TSTP Solution File: SET077-6 by ConnectPP---0.2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : SET077-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n002.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 : Wed Mar 6 09:18:41 EST 2024
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET077-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Mar 3 20:26:26 EST 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.42 % SZS output start Proof for theBenchmark
% 0.19/0.42
% 0.19/0.42 % Problem matrix:
% 0.19/0.42 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.42 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.42 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.42 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( not_subclass_element(__eqx_0, __eqx_1) = not_subclass_element(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( first(__eqx_0) = first(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( second(__eqx_0) = second(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( complement(__eqx_0) = complement(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( symmetric_difference(__eqx_0, __eqx_1) = symmetric_difference(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( restrict(__eqx_0, __eqx_1, __eqx_2) = restrict(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.19/0.42 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( domain_of(__eqx_0) = domain_of(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( rotate(__eqx_0) = rotate(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( flip(__eqx_0) = flip(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( inverse(__eqx_0) = inverse(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( range_of(__eqx_0) = range_of(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( domain(__eqx_0, __eqx_1, __eqx_2) = domain(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.19/0.42 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( range(__eqx_0, __eqx_1, __eqx_2) = range(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.19/0.42 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( image(__eqx_0, __eqx_1) = image(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( successor(__eqx_0) = successor(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( sum_class(__eqx_0) = sum_class(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( power_class(__eqx_0) = power_class(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( compose(__eqx_0, __eqx_1) = compose(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( regular(__eqx_0) = regular(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 0.19/0.42 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( diagonalise(__eqx_0) = diagonalise(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( cantor(__eqx_0) = cantor(__eqy_0)) )).
% 0.19/0.42 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( not_homomorphism1(__eqx_0, __eqx_1, __eqx_2) = not_homomorphism1(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.19/0.42 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( not_homomorphism2(__eqx_0, __eqx_1, __eqx_2) = not_homomorphism2(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.19/0.42 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subclass(__eqx_0, __eqx_1) | subclass(__eqy_0, __eqy_1) )).
% 0.19/0.42 cnf(matrix-34, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 0.19/0.42 cnf(matrix-35, plain, ( ( __eqx_0 != __eqy_0) | ~inductive(__eqx_0) | inductive(__eqy_0) )).
% 0.19/0.42 cnf(matrix-36, plain, ( ( __eqx_0 != __eqy_0) | ~single_valued_class(__eqx_0) | single_valued_class(__eqy_0) )).
% 0.19/0.42 cnf(matrix-37, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 0.19/0.42 cnf(matrix-38, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one(__eqx_0) | one_to_one(__eqy_0) )).
% 0.19/0.42 cnf(matrix-39, plain, ( ( __eqx_0 != __eqy_0) | ~operation(__eqx_0) | operation(__eqy_0) )).
% 0.19/0.42 cnf(matrix-40, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~compatible(__eqx_0, __eqx_1, __eqx_2) | compatible(__eqy_0, __eqy_1, __eqy_2) )).
% 0.19/0.42 cnf(matrix-41, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~homomorphism(__eqx_0, __eqx_1, __eqx_2) | homomorphism(__eqy_0, __eqy_1, __eqy_2) )).
% 0.19/0.42 cnf(matrix-42, plain, ( ~subclass(X, Y) | ~member(U, X) | member(U, Y) )).
% 0.19/0.42 cnf(matrix-43, plain, ( member(not_subclass_element(X, Y), X) | subclass(X, Y) )).
% 0.19/0.42 cnf(matrix-44, plain, ( ~member(not_subclass_element(X, Y), Y) | subclass(X, Y) )).
% 0.19/0.42 cnf(matrix-45, plain, ( subclass(X, universal_class) )).
% 0.19/0.42 cnf(matrix-46, plain, ( ( X != Y) | subclass(X, Y) )).
% 0.19/0.42 cnf(matrix-47, plain, ( ( X != Y) | subclass(Y, X) )).
% 0.19/0.42 cnf(matrix-48, plain, ( ~subclass(X, Y) | ~subclass(Y, X) | ( X = Y) )).
% 0.19/0.42 cnf(matrix-49, plain, ( ~member(U, unordered_pair(X, Y)) | ( U = X) | ( U = Y) )).
% 0.19/0.42 cnf(matrix-50, plain, ( ~member(X, universal_class) | member(X, unordered_pair(X, Y)) )).
% 0.19/0.42 cnf(matrix-51, plain, ( ~member(Y, universal_class) | member(Y, unordered_pair(X, Y)) )).
% 0.19/0.42 cnf(matrix-52, plain, ( member(unordered_pair(X, Y), universal_class) )).
% 0.19/0.42 cnf(matrix-53, plain, ( ( unordered_pair(X, X) = singleton(X)) )).
% 0.19/0.42 cnf(matrix-54, plain, ( ( unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) )).
