%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET105-7 : 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 : n027.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 05:07:20 PM UTC 2026
% Result : Unsatisfiable 1.89s 1.91s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 17 unt; 5 nHn; 10 RR)
% Number of literals : 29 ( 17 equ; 9 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 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(prove_property_3_of_ordered_pair_1,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_1) ).
cnf(null_unordered_pair,axiom,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
cnf(prove_property_3_of_ordered_pair_3,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_3) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(prove_property_3_of_ordered_pair_2,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_2) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(c_0_8,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_9,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_10,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
prove_property_3_of_ordered_pair_1 ).
cnf(c_0_11,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_8,c_0_9]),c_0_9]) ).
cnf(c_0_12,negated_conjecture,
unordered_pair(null_class,unordered_pair(null_class,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_10,c_0_9]),c_0_11]) ).
cnf(c_0_13,axiom,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
null_unordered_pair ).
cnf(c_0_14,negated_conjecture,
~ member(y,universal_class),
prove_property_3_of_ordered_pair_3 ).
cnf(c_0_15,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_16,negated_conjecture,
unordered_pair(unordered_pair(null_class,x),unordered_pair(x,x)) != unordered_pair(null_class,unordered_pair(null_class,null_class)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_15]) ).
cnf(c_0_17,negated_conjecture,
~ member(x,universal_class),
prove_property_3_of_ordered_pair_2 ).
cnf(c_0_18,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(c_0_19,negated_conjecture,
unordered_pair(null_class,unordered_pair(null_class,x)) != unordered_pair(null_class,unordered_pair(null_class,null_class)),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_17]),c_0_15]) ).
cnf(c_0_20,plain,
( unordered_pair(X2,X1) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET105-7 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:11:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.89/1.91 % Version : CSE_E---1.7
% 1.89/1.91 % Problem : theBenchmark.p
% 1.89/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.89/1.91 % SZS output start CNFRefutation
% See solution above
% 1.89/1.91 % Total time : 1.372s
%------------------------------------------------------------------------------