%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP020+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:42:37 AM UTC 2025
% Result : Theorem 79.02s 79.19s
% Output : Proof 79.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : TOP020+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:52:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 79.02/79.19 % SZS status Theorem
% 79.02/79.19 % SZS output start Proof
% 79.02/79.19 tff(a_member_of_type, type, (
% 79.02/79.19 a_member_of: ( $i * $i ) > $o)).
% 79.02/79.19 tff(tptp_fun_G1_2_type, type, (
% 79.02/79.19 tptp_fun_G1_2: ( $i * $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_S_9_type, type, (
% 79.02/79.19 tptp_fun_S_9: $i)).
% 79.02/79.19 tff(tptp_fun_B_3_type, type, (
% 79.02/79.19 tptp_fun_B_3: ( $i * $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_Y_0_type, type, (
% 79.02/79.19 tptp_fun_Y_0: ( $i * $i ) > $i)).
% 79.02/79.19 tff(the_product_top_space_of_type, type, (
% 79.02/79.19 the_product_top_space_of: ( $i * $i ) > $i)).
% 79.02/79.19 tff(coerce_to_class_type, type, (
% 79.02/79.19 coerce_to_class: $i > $i)).
% 79.02/79.19 tff(the_diagonal_top_type, type, (
% 79.02/79.19 the_diagonal_top: $i > $i)).
% 79.02/79.19 tff(tptp_fun_A_4_type, type, (
% 79.02/79.19 tptp_fun_A_4: ( $i * $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_B_5_type, type, (
% 79.02/79.19 tptp_fun_B_5: ( $i * $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_Y_7_type, type, (
% 79.02/79.19 tptp_fun_Y_7: ( $i * $i ) > $i)).
% 79.02/79.19 tff(the_product_of_type, type, (
% 79.02/79.19 the_product_of: ( $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_G2_1_type, type, (
% 79.02/79.19 tptp_fun_G2_1: ( $i * $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_A_8_type, type, (
% 79.02/79.19 tptp_fun_A_8: ( $i * $i ) > $i)).
% 79.02/79.19 tff(tptp_fun_A_6_type, type, (
% 79.02/79.19 tptp_fun_A_6: ( $i * $i * $i ) > $i)).
% 79.02/79.19 tff(the_ordered_pair_type, type, (
% 79.02/79.19 the_ordered_pair: ( $i * $i ) > $i)).
% 79.02/79.19 tff(disjoint_type, type, (
% 79.02/79.19 disjoint: ( $i * $i ) > $o)).
% 79.02/79.19 tff(open_in_type, type, (
% 79.02/79.19 open_in: ( $i * $i ) > $o)).
% 79.02/79.19 tff(closed_in_type, type, (
% 79.02/79.19 closed_in: ( $i * $i ) > $o)).
% 79.02/79.19 tff(a_hausdorff_top_space_type, type, (
% 79.02/79.19 a_hausdorff_top_space: $i > $o)).
% 79.02/79.19 tff(1,plain,
% 79.02/79.19 (^[X: $i, S: $i] : refl((~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))) <=> (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))))),
% 79.02/79.19 inference(bind,[status(th)],[])).
% 79.02/79.19 tff(2,plain,
% 79.02/79.19 (![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))) <=> ![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))),
% 79.02/79.19 inference(quant_intro,[status(thm)],[1])).
% 79.02/79.19 tff(3,plain,
% 79.02/79.19 (^[X: $i, S: $i] : rewrite((~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))) <=> (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))))),
% 79.02/79.19 inference(bind,[status(th)],[])).
% 79.02/79.19 tff(4,plain,
% 79.02/79.19 (![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))) <=> ![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))),
% 79.02/79.19 inference(quant_intro,[status(thm)],[3])).
% 79.02/79.19 tff(5,plain,
% 79.02/79.19 (![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))) <=> ![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))),
% 79.02/79.19 inference(transitivity,[status(thm)],[4, 2])).
% 79.02/79.19 tff(6,plain,
% 79.02/79.19 (^[X: $i, S: $i] : trans(monotonicity(rewrite(((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S)) & (X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))) <=> ((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))), rewrite((a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : (~(a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A))))) <=> (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))), ((((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S)) & (X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))) & (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : (~(a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A)))))) <=> (((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))))) & (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))))), rewrite((((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))))) & (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A)))))) <=> (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))), ((((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S)) & (X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))) & (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : (~(a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A)))))) <=> (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))))),
% 79.02/79.19 inference(bind,[status(th)],[])).
% 79.02/79.19 tff(7,plain,
% 79.02/79.19 (![X: $i, S: $i] : (((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S)) & (X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))) & (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : (~(a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A)))))) <=> ![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))),
% 79.02/79.19 inference(quant_intro,[status(thm)],[6])).
% 79.02/79.19 tff(8,plain,
% 79.02/79.19 (![X: $i, S: $i] : (a_member_of(X, coerce_to_class(the_diagonal_top(S))) <=> ?[A: $i] : (a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A)))) <=> ![X: $i, S: $i] : (a_member_of(X, coerce_to_class(the_diagonal_top(S))) <=> ?[A: $i] : (a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A))))),
% 79.02/79.19 inference(rewrite,[status(thm)],[])).
% 79.02/79.19 tff(9,axiom,(![X: $i, S: $i] : (a_member_of(X, coerce_to_class(the_diagonal_top(S))) <=> ?[A: $i] : (a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagonal_top')).
% 79.02/79.19 tff(10,plain,
% 79.02/79.19 (![X: $i, S: $i] : (a_member_of(X, coerce_to_class(the_diagonal_top(S))) <=> ?[A: $i] : (a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A))))),
% 79.02/79.19 inference(modus_ponens,[status(thm)],[9, 8])).
% 79.02/79.19 tff(11,plain,(
% 79.02/79.19 ![X: $i, S: $i] : (((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S)) & (X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X))))) & (a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : (~(a_member_of(A, coerce_to_class(S)) & (X = the_ordered_pair(A, A))))))),
% 79.02/79.19 inference(skolemize,[status(sab)],[10])).
