TSTP Solution File: SET055-7 by ConnectPP---0.3.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET055-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n021.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 : Mon Mar 25 14:30:56 EDT 2024
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET055-7 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n021.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 : Wed Mar 20 21:22:48 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% 0.20/0.43
% 0.20/0.43 % Problem matrix:
% 0.20/0.43 cnf(matrix-0, plain, ( ~equalish(X, Y) | equalish(Y, X) )).
% 0.20/0.43 cnf(matrix-1, plain, ( ~equalish(X, Y) | ~equalish(Y, Z) | equalish(X, Z) )).
% 0.20/0.43 cnf(matrix-2, plain, ( ~equalish(D, E) | equalish(apply(D, F), apply(E, F)) )).
% 0.20/0.43 cnf(matrix-3, plain, ( ~equalish(G, H) | equalish(apply(I, G), apply(I, H)) )).
% 0.20/0.43 cnf(matrix-4, plain, ( ~equalish(J, K) | equalish(cantor(J), cantor(K)) )).
% 0.20/0.43 cnf(matrix-5, plain, ( ~equalish(L, M) | equalish(complement(L), complement(M)) )).
% 0.20/0.43 cnf(matrix-6, plain, ( ~equalish(N, O) | equalish(compose(N, P), compose(O, P)) )).
% 0.20/0.43 cnf(matrix-7, plain, ( ~equalish(Q, R) | equalish(compose(S, Q), compose(S, R)) )).
% 0.20/0.43 cnf(matrix-8, plain, ( ~equalish(T, U) | equalish(cross_product(T, V), cross_product(U, V)) )).
% 0.20/0.43 cnf(matrix-9, plain, ( ~equalish(W, X) | equalish(cross_product(Y, W), cross_product(Y, X)) )).
% 0.20/0.43 cnf(matrix-10, plain, ( ~equalish(Z, A1) | equalish(diagonalise(Z), diagonalise(A1)) )).
% 0.20/0.43 cnf(matrix-11, plain, ( ~equalish(B1, C1) | equalish(symmetric_difference(B1, D1), symmetric_difference(C1, D1)) )).
% 0.20/0.43 cnf(matrix-12, plain, ( ~equalish(E1, F1) | equalish(symmetric_difference(G1, E1), symmetric_difference(G1, F1)) )).
% 0.20/0.43 cnf(matrix-13, plain, ( ~equalish(H1, I1) | equalish(domain(H1, J1, K1), domain(I1, J1, K1)) )).
% 0.20/0.43 cnf(matrix-14, plain, ( ~equalish(L1, M1) | equalish(domain(N1, L1, O1), domain(N1, M1, O1)) )).
% 0.20/0.43 cnf(matrix-15, plain, ( ~equalish(P1, Q1) | equalish(domain(R1, S1, P1), domain(R1, S1, Q1)) )).
% 0.20/0.43 cnf(matrix-16, plain, ( ~equalish(T1, U1) | equalish(domain_of(T1), domain_of(U1)) )).
% 0.20/0.43 cnf(matrix-17, plain, ( ~equalish(V1, W1) | equalish(first(V1), first(W1)) )).
% 0.20/0.43 cnf(matrix-18, plain, ( ~equalish(X1, Y1) | equalish(flip(X1), flip(Y1)) )).
% 0.20/0.43 cnf(matrix-19, plain, ( ~equalish(Z1, A2) | equalish(image(Z1, B2), image(A2, B2)) )).
% 0.20/0.43 cnf(matrix-20, plain, ( ~equalish(C2, D2) | equalish(image(E2, C2), image(E2, D2)) )).
% 0.20/0.43 cnf(matrix-21, plain, ( ~equalish(F2, G2) | equalish(intersection(F2, H2), intersection(G2, H2)) )).
% 0.20/0.43 cnf(matrix-22, plain, ( ~equalish(I2, J2) | equalish(intersection(K2, I2), intersection(K2, J2)) )).
