%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET553-6 : 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 : n022.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 05:07:59 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.73s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 11 unt; 3 nHn; 8 RR)
% Number of literals : 27 ( 7 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cantor_class,axiom,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cantor_class) ).
cnf(diagonalisation,axiom,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',diagonalisation) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(prove_cantor_class_alternate_defn_1,negated_conjecture,
~ subclass(cantor(x),domain_of(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cantor_class_alternate_defn_1) ).
cnf(c_0_7,axiom,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
cantor_class ).
cnf(c_0_8,axiom,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
diagonalisation ).
cnf(c_0_9,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_10,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_11,plain,
intersection(domain_of(X1),complement(domain_of(intersection(compose(domain_of(flip(cross_product(element_relation,universal_class))),X1),identity_relation)))) = cantor(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_12,plain,
( member(X1,domain_of(X2))
| ~ member(X1,cantor(X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_14,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_15,plain,
( member(not_subclass_element(cantor(X1),X2),domain_of(X1))
| subclass(cantor(X1),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ subclass(cantor(x),domain_of(x)),
prove_cantor_class_alternate_defn_1 ).
cnf(c_0_17,plain,
subclass(cantor(X1),domain_of(X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET553-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.14/0.31 % Computer : n022.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 02:27:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.34/1.73 % Version : CSE_E---1.7
% 1.34/1.73 % Problem : theBenchmark.p
% 1.34/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.73 % SZS output start CNFRefutation
% See solution above
% 1.34/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------