% 79.02/79.19 tff(12,plain,
% 79.02/79.19 (![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))),
% 79.02/79.19 inference(modus_ponens,[status(thm)],[11, 7])).
% 79.02/79.19 tff(13,plain,
% 79.02/79.19 (![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))),
% 79.02/79.19 inference(modus_ponens,[status(thm)],[12, 5])).
% 79.02/79.19 tff(14,plain,
% 79.02/79.19 (((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))))) <=> ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))))))),
% 79.02/79.20 inference(rewrite,[status(thm)],[])).
% 79.02/79.20 tff(15,plain,
% 79.02/79.20 ((~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))))) <=> (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))))),
% 79.02/79.20 inference(rewrite,[status(thm)],[])).
% 79.02/79.20 tff(16,plain,
% 79.02/79.20 (((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A))))))))) <=> ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))))))),
% 79.02/79.20 inference(monotonicity,[status(thm)],[15])).
% 79.02/79.20 tff(17,plain,
% 79.02/79.20 (((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A))))))))) <=> ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))))))),
% 79.02/79.20 inference(transitivity,[status(thm)],[16, 14])).
% 79.02/79.20 tff(18,plain,
% 79.02/79.20 ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A))))))))),
% 79.02/79.21 inference(quant_inst,[status(thm)],[])).
% 79.02/79.21 tff(19,plain,
% 79.02/79.21 ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))))),
% 79.02/79.21 inference(modus_ponens,[status(thm)],[18, 17])).
% 79.02/79.21 tff(20,plain,
% 79.02/79.21 (~((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))))),
% 79.02/79.21 inference(unit_resolution,[status(thm)],[19, 13])).
% 79.02/79.21 tff(21,plain,
% 79.02/79.21 (((~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))) | ((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.02/79.21 inference(tautology,[status(thm)],[])).
% 79.02/79.21 tff(22,plain,
% 79.02/79.21 ((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.02/79.21 inference(unit_resolution,[status(thm)],[21, 20])).
% 79.02/79.21 tff(23,plain,
% 79.02/79.21 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))) <=> (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))))),
% 79.02/79.21 inference(bind,[status(th)],[])).
% 79.02/79.21 tff(24,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))),
% 79.02/79.21 inference(quant_intro,[status(thm)],[23])).
% 79.02/79.21 tff(25,plain,
% 79.02/79.21 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))) <=> (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))))),
% 79.02/79.21 inference(bind,[status(th)],[])).
% 79.02/79.21 tff(26,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))),
% 79.02/79.21 inference(quant_intro,[status(thm)],[25])).
% 79.02/79.21 tff(27,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))),
% 79.02/79.21 inference(transitivity,[status(thm)],[26, 24])).
% 79.02/79.21 tff(28,plain,
% 79.02/79.21 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B)) <=> (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B))))), ((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) <=> (disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B))))))), rewrite((disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B))))) <=> (disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))), ((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) <=> (disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((a_member_of(Y, A) & a_member_of(Y, B)) <=> (~((~a_member_of(Y, B)) | (~a_member_of(Y, A))))), ((~(a_member_of(Y, A) & a_member_of(Y, B))) <=> (~(~((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))), rewrite((~(~((~a_member_of(Y, B)) | (~a_member_of(Y, A))))) <=> ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))), ((~(a_member_of(Y, A) & a_member_of(Y, B))) <=> ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))), (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) <=> ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))), ((![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B))) <=> (![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))) | (~disjoint(A, B))))), rewrite((![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))), ((![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))), (((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B))))) & ((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))))), rewrite(((disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B))))) & ((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A))))) <=> (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))), (((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))))),
% 79.02/79.21 inference(bind,[status(th)],[])).
% 79.02/79.21 tff(29,plain,
% 79.02/79.21 (![A: $i, B: $i] : ((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))),
% 79.02/79.21 inference(quant_intro,[status(thm)],[28])).
% 79.02/79.21 tff(30,plain,
% 79.02/79.21 (^[A: $i, B: $i] : rewrite((((a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B)) | disjoint(A, B)) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B)))))),
% 79.02/79.21 inference(bind,[status(th)],[])).
% 79.02/79.21 tff(31,plain,
% 79.02/79.21 (![A: $i, B: $i] : (((a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B)) | disjoint(A, B)) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : ((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B))))),
% 79.02/79.21 inference(quant_intro,[status(thm)],[30])).
% 79.02/79.21 tff(32,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B))) <=> ![A: $i, B: $i] : (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))),
% 79.02/79.21 inference(rewrite,[status(thm)],[])).
% 79.02/79.21 tff(33,plain,
% 79.02/79.21 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B))) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))), ((disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))) <=> (disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))))), rewrite((disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))) <=> (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))), ((disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))) <=> (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B))))), rewrite((~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B))) <=> (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))), ((disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))) <=> (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))))),
% 79.02/79.21 inference(bind,[status(th)],[])).
% 79.02/79.21 tff(34,plain,
% 79.02/79.21 (![A: $i, B: $i] : (disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)))) <=> ![A: $i, B: $i] : (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))),
% 79.02/79.21 inference(quant_intro,[status(thm)],[33])).
% 79.02/79.21 tff(35,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (~?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','disjoint_defn')).
% 79.02/79.21 tff(36,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))),
% 79.02/79.21 inference(modus_ponens,[status(thm)],[35, 34])).
% 79.02/79.21 tff(37,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~(?[Y: $i] : (a_member_of(Y, A) & a_member_of(Y, B)) <=> disjoint(A, B)))),
% 79.02/79.21 inference(modus_ponens,[status(thm)],[36, 32])).
% 79.02/79.21 tff(38,plain,(
% 79.02/79.21 ![A: $i, B: $i] : (((a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B)) | disjoint(A, B)) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B))))),
% 79.02/79.21 inference(skolemize,[status(sab)],[37])).