% 0.20/0.43 cnf(matrix-23, plain, ( ~equalish(L2, M2) | equalish(inverse(L2), inverse(M2)) )).
% 0.20/0.43 cnf(matrix-24, plain, ( ~equalish(N2, O2) | equalish(not_homomorphism1(N2, P2, Q2), not_homomorphism1(O2, P2, Q2)) )).
% 0.20/0.43 cnf(matrix-25, plain, ( ~equalish(R2, S2) | equalish(not_homomorphism1(T2, R2, U2), not_homomorphism1(T2, S2, U2)) )).
% 0.20/0.43 cnf(matrix-26, plain, ( ~equalish(V2, W2) | equalish(not_homomorphism1(X2, Y2, V2), not_homomorphism1(X2, Y2, W2)) )).
% 0.20/0.43 cnf(matrix-27, plain, ( ~equalish(Z2, A3) | equalish(not_homomorphism2(Z2, B3, C3), not_homomorphism2(A3, B3, C3)) )).
% 0.20/0.43 cnf(matrix-28, plain, ( ~equalish(D3, E3) | equalish(not_homomorphism2(F3, D3, G3), not_homomorphism2(F3, E3, G3)) )).
% 0.20/0.43 cnf(matrix-29, plain, ( ~equalish(H3, I3) | equalish(not_homomorphism2(J3, K3, H3), not_homomorphism2(J3, K3, I3)) )).
% 0.20/0.43 cnf(matrix-30, plain, ( ~equalish(L3, M3) | equalish(not_subclass_element(L3, N3), not_subclass_element(M3, N3)) )).
% 0.20/0.43 cnf(matrix-31, plain, ( ~equalish(O3, P3) | equalish(not_subclass_element(Q3, O3), not_subclass_element(Q3, P3)) )).
% 0.20/0.43 cnf(matrix-32, plain, ( ~equalish(R3, S3) | equalish(ordered_pair(R3, T3), ordered_pair(S3, T3)) )).
% 0.20/0.43 cnf(matrix-33, plain, ( ~equalish(U3, V3) | equalish(ordered_pair(W3, U3), ordered_pair(W3, V3)) )).
% 0.20/0.43 cnf(matrix-34, plain, ( ~equalish(X3, Y3) | equalish(power_class(X3), power_class(Y3)) )).
% 0.20/0.43 cnf(matrix-35, plain, ( ~equalish(Z3, A4) | equalish(range(Z3, B4, C4), range(A4, B4, C4)) )).
% 0.20/0.43 cnf(matrix-36, plain, ( ~equalish(D4, E4) | equalish(range(F4, D4, G4), range(F4, E4, G4)) )).
% 0.20/0.43 cnf(matrix-37, plain, ( ~equalish(H4, I4) | equalish(range(J4, K4, H4), range(J4, K4, I4)) )).
% 0.20/0.43 cnf(matrix-38, plain, ( ~equalish(L4, M4) | equalish(range_of(L4), range_of(M4)) )).
% 0.20/0.43 cnf(matrix-39, plain, ( ~equalish(N4, O4) | equalish(regular(N4), regular(O4)) )).
% 0.20/0.43 cnf(matrix-40, plain, ( ~equalish(P4, Q4) | equalish(restrict(P4, R4, S4), restrict(Q4, R4, S4)) )).
% 0.20/0.43 cnf(matrix-41, plain, ( ~equalish(T4, U4) | equalish(restrict(V4, T4, W4), restrict(V4, U4, W4)) )).
% 0.20/0.43 cnf(matrix-42, plain, ( ~equalish(X4, Y4) | equalish(restrict(Z4, A5, X4), restrict(Z4, A5, Y4)) )).
% 0.20/0.43 cnf(matrix-43, plain, ( ~equalish(B5, C5) | equalish(rotate(B5), rotate(C5)) )).