% 0.19/0.42 cnf(matrix-55, plain, ( ~member(ordered_pair(U, V), cross_product(X, Y)) | member(U, X) )).
% 0.19/0.42 cnf(matrix-56, plain, ( ~member(ordered_pair(U, V), cross_product(X, Y)) | member(V, Y) )).
% 0.19/0.42 cnf(matrix-57, plain, ( ~member(U, X) | ~member(V, Y) | member(ordered_pair(U, V), cross_product(X, Y)) )).
% 0.19/0.42 cnf(matrix-58, plain, ( ~member(Z, cross_product(X, Y)) | ( ordered_pair(first(Z), second(Z)) = Z) )).
% 0.19/0.42 cnf(matrix-59, plain, ( subclass(element_relation, cross_product(universal_class, universal_class)) )).
% 0.19/0.42 cnf(matrix-60, plain, ( ~member(ordered_pair(X, Y), element_relation) | member(X, Y) )).
% 0.19/0.42 cnf(matrix-61, plain, ( ~member(ordered_pair(X, Y), cross_product(universal_class, universal_class)) | ~member(X, Y) | member(ordered_pair(X, Y), element_relation) )).
% 0.19/0.42 cnf(matrix-62, plain, ( ~member(Z, intersection(X, Y)) | member(Z, X) )).
% 0.19/0.42 cnf(matrix-63, plain, ( ~member(Z, intersection(X, Y)) | member(Z, Y) )).
% 0.19/0.42 cnf(matrix-64, plain, ( ~member(Z, X) | ~member(Z, Y) | member(Z, intersection(X, Y)) )).
% 0.19/0.42 cnf(matrix-65, plain, ( ~member(Z, complement(X)) | ~member(Z, X) )).
% 0.19/0.42 cnf(matrix-66, plain, ( ~member(Z, universal_class) | member(Z, complement(X)) | member(Z, X) )).
% 0.19/0.42 cnf(matrix-67, plain, ( ( complement(intersection(complement(X), complement(Y))) = union(X, Y)) )).
% 0.19/0.42 cnf(matrix-68, plain, ( ( intersection(complement(intersection(X, Y)), complement(intersection(complement(X), complement(Y)))) = symmetric_difference(X, Y)) )).
% 0.19/0.42 cnf(matrix-69, plain, ( ( intersection(Xr, cross_product(X, Y)) = restrict(Xr, X, Y)) )).
% 0.19/0.42 cnf(matrix-70, plain, ( ( intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y)) )).
% 0.19/0.42 cnf(matrix-71, plain, ( ( restrict(X, singleton(Z), universal_class) != null_class) | ~member(Z, domain_of(X)) )).
% 0.19/0.42 cnf(matrix-72, plain, ( ~member(Z, universal_class) | ( restrict(X, singleton(Z), universal_class) = null_class) | member(Z, domain_of(X)) )).
% 0.19/0.42 cnf(matrix-73, plain, ( subclass(rotate(X), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.42 cnf(matrix-74, plain, ( ~member(ordered_pair(ordered_pair(U, V), W), rotate(X)) | member(ordered_pair(ordered_pair(V, W), U), X) )).
% 0.19/0.42 cnf(matrix-75, plain, ( ~member(ordered_pair(ordered_pair(V, W), U), X) | ~member(ordered_pair(ordered_pair(U, V), W), cross_product(cross_product(universal_class, universal_class), universal_class)) | member(ordered_pair(ordered_pair(U, V), W), rotate(X)) )).
% 0.19/0.42 cnf(matrix-76, plain, ( subclass(flip(X), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.19/0.42 cnf(matrix-77, plain, ( ~member(ordered_pair(ordered_pair(U, V), W), flip(X)) | member(ordered_pair(ordered_pair(V, U), W), X) )).
% 0.19/0.42 cnf(matrix-78, plain, ( ~member(ordered_pair(ordered_pair(V, U), W), X) | ~member(ordered_pair(ordered_pair(U, V), W), cross_product(cross_product(universal_class, universal_class), universal_class)) | member(ordered_pair(ordered_pair(U, V), W), flip(X)) )).
% 0.19/0.42 cnf(matrix-79, plain, ( ( domain_of(flip(cross_product(Y, universal_class))) = inverse(Y)) )).
% 0.19/0.42 cnf(matrix-80, plain, ( ( domain_of(inverse(Z)) = range_of(Z)) )).
% 0.19/0.42 cnf(matrix-81, plain, ( ( first(not_subclass_element(restrict(Z, X, singleton(Y)), null_class)) = domain(Z, X, Y)) )).
% 0.19/0.42 cnf(matrix-82, plain, ( ( second(not_subclass_element(restrict(Z, singleton(X), Y), null_class)) = range(Z, X, Y)) )).