% 79.02/79.21 tff(39,plain,
% 79.02/79.21 (![A: $i, B: $i] : ((disjoint(A, B) | (a_member_of(tptp_fun_Y_7(B, A), A) & a_member_of(tptp_fun_Y_7(B, A), B))) & (![Y: $i] : (~(a_member_of(Y, A) & a_member_of(Y, B))) | (~disjoint(A, B))))),
% 79.02/79.21 inference(modus_ponens,[status(thm)],[38, 31])).
% 79.02/79.21 tff(40,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))),
% 79.02/79.21 inference(modus_ponens,[status(thm)],[39, 29])).
% 79.02/79.21 tff(41,plain,
% 79.02/79.21 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))),
% 79.02/79.21 inference(modus_ponens,[status(thm)],[40, 27])).
% 79.02/79.21 tff(42,plain,
% 79.02/79.21 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))),
% 79.02/79.22 inference(rewrite,[status(thm)],[])).
% 79.02/79.22 tff(43,plain,
% 79.02/79.22 ((~((~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))))))) | (~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))) <=> (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.02/79.22 inference(rewrite,[status(thm)],[])).
% 79.02/79.22 tff(44,plain,
% 79.02/79.22 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))))))) | (~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))),
% 79.02/79.22 inference(monotonicity,[status(thm)],[43])).
% 79.02/79.22 tff(45,plain,
% 79.02/79.22 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))))))) | (~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))))),
% 79.02/79.22 inference(transitivity,[status(thm)],[44, 42])).
% 79.02/79.22 tff(46,plain,
% 79.02/79.22 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))))))) | (~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.02/79.23 inference(quant_inst,[status(thm)],[])).
% 79.02/79.23 tff(47,plain,
% 79.02/79.23 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[46, 45])).
% 79.02/79.23 tff(48,plain,
% 79.02/79.23 (~((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.02/79.23 inference(unit_resolution,[status(thm)],[47, 41])).
% 79.02/79.23 tff(49,plain,
% 79.02/79.23 (((~((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![Y: $i] : ((~a_member_of(Y, coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(Y, the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))) | (disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))),
% 79.02/79.23 inference(tautology,[status(thm)],[])).
% 79.02/79.23 tff(50,plain,
% 79.02/79.23 (disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.02/79.23 inference(unit_resolution,[status(thm)],[49, 48])).
% 79.02/79.23 tff(51,plain,
% 79.02/79.23 ((~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))) <=> (~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S))))),
% 79.02/79.23 inference(rewrite,[status(thm)],[])).
% 79.02/79.23 tff(52,plain,
% 79.02/79.23 ((~![S: $i] : (a_hausdorff_top_space(S) => closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))) <=> (~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S))))),
% 79.02/79.23 inference(rewrite,[status(thm)],[])).
% 79.02/79.23 tff(53,axiom,(~![S: $i] : (a_hausdorff_top_space(S) => closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','challenge_AMR_1_4_4')).
% 79.02/79.23 tff(54,plain,
% 79.02/79.23 (~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[53, 52])).
% 79.02/79.23 tff(55,plain,
% 79.02/79.23 (~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[54, 51])).
% 79.02/79.23 tff(56,plain,
% 79.02/79.23 (~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[55, 51])).
% 79.02/79.23 tff(57,plain,
% 79.02/79.23 (~![S: $i] : ((~a_hausdorff_top_space(S)) | closed_in(coerce_to_class(the_diagonal_top(S)), the_product_top_space_of(S, S)))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[56, 51])).
% 79.02/79.23 tff(58,plain,(
% 79.02/79.23 ~((~a_hausdorff_top_space(S!9)) | closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))),
% 79.02/79.23 inference(skolemize,[status(sab)],[57])).
% 79.02/79.23 tff(59,plain,
% 79.02/79.23 (~closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))),
% 79.02/79.23 inference(or_elim,[status(thm)],[58])).
% 79.02/79.23 tff(60,plain,
% 79.02/79.23 (^[X: $i, A: $i] : refl((closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))) <=> (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))))),
% 79.02/79.23 inference(bind,[status(th)],[])).
% 79.02/79.23 tff(61,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))) <=> ![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))),
% 79.02/79.23 inference(quant_intro,[status(thm)],[60])).
% 79.02/79.23 tff(62,plain,
% 79.02/79.23 (^[X: $i, A: $i] : rewrite((closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))) <=> (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))))),
% 79.02/79.23 inference(bind,[status(th)],[])).
% 79.02/79.23 tff(63,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))) <=> ![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))),
% 79.02/79.23 inference(quant_intro,[status(thm)],[62])).
% 79.02/79.23 tff(64,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))) <=> ![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))),
% 79.02/79.23 inference(transitivity,[status(thm)],[63, 61])).
% 79.02/79.23 tff(65,plain,
% 79.02/79.23 (^[X: $i, A: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[G: $i] : trans(monotonicity(rewrite((a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)) <=> (~((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))), ((~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))) <=> (~(~((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))), rewrite((~(~((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))) <=> ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))), ((~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))) <=> ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))), (![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))) <=> ![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))), ((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) <=> (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))), rewrite((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))) <=> (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))), ((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) <=> (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))), ((closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))))) <=> (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))))), rewrite((closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A))))))) <=> (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))), ((closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))))) <=> (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))))),
% 79.02/79.23 inference(bind,[status(th)],[])).
% 79.02/79.23 tff(66,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))))) <=> ![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))),
% 79.02/79.23 inference(quant_intro,[status(thm)],[65])).
% 79.02/79.23 tff(67,plain,
% 79.02/79.23 (^[X: $i, A: $i] : trans(monotonicity(rewrite(((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A))) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) <=> (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A))))), ((((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A))) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X)) <=> ((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X)))), rewrite(((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X)) <=> (closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))))), ((((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A))) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X)) <=> (closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))))))),
% 79.02/79.23 inference(bind,[status(th)],[])).
