != unordered_pair(u,u) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
member_of(unordered_pair(u,u)) != u,
inference(rw,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_17,plain,
( unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) = unordered_pair(X1,X1)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_7]),c_0_7]),c_0_7]) ).
cnf(c_0_18,negated_conjecture,
member_of(unordered_pair(u,u)) = unordered_pair(u,u),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
unordered_pair(unordered_pair(u,u),unordered_pair(u,u)) = unordered_pair(u,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_9])]) ).
cnf(c_0_20,negated_conjecture,
unordered_pair(u,u) != u,
inference(rw,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET090-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:09:50 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.86/1.90 % Version : CSE_E---1.7
% 1.86/1.90 % Problem : theBenchmark.p
% 1.86/1.90 % SZS status Unsatisfiable for theBenchmark.p
% 1.86/1.90 % SZS output start CNFRefutation
% See solution above
% 1.86/1.91 % Total time : 1.372s
%------------------------------------------------------------------------------