%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET245-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 05:07:39 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.82s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 11 unt; 4 nHn; 14 RR)
% Number of literals : 37 ( 12 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(prove_restriction_with_null_class1_1,negated_conjecture,
restrict(null_class,x,y) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_with_null_class1_1) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(c_0_7,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_8,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_9,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_10,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_11,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_16,negated_conjecture,
restrict(null_class,x,y) != null_class,
prove_restriction_with_null_class1_1 ).
cnf(c_0_17,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_18,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_14]),c_0_11]) ).
cnf(c_0_19,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
intersection(null_class,cross_product(x,y)) != null_class,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
intersection(null_class,X1) = null_class,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.18 % Problem : SET245-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.07/0.18 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.10/0.42 % Computer : n012.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8042.1875MB
% 0.10/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Tue May 5 02:15:31 EDT 2026
% 0.10/0.42 % CPUTime :
% 0.12/0.43 % start to proof: theBenchmark
% 1.23/1.82 % Version : CSE_E---1.7
% 1.23/1.82 % Problem : theBenchmark.p
% 1.23/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 1.23/1.82 % SZS output start CNFRefutation
% See solution above
% 1.23/1.82 % Total time : 1.366s
%------------------------------------------------------------------------------