%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET479-6 : 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 : n002.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 05:07:54 PM UTC 2026
% Result : Unsatisfiable 3.37s 3.32s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 12 unt; 0 nHn; 18 RR)
% Number of literals : 36 ( 5 equ; 15 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 5 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(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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(definition_of_domain_relation1,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',definition_of_domain_relation1) ).
cnf(definition_of_domain_relation3,axiom,
( member(ordered_pair(X1,domain_of(X1)),domain_relation)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-1.ax',definition_of_domain_relation3) ).
cnf(prove_replacement_property1_2,negated_conjecture,
~ member(domain_of(x),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_replacement_property1_2) ).
cnf(prove_replacement_property1_1,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_replacement_property1_1) ).
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,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
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,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_13,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
definition_of_domain_relation1 ).
cnf(c_0_14,plain,
( member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,domain_relation) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( member(ordered_pair(X1,domain_of(X1)),domain_relation)
| ~ member(X1,universal_class) ),
definition_of_domain_relation3 ).
cnf(c_0_17,plain,
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),domain_relation) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),domain_relation)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
~ member(domain_of(x),universal_class),
prove_replacement_property1_2 ).
cnf(c_0_20,plain,
( member(domain_of(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
member(x,universal_class),
prove_replacement_property1_1 ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.22 % Problem : SET479-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.02/0.22 % 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
% 0.11/0.44 % Computer : n002.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8042.1875MB
% 0.11/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.44 % CPULimit : 300
% 0.11/0.44 % WCLimit : 300
% 0.11/0.44 % DateTime : Tue May 5 02:25:01 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 3.37/3.32 % Version : CSE_E---1.7
% 3.37/3.32 % Problem : theBenchmark.p
% 3.37/3.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.37/3.32 % SZS output start CNFRefutation
% See solution above
% 3.37/3.33 % Total time : 2.384s
%------------------------------------------------------------------------------