% 0.20/0.43 cnf(matrix-44, plain, ( ~equalish(D5, E5) | equalish(second(D5), second(E5)) )).
% 0.20/0.43 cnf(matrix-45, plain, ( ~equalish(F5, G5) | equalish(singleton(F5), singleton(G5)) )).
% 0.20/0.43 cnf(matrix-46, plain, ( ~equalish(H5, I5) | equalish(successor(H5), successor(I5)) )).
% 0.20/0.43 cnf(matrix-47, plain, ( ~equalish(J5, K5) | equalish(sum_class(J5), sum_class(K5)) )).
% 0.20/0.43 cnf(matrix-48, plain, ( ~equalish(L5, M5) | equalish(union(L5, N5), union(M5, N5)) )).
% 0.20/0.43 cnf(matrix-49, plain, ( ~equalish(O5, P5) | equalish(union(Q5, O5), union(Q5, P5)) )).
% 0.20/0.43 cnf(matrix-50, plain, ( ~equalish(R5, S5) | equalish(unordered_pair(R5, T5), unordered_pair(S5, T5)) )).
% 0.20/0.43 cnf(matrix-51, plain, ( ~equalish(U5, V5) | equalish(unordered_pair(W5, U5), unordered_pair(W5, V5)) )).
% 0.20/0.43 cnf(matrix-52, plain, ( ~equalish(X5, Y5) | ~compatible(X5, Z5, A6) | compatible(Y5, Z5, A6) )).
% 0.20/0.43 cnf(matrix-53, plain, ( ~equalish(B6, C6) | ~compatible(D6, B6, E6) | compatible(D6, C6, E6) )).
% 0.20/0.43 cnf(matrix-54, plain, ( ~equalish(F6, G6) | ~compatible(H6, I6, F6) | compatible(H6, I6, G6) )).
% 0.20/0.43 cnf(matrix-55, plain, ( ~equalish(J6, K6) | ~function(J6) | function(K6) )).
% 0.20/0.43 cnf(matrix-56, plain, ( ~equalish(L6, M6) | ~homomorphism(L6, N6, O6) | homomorphism(M6, N6, O6) )).
% 0.20/0.43 cnf(matrix-57, plain, ( ~equalish(P6, Q6) | ~homomorphism(R6, P6, S6) | homomorphism(R6, Q6, S6) )).
% 0.20/0.43 cnf(matrix-58, plain, ( ~equalish(T6, U6) | ~homomorphism(V6, W6, T6) | homomorphism(V6, W6, U6) )).
% 0.20/0.43 cnf(matrix-59, plain, ( ~equalish(X6, Y6) | ~inductive(X6) | inductive(Y6) )).
% 0.20/0.43 cnf(matrix-60, plain, ( ~equalish(Z6, A7) | ~member(Z6, B7) | member(A7, B7) )).
% 0.20/0.43 cnf(matrix-61, plain, ( ~equalish(C7, D7) | ~member(E7, C7) | member(E7, D7) )).
% 0.20/0.43 cnf(matrix-62, plain, ( ~equalish(F7, G7) | ~one_to_one(F7) | one_to_one(G7) )).
% 0.20/0.43 cnf(matrix-63, plain, ( ~equalish(H7, I7) | ~operation(H7) | operation(I7) )).
% 0.20/0.43 cnf(matrix-64, plain, ( ~equalish(J7, K7) | ~single_valued_class(J7) | single_valued_class(K7) )).
% 0.20/0.43 cnf(matrix-65, plain, ( ~equalish(L7, M7) | ~subclass(L7, N7) | subclass(M7, N7) )).
% 0.20/0.43 cnf(matrix-66, plain, ( ~equalish(O7, P7) | ~subclass(Q7, O7) | subclass(Q7, P7) )).
% 0.20/0.43 cnf(matrix-67, plain, ( ~subclass(X, Y) | ~member(U, X) | member(U, Y) )).
