%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM045-1 : 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 : n026.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 04:52:46 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 45 ( 20 unt; 7 nHn; 34 RR)
% Number of literals : 77 ( 10 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(irreflexive2,axiom,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
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(prove_irreflexive_class_property7_2,negated_conjecture,
~ irreflexive(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property7_2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_irreflexive_class_property7_1,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property7_1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(c_0_14,axiom,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
irreflexive2 ).
cnf(c_0_15,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_16,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_17,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_18,negated_conjecture,
~ irreflexive(x,y),
prove_irreflexive_class_property7_2 ).
cnf(c_0_19,plain,
( irreflexive(X1,X2)
| ~ subclass(intersection(X1,cross_product(X2,X2)),complement(identity_relation)) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_21,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_22,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) = null_class,
prove_irreflexive_class_property7_1 ).
cnf(c_0_24,negated_conjecture,
~ subclass(intersection(x,cross_product(y,y)),complement(identity_relation)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_26,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_29,negated_conjecture,
intersection(intersection(x,identity_relation),cross_product(y,y)) = null_class,
inference(rw,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_30,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_31,negated_conjecture,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,cross_product(y,y))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( member(X1,null_class)
| ~ member(X1,cross_product(y,y))
| ~ member(X1,intersection(x,identity_relation)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),cross_product(y,y)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_32]),c_0_22]) ).
cnf(c_0_36,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_37,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_38,negated_conjecture,
~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,identity_relation)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),x),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),complement(identity_relation)),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_41,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_42,negated_conjecture,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_43,negated_conjecture,
~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_39])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM045-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n026.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:08:38 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------