%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET103-7 : 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 : n023.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 05:07:19 PM UTC 2026
% Result : Unsatisfiable 1.51s 2.03s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 12 unt; 3 nHn; 7 RR)
% Number of literals : 18 ( 12 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(singleton_is_null_class,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(prove_property_1_of_ordered_pair_1,negated_conjecture,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_1) ).
cnf(prove_property_1_of_ordered_pair_2,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_1_of_ordered_pair_2) ).
cnf(c_0_5,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_6,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_7,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
singleton_is_null_class ).
cnf(c_0_8,negated_conjecture,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
prove_property_1_of_ordered_pair_1 ).
cnf(c_0_9,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ member(y,universal_class),
prove_property_1_of_ordered_pair_2 ).
cnf(c_0_11,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_12,negated_conjecture,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_6]),c_0_9]) ).
cnf(c_0_13,negated_conjecture,
unordered_pair(y,y) = null_class,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : SET103-7 : 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
% 0.13/0.46 % Computer : n023.cluster.edu
% 0.13/0.46 % Model : x86_64 x86_64
% 0.13/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.46 % Memory : 8042.1875MB
% 0.13/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.46 % CPULimit : 300
% 0.13/0.46 % WCLimit : 300
% 0.13/0.46 % DateTime : Tue May 5 02:11:09 EDT 2026
% 0.13/0.46 % CPUTime :
% 0.13/0.47 % start to proof: theBenchmark
% 1.51/2.03 % Version : CSE_E---1.7
% 1.51/2.03 % Problem : theBenchmark.p
% 1.51/2.03 % SZS status Unsatisfiable for theBenchmark.p
% 1.51/2.03 % SZS output start CNFRefutation
% See solution above
% 1.51/2.03 % Total time : 1.401s
%------------------------------------------------------------------------------