% 0.20/0.43 cnf(matrix-68, plain, ( member(not_subclass_element(X, Y), X) | subclass(X, Y) )).
% 0.20/0.43 cnf(matrix-69, plain, ( ~member(not_subclass_element(X, Y), Y) | subclass(X, Y) )).
% 0.20/0.43 cnf(matrix-70, plain, ( subclass(X, universal_class) )).
% 0.20/0.43 cnf(matrix-71, plain, ( ~equalish(X, Y) | subclass(X, Y) )).
% 0.20/0.43 cnf(matrix-72, plain, ( ~equalish(X, Y) | subclass(Y, X) )).
% 0.20/0.43 cnf(matrix-73, plain, ( ~subclass(X, Y) | ~subclass(Y, X) | equalish(X, Y) )).
% 0.20/0.43 cnf(matrix-74, plain, ( ~member(U, unordered_pair(X, Y)) | equalish(U, X) | equalish(U, Y) )).
% 0.20/0.43 cnf(matrix-75, plain, ( ~member(X, universal_class) | member(X, unordered_pair(X, Y)) )).
% 0.20/0.43 cnf(matrix-76, plain, ( ~member(Y, universal_class) | member(Y, unordered_pair(X, Y)) )).
% 0.20/0.43 cnf(matrix-77, plain, ( member(unordered_pair(X, Y), universal_class) )).
% 0.20/0.43 cnf(matrix-78, plain, ( equalish(unordered_pair(X, X), singleton(X)) )).
% 0.20/0.43 cnf(matrix-79, plain, ( equalish(unordered_pair(singleton(X), unordered_pair(X, singleton(Y))), ordered_pair(X, Y)) )).
% 0.20/0.43 cnf(matrix-80, plain, ( ~member(ordered_pair(U, V), cross_product(X, Y)) | member(U, X) )).
% 0.20/0.43 cnf(matrix-81, plain, ( ~member(ordered_pair(U, V), cross_product(X, Y)) | member(V, Y) )).
% 0.20/0.43 cnf(matrix-82, plain, ( ~member(U, X) | ~member(V, Y) | member(ordered_pair(U, V), cross_product(X, Y)) )).
% 0.20/0.43 cnf(matrix-83, plain, ( ~member(Z, cross_product(X, Y)) | equalish(ordered_pair(first(Z), second(Z)), Z) )).
% 0.20/0.43 cnf(matrix-84, plain, ( subclass(element_relation, cross_product(universal_class, universal_class)) )).
% 0.20/0.43 cnf(matrix-85, plain, ( ~member(ordered_pair(X, Y), element_relation) | member(X, Y) )).
% 0.20/0.43 cnf(matrix-86, plain, ( ~member(ordered_pair(X, Y), cross_product(universal_class, universal_class)) | ~member(X, Y) | member(ordered_pair(X, Y), element_relation) )).
% 0.20/0.43 cnf(matrix-87, plain, ( ~member(Z, intersection(X, Y)) | member(Z, X) )).
% 0.20/0.43 cnf(matrix-88, plain, ( ~member(Z, intersection(X, Y)) | member(Z, Y) )).
% 0.20/0.43 cnf(matrix-89, plain, ( ~member(Z, X) | ~member(Z, Y) | member(Z, intersection(X, Y)) )).
% 0.20/0.43 cnf(matrix-90, plain, ( ~member(Z, complement(X)) | ~member(Z, X) )).
% 0.20/0.43 cnf(matrix-91, plain, ( ~member(Z, universal_class) | member(Z, complement(X)) | member(Z, X) )).
% 0.20/0.43 cnf(matrix-92, plain, ( equalish(complement(intersection(complement(X), complement(Y))), union(X, Y)) )).
% 0.20/0.43 cnf(matrix-93, plain, ( equalish(intersection(complement(intersection(X, Y)), complement(intersection(complement(X), complement(Y)))), symmetric_difference(X, Y)) )).