% 79.02/79.23 tff(68,plain,
% 79.02/79.23 (![X: $i, A: $i] : (((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A))) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X)) <=> ![X: $i, A: $i] : (closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))))),
% 79.02/79.23 inference(quant_intro,[status(thm)],[67])).
% 79.02/79.23 tff(69,plain,
% 79.02/79.23 (![X: $i, A: $i] : ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X)) <=> ![X: $i, A: $i] : ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))),
% 79.02/79.23 inference(rewrite,[status(thm)],[])).
% 79.02/79.23 tff(70,plain,
% 79.02/79.23 (^[X: $i, A: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(quant_intro(proof_bind(^[G: $i] : rewrite(((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A)) <=> (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))), (?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A)) <=> ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))), (((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) <=> ((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A))))), rewrite(((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A))) <=> ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))), (((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) <=> ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))))), (![Y: $i] : ((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) <=> ![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A))))), ((![Y: $i] : ((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) => closed_in(A, X)) <=> (![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A))) => closed_in(A, X)))), rewrite((![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A))) => closed_in(A, X)) <=> ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))), ((![Y: $i] : ((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) => closed_in(A, X)) <=> ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))))),
% 79.02/79.23 inference(bind,[status(th)],[])).
% 79.02/79.23 tff(71,plain,
% 79.02/79.23 (![X: $i, A: $i] : (![Y: $i] : ((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) => closed_in(A, X)) <=> ![X: $i, A: $i] : ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))),
% 79.02/79.23 inference(quant_intro,[status(thm)],[70])).
% 79.02/79.23 tff(72,axiom,(![X: $i, A: $i] : (![Y: $i] : ((a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A))) => ?[G: $i] : ((a_member_of(Y, G) & open_in(G, X)) & disjoint(G, A))) => closed_in(A, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','closed_subset_thm')).
% 79.02/79.23 tff(73,plain,
% 79.02/79.23 (![X: $i, A: $i] : ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[72, 71])).
% 79.02/79.23 tff(74,plain,
% 79.02/79.23 (![X: $i, A: $i] : ((~![Y: $i] : ((~(a_member_of(Y, coerce_to_class(X)) & (~a_member_of(Y, A)))) | ?[G: $i] : (a_member_of(Y, G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[73, 69])).
% 79.02/79.23 tff(75,plain,(
% 79.02/79.23 ![X: $i, A: $i] : (((a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A))) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))) | closed_in(A, X))),
% 79.02/79.23 inference(skolemize,[status(sab)],[74])).
% 79.02/79.23 tff(76,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X)) & (~a_member_of(tptp_fun_Y_0(A, X), A)) & ![G: $i] : (~(a_member_of(tptp_fun_Y_0(A, X), G) & open_in(G, X) & disjoint(G, A)))))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[75, 68])).
% 79.02/79.23 tff(77,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[76, 66])).
% 79.02/79.23 tff(78,plain,
% 79.02/79.23 (![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))),
% 79.02/79.23 inference(modus_ponens,[status(thm)],[77, 64])).
% 79.02/79.23 tff(79,plain,
% 79.02/79.23 (((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))))) <=> ((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))))),
% 79.02/79.23 inference(rewrite,[status(thm)],[])).
% 79.02/79.23 tff(80,plain,
% 79.02/79.23 ((closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))))) <=> (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))))),
% 79.02/79.23 inference(rewrite,[status(thm)],[])).
% 79.02/79.23 tff(81,plain,
% 79.02/79.23 ((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))))) <=> (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))))),
% 79.02/79.23 inference(rewrite,[status(thm)],[])).
% 79.02/79.23 tff(82,plain,
% 79.02/79.23 ((closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9))))))))) <=> (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))))),
% 79.02/79.23 inference(monotonicity,[status(thm)],[81])).
% 79.02/79.23 tff(83,plain,
% 79.02/79.23 ((closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9))))))))) <=> (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))))),
% 79.02/79.23 inference(transitivity,[status(thm)],[82, 80])).
% 79.02/79.23 tff(84,plain,
% 79.02/79.23 (((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))))))) <=> ((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))))))),
% 79.02/79.24 inference(monotonicity,[status(thm)],[83])).
% 79.02/79.24 tff(85,plain,
% 79.02/79.24 (((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))))))) <=> ((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))))),
% 79.02/79.24 inference(transitivity,[status(thm)],[84, 79])).
% 79.02/79.24 tff(86,plain,
% 79.02/79.24 ((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | (closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))))))),
% 79.02/79.24 inference(quant_inst,[status(thm)],[])).
% 79.02/79.24 tff(87,plain,
% 79.02/79.24 ((~![X: $i, A: $i] : (closed_in(A, X) | (~(a_member_of(tptp_fun_Y_0(A, X), A) | (~a_member_of(tptp_fun_Y_0(A, X), coerce_to_class(X))) | (~![G: $i] : ((~a_member_of(tptp_fun_Y_0(A, X), G)) | (~open_in(G, X)) | (~disjoint(G, A)))))))) | closed_in(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) | (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[86, 85])).
% 79.02/79.24 tff(88,plain,
% 79.02/79.24 (~((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))),
% 79.02/79.24 inference(unit_resolution,[status(thm)],[87, 78, 59])).
% 79.02/79.24 tff(89,plain,
% 79.02/79.24 (((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))),
% 79.02/79.24 inference(tautology,[status(thm)],[])).
% 79.02/79.24 tff(90,plain,
% 79.02/79.24 (a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))),
% 79.02/79.24 inference(unit_resolution,[status(thm)],[89, 88])).
% 79.02/79.24 tff(91,plain,
% 79.02/79.24 (^[S: $i, T: $i, X: $i] : refl(((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S))))))) <=> ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S))))))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(92,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S))))))) <=> ![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[91])).