% 0.19/0.42 cnf(matrix-83, plain, ( ( range_of(restrict(Xr, X, universal_class)) = image(Xr, X)) )).
% 0.19/0.42 cnf(matrix-84, plain, ( ( union(X, singleton(X)) = successor(X)) )).
% 0.19/0.42 cnf(matrix-85, plain, ( subclass(successor_relation, cross_product(universal_class, universal_class)) )).
% 0.19/0.42 cnf(matrix-86, plain, ( ~member(ordered_pair(X, Y), successor_relation) | ( successor(X) = Y) )).
% 0.19/0.42 cnf(matrix-87, plain, ( ( successor(X) != Y) | ~member(ordered_pair(X, Y), cross_product(universal_class, universal_class)) | member(ordered_pair(X, Y), successor_relation) )).
% 0.19/0.42 cnf(matrix-88, plain, ( ~inductive(X) | member(null_class, X) )).
% 0.19/0.42 cnf(matrix-89, plain, ( ~inductive(X) | subclass(image(successor_relation, X), X) )).
% 0.19/0.42 cnf(matrix-90, plain, ( ~member(null_class, X) | ~subclass(image(successor_relation, X), X) | inductive(X) )).
% 0.19/0.42 cnf(matrix-91, plain, ( inductive(omega) )).
% 0.19/0.42 cnf(matrix-92, plain, ( ~inductive(Y) | subclass(omega, Y) )).
% 0.19/0.42 cnf(matrix-93, plain, ( member(omega, universal_class) )).
% 0.19/0.42 cnf(matrix-94, plain, ( ( domain_of(restrict(element_relation, universal_class, X)) = sum_class(X)) )).
% 0.19/0.42 cnf(matrix-95, plain, ( ~member(X, universal_class) | member(sum_class(X), universal_class) )).
% 0.19/0.42 cnf(matrix-96, plain, ( ( complement(image(element_relation, complement(X))) = power_class(X)) )).
% 0.19/0.42 cnf(matrix-97, plain, ( ~member(U, universal_class) | member(power_class(U), universal_class) )).
% 0.19/0.42 cnf(matrix-98, plain, ( subclass(compose(Yr, Xr), cross_product(universal_class, universal_class)) )).
% 0.19/0.42 cnf(matrix-99, plain, ( ~member(ordered_pair(Y, Z), compose(Yr, Xr)) | member(Z, image(Yr, image(Xr, singleton(Y)))) )).
% 0.19/0.42 cnf(matrix-100, plain, ( ~member(Z, image(Yr, image(Xr, singleton(Y)))) | ~member(ordered_pair(Y, Z), cross_product(universal_class, universal_class)) | member(ordered_pair(Y, Z), compose(Yr, Xr)) )).
% 0.19/0.42 cnf(matrix-101, plain, ( ~single_valued_class(X) | subclass(compose(X, inverse(X)), identity_relation) )).
% 0.19/0.42 cnf(matrix-102, plain, ( ~subclass(compose(X, inverse(X)), identity_relation) | single_valued_class(X) )).
% 0.19/0.42 cnf(matrix-103, plain, ( ~function(Xf) | subclass(Xf, cross_product(universal_class, universal_class)) )).
% 0.19/0.42 cnf(matrix-104, plain, ( ~function(Xf) | subclass(compose(Xf, inverse(Xf)), identity_relation) )).
% 0.19/0.42 cnf(matrix-105, plain, ( ~subclass(Xf, cross_product(universal_class, universal_class)) | ~subclass(compose(Xf, inverse(Xf)), identity_relation) | function(Xf) )).
% 0.19/0.42 cnf(matrix-106, plain, ( ~function(Xf) | ~member(X, universal_class) | member(image(Xf, X), universal_class) )).
% 0.19/0.42 cnf(matrix-107, plain, ( ( X = null_class) | member(regular(X), X) )).
% 0.19/0.42 cnf(matrix-108, plain, ( ( X = null_class) | ( intersection(X, regular(X)) = null_class) )).
% 0.19/0.42 cnf(matrix-109, plain, ( ( sum_class(image(Xf, singleton(Y))) = apply(Xf, Y)) )).
% 0.19/0.42 cnf(matrix-110, plain, ( function(choice) )).
% 0.19/0.42 cnf(matrix-111, plain, ( ~member(Y, universal_class) | ( Y = null_class) | member(apply(choice, Y), Y) )).
% 0.19/0.42 cnf(matrix-112, plain, ( ~one_to_one(Xf) | function(Xf) )).
% 0.19/0.42 cnf(matrix-113, plain, ( ~one_to_one(Xf) | function(inverse(Xf)) )).
% 0.19/0.42 cnf(matrix-114, plain, ( ~function(inverse(Xf)) | ~function(Xf) | one_to_one(Xf) )).
