%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM030-1 : 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 : n028.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 04:52:45 PM UTC 2026
% Result : Unsatisfiable 25.95s 15.79s
% Output : CNFRefutation 26.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 17 unt; 6 nHn; 21 RR)
% Number of literals : 55 ( 9 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_symmetrization_property3_1,negated_conjecture,
symmetrization_of(x) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetrization_property3_1) ).
cnf(symmetrization,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(prove_symmetrization_property3_2,negated_conjecture,
~ subclass(inverse(x),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetrization_property3_2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
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(c_0_12,negated_conjecture,
symmetrization_of(x) = x,
prove_symmetrization_property3_1 ).
cnf(c_0_13,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
symmetrization ).
cnf(c_0_14,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_15,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_16,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_17,negated_conjecture,
complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_18,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_19,negated_conjecture,
( member(X1,intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))
| member(X1,x)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_21,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_22,negated_conjecture,
~ subclass(inverse(x),x),
prove_symmetrization_property3_2 ).
cnf(c_0_23,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_24,negated_conjecture,
( member(X1,complement(domain_of(flip(cross_product(x,universal_class)))))
| member(X1,x)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(rw,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_27,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_28,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_29,negated_conjecture,
( member(X1,x)
| ~ member(X1,domain_of(flip(cross_product(x,universal_class)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),x),domain_of(flip(cross_product(x,universal_class)))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
~ member(not_subclass_element(domain_of(flip(cross_product(x,universal_class))),x),x),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM030-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 00:07:01 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 25.95/15.79 % Version : CSE_E---1.7
% 25.95/15.79 % Problem : theBenchmark.p
% 25.95/15.79 % SZS status Unsatisfiable for theBenchmark.p
% 25.95/15.79 % SZS output start CNFRefutation
% See solution above
% 26.15/15.90 % Total time : 11.396s
%------------------------------------------------------------------------------