% 79.02/79.24 tff(93,plain,
% 79.02/79.24 (^[S: $i, T: $i, X: $i] : rewrite(((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S)) & a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T)) & (X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S))))) <=> ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S))))))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(94,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S)) & a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T)) & (X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S))))) <=> ![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[93])).
% 79.02/79.24 tff(95,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B)))) <=> ![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(rewrite,[status(thm)],[])).
% 79.02/79.24 tff(96,plain,
% 79.02/79.24 (^[S: $i, T: $i, X: $i] : trans(monotonicity(quant_intro(proof_bind(^[A: $i, B: $i] : rewrite(((a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T))) & (X = the_ordered_pair(A, B))) <=> (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))), (?[A: $i, B: $i] : ((a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T))) & (X = the_ordered_pair(A, B))) <=> ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))), ((a_member_of(X, coerce_to_class(the_product_top_space_of(S, T))) => ?[A: $i, B: $i] : ((a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T))) & (X = the_ordered_pair(A, B)))) <=> (a_member_of(X, coerce_to_class(the_product_top_space_of(S, T))) => ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B)))))), rewrite((a_member_of(X, coerce_to_class(the_product_top_space_of(S, T))) => ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B)))) <=> ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))), ((a_member_of(X, coerce_to_class(the_product_top_space_of(S, T))) => ?[A: $i, B: $i] : ((a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T))) & (X = the_ordered_pair(A, B)))) <=> ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(97,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : (a_member_of(X, coerce_to_class(the_product_top_space_of(S, T))) => ?[A: $i, B: $i] : ((a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T))) & (X = the_ordered_pair(A, B)))) <=> ![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[96])).
% 79.02/79.24 tff(98,axiom,(![S: $i, T: $i, X: $i] : (a_member_of(X, coerce_to_class(the_product_top_space_of(S, T))) => ?[A: $i, B: $i] : ((a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T))) & (X = the_ordered_pair(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_top')).
% 79.02/79.24 tff(99,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[98, 97])).
% 79.02/79.24 tff(100,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | ?[A: $i, B: $i] : (a_member_of(A, coerce_to_class(S)) & a_member_of(B, coerce_to_class(T)) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[99, 95])).
% 79.02/79.24 tff(101,plain,(
% 79.02/79.24 ![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S)) & a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T)) & (X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))),
% 79.02/79.24 inference(skolemize,[status(sab)],[100])).
% 79.02/79.24 tff(102,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[101, 94])).
% 79.02/79.24 tff(103,plain,
% 79.02/79.24 (![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[102, 92])).
% 79.02/79.24 tff(104,plain,
% 79.02/79.24 (((~![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))) | ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))) <=> ((~![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))),
% 79.02/79.24 inference(rewrite,[status(thm)],[])).
% 79.02/79.24 tff(105,plain,
% 79.02/79.24 ((~![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))) | ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))),
% 79.02/79.24 inference(quant_inst,[status(thm)],[])).
% 79.02/79.24 tff(106,plain,
% 79.02/79.24 ((~![S: $i, T: $i, X: $i] : ((~a_member_of(X, coerce_to_class(the_product_top_space_of(S, T)))) | (~((~a_member_of(tptp_fun_A_4(X, T, S), coerce_to_class(S))) | (~a_member_of(tptp_fun_B_3(X, T, S), coerce_to_class(T))) | (~(X = the_ordered_pair(tptp_fun_A_4(X, T, S), tptp_fun_B_3(X, T, S)))))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | (~((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[105, 104])).
% 79.02/79.24 tff(107,plain,
% 79.02/79.24 (~((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))),
% 79.02/79.24 inference(unit_resolution,[status(thm)],[106, 103, 90])).
% 79.02/79.24 tff(108,plain,
% 79.02/79.24 (((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))) | (tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))),
% 79.02/79.24 inference(tautology,[status(thm)],[])).
% 79.02/79.24 tff(109,plain,
% 79.02/79.24 (tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))),
% 79.02/79.24 inference(unit_resolution,[status(thm)],[108, 107])).
% 79.02/79.24 tff(110,plain,
% 79.02/79.24 (the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))),
% 79.02/79.24 inference(symmetry,[status(thm)],[109])).
% 79.02/79.24 tff(111,plain,
% 79.02/79.24 (a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) <=> a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.02/79.24 inference(monotonicity,[status(thm)],[110])).
% 79.02/79.24 tff(112,plain,
% 79.02/79.24 (a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) <=> a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.02/79.24 inference(symmetry,[status(thm)],[111])).
% 79.02/79.24 tff(113,plain,
% 79.02/79.24 ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) <=> (~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.02/79.24 inference(monotonicity,[status(thm)],[112])).
% 79.02/79.24 tff(114,assumption,(~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), introduced(assumption)).
% 79.02/79.24 tff(115,plain,
% 79.02/79.24 (~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[114, 113])).
% 79.02/79.24 tff(116,plain,
% 79.02/79.24 (^[X: $i, S: $i, T: $i] : refl((~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))) <=> (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(117,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))) <=> ![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[116])).
% 79.02/79.24 tff(118,plain,
% 79.02/79.24 (^[X: $i, S: $i, T: $i] : rewrite((~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))) <=> (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(119,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))) <=> ![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[118])).
% 79.02/79.24 tff(120,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))) <=> ![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))),
% 79.02/79.24 inference(transitivity,[status(thm)],[119, 117])).