% 0.19/0.42 cnf(matrix-115, plain, ( ( intersection(cross_product(universal_class, universal_class), intersection(cross_product(universal_class, universal_class), complement(compose(complement(element_relation), inverse(element_relation))))) = subset_relation) )).
% 0.19/0.42 cnf(matrix-116, plain, ( ( intersection(inverse(subset_relation), subset_relation) = identity_relation) )).
% 0.19/0.42 cnf(matrix-117, plain, ( ( complement(domain_of(intersection(Xr, identity_relation))) = diagonalise(Xr)) )).
% 0.19/0.42 cnf(matrix-118, plain, ( ( intersection(domain_of(X), diagonalise(compose(inverse(element_relation), X))) = cantor(X)) )).
% 0.19/0.42 cnf(matrix-119, plain, ( ~operation(Xf) | function(Xf) )).
% 0.19/0.42 cnf(matrix-120, plain, ( ~operation(Xf) | ( cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) = domain_of(Xf)) )).
% 0.19/0.42 cnf(matrix-121, plain, ( ~operation(Xf) | subclass(range_of(Xf), domain_of(domain_of(Xf))) )).
% 0.19/0.42 cnf(matrix-122, plain, ( ~function(Xf) | ( cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))) != domain_of(Xf)) | ~subclass(range_of(Xf), domain_of(domain_of(Xf))) | operation(Xf) )).
% 0.19/0.42 cnf(matrix-123, plain, ( ~compatible(Xh, Xf1, Xf2) | function(Xh) )).
% 0.19/0.42 cnf(matrix-124, plain, ( ~compatible(Xh, Xf1, Xf2) | ( domain_of(domain_of(Xf1)) = domain_of(Xh)) )).
% 0.19/0.42 cnf(matrix-125, plain, ( ~compatible(Xh, Xf1, Xf2) | subclass(range_of(Xh), domain_of(domain_of(Xf2))) )).
% 0.19/0.42 cnf(matrix-126, plain, ( ~function(Xh) | ( domain_of(domain_of(Xf1)) != domain_of(Xh)) | ~subclass(range_of(Xh), domain_of(domain_of(Xf2))) | compatible(Xh, Xf1, Xf2) )).
% 0.19/0.42 cnf(matrix-127, plain, ( ~homomorphism(Xh, Xf1, Xf2) | operation(Xf1) )).
% 0.19/0.42 cnf(matrix-128, plain, ( ~homomorphism(Xh, Xf1, Xf2) | operation(Xf2) )).
% 0.19/0.42 cnf(matrix-129, plain, ( ~homomorphism(Xh, Xf1, Xf2) | compatible(Xh, Xf1, Xf2) )).
% 0.19/0.42 cnf(matrix-130, plain, ( ~homomorphism(Xh, Xf1, Xf2) | ~member(ordered_pair(X, Y), domain_of(Xf1)) | ( apply(Xf2, ordered_pair(apply(Xh, X), apply(Xh, Y))) = apply(Xh, apply(Xf1, ordered_pair(X, Y)))) )).
% 0.19/0.42 cnf(matrix-131, plain, ( ~operation(Xf1) | ~operation(Xf2) | ~compatible(Xh, Xf1, Xf2) | member(ordered_pair(not_homomorphism1(Xh, Xf1, Xf2), not_homomorphism2(Xh, Xf1, Xf2)), domain_of(Xf1)) | homomorphism(Xh, Xf1, Xf2) )).
% 0.19/0.42 cnf(matrix-132, plain, ( ~operation(Xf1) | ~operation(Xf2) | ~compatible(Xh, Xf1, Xf2) | ( apply(Xf2, ordered_pair(apply(Xh, not_homomorphism1(Xh, Xf1, Xf2)), apply(Xh, not_homomorphism2(Xh, Xf1, Xf2)))) != apply(Xh, apply(Xf1, ordered_pair(not_homomorphism1(Xh, Xf1, Xf2), not_homomorphism2(Xh, Xf1, Xf2))))) | homomorphism(Xh, Xf1, Xf2) )).
% 0.19/0.42 cnf(matrix-133, plain, ( ~member(singleton(x), universal_class) )).
% 0.19/0.42
% 0.19/0.42 % Proof stack:
% 0.19/0.42 cnf(proof-stack, plain,
% 0.19/0.42 proof_stack(
% 0.19/0.42 start(133),
% 0.19/0.42 left_branch(0, 34, 3, 2),
% 0.19/0.42 left_branch(0, 53, 0, 3),
% 0.19/0.42 right_branch(3),
% 0.19/0.42 left_branch(0, 52, 0, 4),
% 0.19/0.42 right_branch(4),
% 0.19/0.42 left_branch(0, 0, 0, 5),
% 0.19/0.42 right_branch(5),
% 0.19/0.42 right_branch(2)
% 0.19/0.42 )).
% 0.19/0.42 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------