% 0.20/0.43 cnf(matrix-94, plain, ( equalish(intersection(Xr, cross_product(X, Y)), restrict(Xr, X, Y)) )).
% 0.20/0.43 cnf(matrix-95, plain, ( equalish(intersection(cross_product(X, Y), Xr), restrict(Xr, X, Y)) )).
% 0.20/0.43 cnf(matrix-96, plain, ( ~equalish(restrict(X, singleton(Z), universal_class), null_class) | ~member(Z, domain_of(X)) )).
% 0.20/0.43 cnf(matrix-97, plain, ( ~member(Z, universal_class) | equalish(restrict(X, singleton(Z), universal_class), null_class) | member(Z, domain_of(X)) )).
% 0.20/0.43 cnf(matrix-98, plain, ( subclass(rotate(X), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.20/0.43 cnf(matrix-99, plain, ( ~member(ordered_pair(ordered_pair(U, V), W), rotate(X)) | member(ordered_pair(ordered_pair(V, W), U), X) )).
% 0.20/0.43 cnf(matrix-100, 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)) )).
% 0.20/0.43 cnf(matrix-101, plain, ( subclass(flip(X), cross_product(cross_product(universal_class, universal_class), universal_class)) )).
% 0.20/0.43 cnf(matrix-102, plain, ( ~member(ordered_pair(ordered_pair(U, V), W), flip(X)) | member(ordered_pair(ordered_pair(V, U), W), X) )).
% 0.20/0.43 cnf(matrix-103, 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)) )).
% 0.20/0.43 cnf(matrix-104, plain, ( equalish(domain_of(flip(cross_product(Y, universal_class))), inverse(Y)) )).
% 0.20/0.43 cnf(matrix-105, plain, ( equalish(domain_of(inverse(Z)), range_of(Z)) )).
% 0.20/0.43 cnf(matrix-106, plain, ( equalish(first(not_subclass_element(restrict(Z, X, singleton(Y)), null_class)), domain(Z, X, Y)) )).
% 0.20/0.43 cnf(matrix-107, plain, ( equalish(second(not_subclass_element(restrict(Z, singleton(X), Y), null_class)), range(Z, X, Y)) )).
% 0.20/0.43 cnf(matrix-108, plain, ( equalish(range_of(restrict(Xr, X, universal_class)), image(Xr, X)) )).
% 0.20/0.43 cnf(matrix-109, plain, ( equalish(union(X, singleton(X)), successor(X)) )).
% 0.20/0.43 cnf(matrix-110, plain, ( subclass(successor_relation, cross_product(universal_class, universal_class)) )).
% 0.20/0.43 cnf(matrix-111, plain, ( ~member(ordered_pair(X, Y), successor_relation) | equalish(successor(X), Y) )).
% 0.20/0.43 cnf(matrix-112, plain, ( ~equalish(successor(X), Y) | ~member(ordered_pair(X, Y), cross_product(universal_class, universal_class)) | member(ordered_pair(X, Y), successor_relation) )).
% 0.20/0.43 cnf(matrix-113, plain, ( ~inductive(X) | member(null_class, X) )).
% 0.20/0.43 cnf(matrix-114, plain, ( ~inductive(X) | subclass(image(successor_relation, X), X) )).
% 0.20/0.43 cnf(matrix-115, plain, ( ~member(null_class, X) | ~subclass(image(successor_relation, X), X) | inductive(X) )).
% 0.20/0.43 cnf(matrix-116, plain, ( inductive(omega) )).
% 0.20/0.43 cnf(matrix-117, plain, ( ~inductive(Y) | subclass(omega, Y) )).
% 0.20/0.43 cnf(matrix-118, plain, ( member(omega, universal_class) )).
% 0.20/0.43 cnf(matrix-119, plain, ( equalish(domain_of(restrict(element_relation, universal_class, X)), sum_class(X)) )).