% 79.02/79.24 tff(121,plain,
% 79.02/79.24 (^[X: $i, S: $i, T: $i] : trans(monotonicity(rewrite(((~a_member_of(X, the_product_of(S, T))) | (a_member_of(tptp_fun_A_6(T, S, X), S) & a_member_of(tptp_fun_B_5(T, S, X), T) & (X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))) <=> ((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))), rewrite((a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : (~(a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B))))) <=> (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))), ((((~a_member_of(X, the_product_of(S, T))) | (a_member_of(tptp_fun_A_6(T, S, X), S) & a_member_of(tptp_fun_B_5(T, S, X), T) & (X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))) & (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : (~(a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B)))))) <=> (((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))))) & (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))))), rewrite((((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))))) & (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B)))))) <=> (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))), ((((~a_member_of(X, the_product_of(S, T))) | (a_member_of(tptp_fun_A_6(T, S, X), S) & a_member_of(tptp_fun_B_5(T, S, X), T) & (X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))) & (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : (~(a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B)))))) <=> (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(122,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (((~a_member_of(X, the_product_of(S, T))) | (a_member_of(tptp_fun_A_6(T, S, X), S) & a_member_of(tptp_fun_B_5(T, S, X), T) & (X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))) & (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : (~(a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B)))))) <=> ![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[121])).
% 79.02/79.24 tff(123,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : (a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B)))) <=> ![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : (a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(rewrite,[status(thm)],[])).
% 79.02/79.24 tff(124,plain,
% 79.02/79.24 (^[X: $i, S: $i, T: $i] : rewrite((a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : ((a_member_of(A, S) & a_member_of(B, T)) & (X = the_ordered_pair(A, B)))) <=> (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : (a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B)))))),
% 79.02/79.24 inference(bind,[status(th)],[])).
% 79.02/79.24 tff(125,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : ((a_member_of(A, S) & a_member_of(B, T)) & (X = the_ordered_pair(A, B)))) <=> ![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : (a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(quant_intro,[status(thm)],[124])).
% 79.02/79.24 tff(126,axiom,(![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : ((a_member_of(A, S) & a_member_of(B, T)) & (X = the_ordered_pair(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product')).
% 79.02/79.24 tff(127,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : (a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[126, 125])).
% 79.02/79.24 tff(128,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (a_member_of(X, the_product_of(S, T)) <=> ?[A: $i, B: $i] : (a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[127, 123])).
% 79.02/79.24 tff(129,plain,(
% 79.02/79.24 ![X: $i, S: $i, T: $i] : (((~a_member_of(X, the_product_of(S, T))) | (a_member_of(tptp_fun_A_6(T, S, X), S) & a_member_of(tptp_fun_B_5(T, S, X), T) & (X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X))))) & (a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : (~(a_member_of(A, S) & a_member_of(B, T) & (X = the_ordered_pair(A, B))))))),
% 79.02/79.24 inference(skolemize,[status(sab)],[128])).
% 79.02/79.24 tff(130,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[129, 122])).
% 79.02/79.24 tff(131,plain,
% 79.02/79.24 (![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))),
% 79.02/79.24 inference(modus_ponens,[status(thm)],[130, 120])).
% 79.02/79.24 tff(132,plain,
% 79.02/79.24 (((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))))) <=> ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))))))),
% 79.02/79.25 inference(rewrite,[status(thm)],[])).
% 79.02/79.25 tff(133,plain,
% 79.02/79.25 ((~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))))) <=> (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))))),
% 79.02/79.25 inference(rewrite,[status(thm)],[])).
% 79.02/79.25 tff(134,plain,
% 79.02/79.25 (((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))))) <=> ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))))))),
% 79.02/79.26 inference(monotonicity,[status(thm)],[133])).
% 79.02/79.26 tff(135,plain,
% 79.02/79.26 (((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))))) <=> ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))))))),
% 79.10/79.26 inference(transitivity,[status(thm)],[134, 132])).
% 79.10/79.26 tff(136,plain,
% 79.10/79.26 ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))))),
% 79.10/79.26 inference(quant_inst,[status(thm)],[])).
% 79.10/79.26 tff(137,plain,
% 79.10/79.26 ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))))),
% 79.10/79.27 inference(modus_ponens,[status(thm)],[136, 135])).
% 79.10/79.27 tff(138,plain,
% 79.10/79.27 (~((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))))),
% 79.10/79.27 inference(unit_resolution,[status(thm)],[137, 131])).
% 79.10/79.27 tff(139,plain,
% 79.10/79.27 (((~((~a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))))))) | (~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))))) | (a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))),
% 79.10/79.27 inference(tautology,[status(thm)],[])).
% 79.10/79.27 tff(140,plain,
% 79.10/79.27 (a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))),
% 79.10/79.27 inference(unit_resolution,[status(thm)],[139, 138])).
% 79.10/79.27 tff(141,assumption,(![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))), introduced(assumption)).
% 79.10/79.27 tff(142,plain,
% 79.10/79.27 ((tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) <=> (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))),
% 79.10/79.27 inference(commutativity,[status(thm)],[])).
% 79.10/79.27 tff(143,plain,
% 79.10/79.27 ((~(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))) <=> (~(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))),
% 79.10/79.27 inference(monotonicity,[status(thm)],[142])).
% 79.10/79.27 tff(144,assumption,(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), introduced(assumption)).
% 79.10/79.27 tff(145,plain,
% 79.10/79.27 (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)),
% 79.10/79.27 inference(symmetry,[status(thm)],[144])).
% 79.10/79.27 tff(146,plain,
% 79.10/79.27 (the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))),
% 79.10/79.27 inference(monotonicity,[status(thm)],[145])).
% 79.10/79.27 tff(147,plain,
% 79.10/79.27 (the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))),
% 79.10/79.27 inference(symmetry,[status(thm)],[146])).
% 79.10/79.27 tff(148,plain,
% 79.10/79.27 (tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))),
% 79.10/79.27 inference(transitivity,[status(thm)],[109, 147])).
% 79.10/79.27 tff(149,plain,
% 79.10/79.27 (((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))) | a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))),
% 79.10/79.27 inference(tautology,[status(thm)],[])).
% 79.10/79.27 tff(150,plain,
% 79.10/79.27 (a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))),
% 79.10/79.27 inference(unit_resolution,[status(thm)],[149, 107])).
% 79.10/79.27 tff(151,plain,
% 79.10/79.27 (((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))))))))))))) <=> ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))))))),
% 79.10/79.27 inference(rewrite,[status(thm)],[])).
