%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM066-1 : 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 04:52:48 PM UTC 2026
% Result : Unsatisfiable 13.31s 10.65s
% Output : CNFRefutation 13.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 18 unt; 0 nHn; 31 RR)
% Number of literals : 83 ( 5 equ; 51 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 7 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(element_relation3,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',element_relation3) ).
cnf(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(well_ordering3,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).
cnf(prove_corollary_to_well_ordering_property1_1,negated_conjecture,
well_ordering(element_relation,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_1) ).
cnf(well_ordering5,axiom,
( ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,least(X1,X3)),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',well_ordering5) ).
cnf(prove_corollary_to_well_ordering_property1_2,negated_conjecture,
subclass(u,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_2) ).
cnf(prove_corollary_to_well_ordering_property1_3,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_3) ).
cnf(prove_corollary_to_well_ordering_property1_4,negated_conjecture,
member(v,least(element_relation,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_4) ).
cnf(c_0_12,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_13,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_14,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2) ),
element_relation3 ).
cnf(c_0_15,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_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_17,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
well_ordering3 ).
cnf(c_0_20,negated_conjecture,
well_ordering(element_relation,y),
prove_corollary_to_well_ordering_property1_1 ).
cnf(c_0_21,axiom,
( ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,least(X1,X3)),X1) ),
well_ordering5 ).
cnf(c_0_22,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
| ~ member(X1,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_23,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_24,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( member(least(element_relation,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
subclass(u,y),
prove_corollary_to_well_ordering_property1_2 ).
cnf(c_0_27,plain,
( ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ well_ordering(X1,X2)
| ~ member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(least(X1,X3),least(X1,X3)))),X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
| ~ member(X2,universal_class)
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( member(least(element_relation,u),u)
| ~ member(X1,u) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
member(v,u),
prove_corollary_to_well_ordering_property1_3 ).
cnf(c_0_31,plain,
( ~ well_ordering(element_relation,X1)
| ~ member(least(element_relation,X2),universal_class)
| ~ member(X3,least(element_relation,X2))
| ~ member(X3,X2)
| ~ subclass(X2,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
member(least(element_relation,u),u),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(least(element_relation,X1),universal_class)
| ~ member(X2,least(element_relation,X1))
| ~ member(X2,X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_34,negated_conjecture,
member(least(element_relation,u),universal_class),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X1,least(element_relation,u))
| ~ member(X1,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_34])]) ).
cnf(c_0_36,negated_conjecture,
member(v,least(element_relation,u)),
prove_corollary_to_well_ordering_property1_4 ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.22 % Problem : NUM066-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.03/0.22 % 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
% 0.12/0.45 % Computer : n002.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8042.1875MB
% 0.12/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Tue May 5 00:10:01 EDT 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.46 % start to proof: theBenchmark
% 13.31/10.65 % Version : CSE_E---1.7
% 13.31/10.65 % Problem : theBenchmark.p
% 13.31/10.65 % SZS status Unsatisfiable for theBenchmark.p
% 13.31/10.65 % SZS output start CNFRefutation
% See solution above
% 13.42/10.70 % Total time : 8.452s
%------------------------------------------------------------------------------