% 0.20/0.43 cnf(matrix-120, plain, ( ~member(X, universal_class) | member(sum_class(X), universal_class) )).
% 0.20/0.43 cnf(matrix-121, plain, ( equalish(complement(image(element_relation, complement(X))), power_class(X)) )).
% 0.20/0.43 cnf(matrix-122, plain, ( ~member(U, universal_class) | member(power_class(U), universal_class) )).
% 0.20/0.43 cnf(matrix-123, plain, ( subclass(compose(Yr, Xr), cross_product(universal_class, universal_class)) )).
% 0.20/0.43 cnf(matrix-124, plain, ( ~member(ordered_pair(Y, Z), compose(Yr, Xr)) | member(Z, image(Yr, image(Xr, singleton(Y)))) )).
% 0.20/0.43 cnf(matrix-125, 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)) )).
% 0.20/0.43 cnf(matrix-126, plain, ( ~single_valued_class(X) | subclass(compose(X, inverse(X)), identity_relation) )).
% 0.20/0.43 cnf(matrix-127, plain, ( ~subclass(compose(X, inverse(X)), identity_relation) | single_valued_class(X) )).
% 0.20/0.43 cnf(matrix-128, plain, ( ~function(Xf) | subclass(Xf, cross_product(universal_class, universal_class)) )).
% 0.20/0.43 cnf(matrix-129, plain, ( ~function(Xf) | subclass(compose(Xf, inverse(Xf)), identity_relation) )).
% 0.20/0.43 cnf(matrix-130, plain, ( ~subclass(Xf, cross_product(universal_class, universal_class)) | ~subclass(compose(Xf, inverse(Xf)), identity_relation) | function(Xf) )).
% 0.20/0.43 cnf(matrix-131, plain, ( ~function(Xf) | ~member(X, universal_class) | member(image(Xf, X), universal_class) )).
% 0.20/0.43 cnf(matrix-132, plain, ( equalish(X, null_class) | member(regular(X), X) )).
% 0.20/0.43 cnf(matrix-133, plain, ( equalish(X, null_class) | equalish(intersection(X, regular(X)), null_class) )).
% 0.20/0.43 cnf(matrix-134, plain, ( equalish(sum_class(image(Xf, singleton(Y))), apply(Xf, Y)) )).
% 0.20/0.43 cnf(matrix-135, plain, ( function(choice) )).
% 0.20/0.43 cnf(matrix-136, plain, ( ~member(Y, universal_class) | equalish(Y, null_class) | member(apply(choice, Y), Y) )).
% 0.20/0.43 cnf(matrix-137, plain, ( ~one_to_one(Xf) | function(Xf) )).
% 0.20/0.43 cnf(matrix-138, plain, ( ~one_to_one(Xf) | function(inverse(Xf)) )).
% 0.20/0.43 cnf(matrix-139, plain, ( ~function(inverse(Xf)) | ~function(Xf) | one_to_one(Xf) )).
% 0.20/0.43 cnf(matrix-140, plain, ( equalish(intersection(cross_product(universal_class, universal_class), intersection(cross_product(universal_class, universal_class), complement(compose(complement(element_relation), inverse(element_relation))))), subset_relation) )).
% 0.20/0.43 cnf(matrix-141, plain, ( equalish(intersection(inverse(subset_relation), subset_relation), identity_relation) )).
% 0.20/0.43 cnf(matrix-142, plain, ( equalish(complement(domain_of(intersection(Xr, identity_relation))), diagonalise(Xr)) )).
% 0.20/0.43 cnf(matrix-143, plain, ( equalish(intersection(domain_of(X), diagonalise(compose(inverse(element_relation), X))), cantor(X)) )).
% 0.20/0.43 cnf(matrix-144, plain, ( ~operation(Xf) | function(Xf) )).
% 0.20/0.43 cnf(matrix-145, plain, ( ~operation(Xf) | equalish(cross_product(domain_of(domain_of(Xf)), domain_of(domain_of(Xf))), domain_of(Xf)) )).