% 79.10/79.27 tff(152,plain,
% 79.10/79.27 ((~((~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))))) <=> (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))))))))))))),
% 79.10/79.27 inference(rewrite,[status(thm)],[])).
% 79.10/79.27 tff(153,plain,
% 79.10/79.27 (((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))))))) <=> ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))))))),
% 79.10/79.27 inference(monotonicity,[status(thm)],[152])).
% 79.10/79.27 tff(154,plain,
% 79.10/79.27 (((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))))))) <=> ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))))))),
% 79.10/79.27 inference(transitivity,[status(thm)],[153, 151])).
% 79.10/79.27 tff(155,plain,
% 79.10/79.27 ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))) | (~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))))))),
% 79.10/79.28 inference(quant_inst,[status(thm)],[])).
% 79.10/79.28 tff(156,plain,
% 79.10/79.28 ((~![X: $i, S: $i] : (~((~((~a_member_of(X, coerce_to_class(the_diagonal_top(S)))) | (~((~a_member_of(tptp_fun_A_8(S, X), coerce_to_class(S))) | (~(X = the_ordered_pair(tptp_fun_A_8(S, X), tptp_fun_A_8(S, X)))))))) | (~(a_member_of(X, coerce_to_class(the_diagonal_top(S))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S))) | (~(X = the_ordered_pair(A, A))))))))) | (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))))))))))))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[155, 154])).
% 79.10/79.28 tff(157,plain,
% 79.10/79.28 (~((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)))))))))))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[156, 13])).
% 79.10/79.28 tff(158,plain,
% 79.10/79.28 (((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | (~((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))), tptp_fun_A_8(S!9, tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9))))))))))) | (a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))),
% 79.10/79.28 inference(tautology,[status(thm)],[])).
% 79.10/79.28 tff(159,plain,
% 79.10/79.28 (a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[158, 157])).
% 79.10/79.28 tff(160,plain,
% 79.10/79.28 (((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))))),
% 79.10/79.28 inference(tautology,[status(thm)],[])).
% 79.10/79.28 tff(161,plain,
% 79.10/79.28 (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[160, 88])).
% 79.10/79.28 tff(162,plain,
% 79.10/79.28 ((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))),
% 79.10/79.28 inference(tautology,[status(thm)],[])).
% 79.10/79.28 tff(163,plain,
% 79.10/79.28 ((~(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A)))))) | ![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[162, 161])).
% 79.10/79.28 tff(164,plain,
% 79.10/79.28 (![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[163, 159])).
% 79.10/79.28 tff(165,plain,
% 79.10/79.28 (((~![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))) <=> ((~![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))),
% 79.10/79.28 inference(rewrite,[status(thm)],[])).
% 79.10/79.28 tff(166,plain,
% 79.10/79.28 ((~![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))),
% 79.10/79.28 inference(quant_inst,[status(thm)],[])).
% 79.10/79.28 tff(167,plain,
% 79.10/79.28 ((~![A: $i] : ((~a_member_of(A, coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(A, A))))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[166, 165])).
% 79.10/79.28 tff(168,plain,
% 79.10/79.28 (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[167, 164, 150])).
% 79.10/79.28 tff(169,plain,
% 79.10/79.28 ($false),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[168, 148])).
% 79.10/79.28 tff(170,plain,(~(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))), inference(lemma,lemma(discharge,[]))).
% 79.10/79.28 tff(171,plain,
% 79.10/79.28 (~(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[170, 143])).
% 79.10/79.28 tff(172,plain,
% 79.10/79.28 (((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))) | a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))),
% 79.10/79.28 inference(tautology,[status(thm)],[])).
% 79.10/79.28 tff(173,plain,
% 79.10/79.28 (a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))),
% 79.10/79.28 inference(unit_resolution,[status(thm)],[172, 107])).
% 79.10/79.28 tff(174,plain,
% 79.10/79.28 (a_hausdorff_top_space(S!9)),
% 79.10/79.28 inference(or_elim,[status(thm)],[58])).
% 79.10/79.28 tff(175,plain,
% 79.10/79.28 (^[X: $i] : refl(((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))) <=> ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))))),
% 79.10/79.28 inference(bind,[status(th)],[])).
% 79.10/79.28 tff(176,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))) <=> ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))),
% 79.10/79.28 inference(quant_intro,[status(thm)],[175])).
% 79.10/79.28 tff(177,plain,
% 79.10/79.28 (^[X: $i] : rewrite(((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))) <=> ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))))),
% 79.10/79.28 inference(bind,[status(th)],[])).
% 79.10/79.28 tff(178,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))) <=> ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))),
% 79.10/79.28 inference(quant_intro,[status(thm)],[177])).
% 79.10/79.28 tff(179,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))) <=> ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))),
% 79.10/79.28 inference(transitivity,[status(thm)],[178, 176])).
% 79.10/79.28 tff(180,plain,
% 79.10/79.28 (^[X: $i] : rewrite(((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | (open_in(tptp_fun_G1_2(B, A, X), X) & open_in(tptp_fun_G2_1(B, A, X), X) & a_member_of(A, tptp_fun_G1_2(B, A, X)) & a_member_of(B, tptp_fun_G2_1(B, A, X)) & disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))) <=> ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))))))),
% 79.10/79.28 inference(bind,[status(th)],[])).
% 79.10/79.28 tff(181,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | (open_in(tptp_fun_G1_2(B, A, X), X) & open_in(tptp_fun_G2_1(B, A, X), X) & a_member_of(A, tptp_fun_G1_2(B, A, X)) & a_member_of(B, tptp_fun_G2_1(B, A, X)) & disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X))))) <=> ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))),
% 79.10/79.28 inference(quant_intro,[status(thm)],[180])).
% 79.10/79.28 tff(182,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2)))) <=> ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))),
% 79.10/79.28 inference(rewrite,[status(thm)],[])).
