%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM042-1 : 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 : n020.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 1.61s 1.85s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 18 unt; 2 nHn; 20 RR)
% Number of literals : 44 ( 8 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_irreflexive_class_property4_2,negated_conjecture,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_2) ).
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(irreflexive2,axiom,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
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(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(prove_irreflexive_class_property4_1,negated_conjecture,
subclass(x,complement(identity_relation)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_1) ).
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(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(c_0_11,negated_conjecture,
~ irreflexive(x,domain_of(symmetrization_of(x))),
prove_irreflexive_class_property4_2 ).
cnf(c_0_12,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
symmetrization ).
cnf(c_0_13,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_14,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_15,axiom,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
irreflexive2 ).
cnf(c_0_16,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_17,negated_conjecture,
~ irreflexive(x,domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]) ).
cnf(c_0_18,plain,
( irreflexive(X1,X2)
| ~ subclass(intersection(X1,cross_product(X2,X2)),complement(identity_relation)) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ subclass(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_21,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_22,negated_conjecture,
subclass(x,complement(identity_relation)),
prove_irreflexive_class_property4_1 ).
cnf(c_0_23,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_24,negated_conjecture,
~ member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),complement(identity_relation)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,complement(identity_relation))
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_27,negated_conjecture,
member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),x),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM042-1 : 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
% 0.15/0.32 % Computer : n020.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:07:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.20/0.37 % start to proof: theBenchmark
% 1.61/1.85 % Version : CSE_E---1.7
% 1.61/1.85 % Problem : theBenchmark.p
% 1.61/1.85 % SZS status Unsatisfiable for theBenchmark.p
% 1.61/1.85 % SZS output start CNFRefutation
% See solution above
% 1.61/1.85 % Total time : 1.410s
%------------------------------------------------------------------------------