% 0.20/0.43 cnf(matrix-146, plain, ( ~operation(Xf) | subclass(range_of(Xf), domain_of(domain_of(Xf))) )).
% 0.20/0.43 cnf(matrix-147, plain, ( ~function(Xf) | ~equalish(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) )).
% 0.20/0.43 cnf(matrix-148, plain, ( ~compatible(Xh, Xf1, Xf2) | function(Xh) )).
% 0.20/0.43 cnf(matrix-149, plain, ( ~compatible(Xh, Xf1, Xf2) | equalish(domain_of(domain_of(Xf1)), domain_of(Xh)) )).
% 0.20/0.43 cnf(matrix-150, plain, ( ~compatible(Xh, Xf1, Xf2) | subclass(range_of(Xh), domain_of(domain_of(Xf2))) )).
% 0.20/0.43 cnf(matrix-151, plain, ( ~function(Xh) | ~equalish(domain_of(domain_of(Xf1)), domain_of(Xh)) | ~subclass(range_of(Xh), domain_of(domain_of(Xf2))) | compatible(Xh1, Xf1, Xf2) )).
% 0.20/0.43 cnf(matrix-152, plain, ( ~homomorphism(Xh, Xf1, Xf2) | operation(Xf1) )).
% 0.20/0.43 cnf(matrix-153, plain, ( ~homomorphism(Xh, Xf1, Xf2) | operation(Xf2) )).
% 0.20/0.43 cnf(matrix-154, plain, ( ~homomorphism(Xh, Xf1, Xf2) | compatible(Xh, Xf1, Xf2) )).
% 0.20/0.43 cnf(matrix-155, plain, ( ~homomorphism(Xh, Xf1, Xf2) | ~member(ordered_pair(X, Y), domain_of(Xf1)) | equalish(apply(Xf2, ordered_pair(apply(Xh, X), apply(Xh, Y))), apply(Xh, apply(Xf1, ordered_pair(X, Y)))) )).
% 0.20/0.43 cnf(matrix-156, 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) )).
% 0.20/0.43 cnf(matrix-157, plain, ( ~operation(Xf1) | ~operation(Xf2) | ~compatible(Xh, Xf1, Xf2) | ~equalish(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) )).
% 0.20/0.43 cnf(matrix-158, plain, ( ~member(ordered_pair(X, Y), cross_product(U, V)) | member(X, unordered_pair(X, Y)) )).
% 0.20/0.43 cnf(matrix-159, plain, ( ~member(ordered_pair(X, Y), cross_product(U, V)) | member(Y, unordered_pair(X, Y)) )).
% 0.20/0.43 cnf(matrix-160, plain, ( ~member(ordered_pair(U, V), cross_product(X, Y)) | member(U, universal_class) )).
% 0.20/0.43 cnf(matrix-161, plain, ( ~member(ordered_pair(U, V), cross_product(X, Y)) | member(V, universal_class) )).
% 0.20/0.43 cnf(matrix-162, plain, ( subclass(X, X) )).
% 0.20/0.43 cnf(matrix-163, plain, ( ~subclass(X, Y) | ~subclass(Y, Z) | subclass(X, Z) )).
% 0.20/0.43 cnf(matrix-164, plain, ( ~equalish(x, x) )).
% 0.20/0.43
% 0.20/0.43 % Proof stack:
% 0.20/0.43 cnf(proof-stack, plain,
% 0.20/0.43 proof_stack(
% 0.20/0.43 start(164),
% 0.20/0.43 left_branch(0, 73, 2, 2),
% 0.20/0.43 left_branch(0, 162, 0, 3),
% 0.20/0.43 right_branch(3),
% 0.20/0.43 lemmata(0, 0),
% 0.20/0.43 right_branch(2)
% 0.20/0.43 )).
% 0.20/0.43 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------