% 79.10/79.28 tff(183,plain,
% 79.10/79.28 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[A: $i, B: $i] : trans(monotonicity(rewrite(((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) <=> (a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))), quant_intro(proof_bind(^[G1: $i, G2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) <=> (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1))), ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) <=> ((open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1)) & a_member_of(B, G2)))), rewrite(((open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1)) & a_member_of(B, G2)) <=> (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2))), ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) <=> (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2)))), (((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2)) <=> ((open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2)) & disjoint(G1, G2)))), rewrite(((open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2)) & disjoint(G1, G2)) <=> (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))), (((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2)) <=> (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))), (?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2)) <=> ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2)))), ((((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2))) <=> ((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B))) => ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))), rewrite(((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B))) => ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))) <=> ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2)))), ((((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2))) <=> ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2)))))), (![A: $i, B: $i] : (((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2))) <=> ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))), ((a_hausdorff_top_space(X) => ![A: $i, B: $i] : (((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2)))) <=> (a_hausdorff_top_space(X) => ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2)))))), rewrite((a_hausdorff_top_space(X) => ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2)))) <=> ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))), ((a_hausdorff_top_space(X) => ![A: $i, B: $i] : (((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2)))) <=> ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))))),
% 79.10/79.28 inference(bind,[status(th)],[])).
% 79.10/79.28 tff(184,plain,
% 79.10/79.28 (![X: $i] : (a_hausdorff_top_space(X) => ![A: $i, B: $i] : (((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2)))) <=> ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))),
% 79.10/79.28 inference(quant_intro,[status(thm)],[183])).
% 79.10/79.28 tff(185,axiom,(![X: $i] : (a_hausdorff_top_space(X) => ![A: $i, B: $i] : (((a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X))) & (~(A = B))) => ?[G1: $i, G2: $i] : ((((open_in(G1, X) & open_in(G2, X)) & a_member_of(A, G1)) & a_member_of(B, G2)) & disjoint(G1, G2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hausdorff')).
% 79.10/79.28 tff(186,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[185, 184])).
% 79.10/79.28 tff(187,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | ?[G1: $i, G2: $i] : (open_in(G1, X) & open_in(G2, X) & a_member_of(A, G1) & a_member_of(B, G2) & disjoint(G1, G2))))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[186, 182])).
% 79.10/79.28 tff(188,plain,(
% 79.10/79.28 ![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((~(a_member_of(A, coerce_to_class(X)) & a_member_of(B, coerce_to_class(X)) & (~(A = B)))) | (open_in(tptp_fun_G1_2(B, A, X), X) & open_in(tptp_fun_G2_1(B, A, X), X) & a_member_of(A, tptp_fun_G1_2(B, A, X)) & a_member_of(B, tptp_fun_G2_1(B, A, X)) & disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))),
% 79.10/79.28 inference(skolemize,[status(sab)],[187])).
% 79.10/79.28 tff(189,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[188, 181])).
% 79.10/79.28 tff(190,plain,
% 79.10/79.28 (![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))),
% 79.10/79.28 inference(modus_ponens,[status(thm)],[189, 179])).
% 79.10/79.28 tff(191,plain,
% 79.10/79.28 (((~![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))) | ((~a_hausdorff_top_space(S!9)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9)))))))) <=> ((~![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))) | (~a_hausdorff_top_space(S!9)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9)))))))),
% 79.13/79.28 inference(rewrite,[status(thm)],[])).
% 79.13/79.28 tff(192,plain,
% 79.13/79.28 ((~![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))) | ((~a_hausdorff_top_space(S!9)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9)))))))),
% 79.13/79.28 inference(quant_inst,[status(thm)],[])).
% 79.13/79.28 tff(193,plain,
% 79.13/79.28 ((~![X: $i] : ((~a_hausdorff_top_space(X)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(X))) | (~a_member_of(B, coerce_to_class(X))) | (~((~open_in(tptp_fun_G1_2(B, A, X), X)) | (~open_in(tptp_fun_G2_1(B, A, X), X)) | (~a_member_of(A, tptp_fun_G1_2(B, A, X))) | (~a_member_of(B, tptp_fun_G2_1(B, A, X))) | (~disjoint(tptp_fun_G1_2(B, A, X), tptp_fun_G2_1(B, A, X)))))))) | (~a_hausdorff_top_space(S!9)) | ![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))),
% 79.13/79.28 inference(modus_ponens,[status(thm)],[192, 191])).
% 79.13/79.28 tff(194,plain,
% 79.13/79.28 (![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))),
% 79.13/79.28 inference(unit_resolution,[status(thm)],[193, 190, 174])).
% 79.13/79.28 tff(195,plain,
% 79.13/79.28 (((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | ((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) <=> ((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.13/79.28 inference(rewrite,[status(thm)],[])).
% 79.13/79.28 tff(196,plain,
% 79.13/79.28 (((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) <=> ((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.13/79.29 inference(rewrite,[status(thm)],[])).
% 79.13/79.29 tff(197,plain,
% 79.13/79.29 ((~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) <=> (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.13/79.29 inference(rewrite,[status(thm)],[])).
% 79.13/79.29 tff(198,plain,
% 79.13/79.29 (((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) <=> ((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.13/79.29 inference(monotonicity,[status(thm)],[197])).
% 79.13/79.29 tff(199,plain,
% 79.13/79.29 (((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) <=> ((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.13/79.29 inference(transitivity,[status(thm)],[198, 196])).
% 79.13/79.29 tff(200,plain,
% 79.13/79.29 (((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | ((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) <=> ((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | ((~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))),
% 79.13/79.29 inference(monotonicity,[status(thm)],[199])).
% 79.13/79.29 tff(201,plain,
% 79.13/79.29 (((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | ((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) <=> ((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.13/79.29 inference(transitivity,[status(thm)],[200, 195])).
% 79.13/79.29 tff(202,plain,
% 79.13/79.29 ((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | ((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.13/79.29 inference(quant_inst,[status(thm)],[])).
% 79.13/79.29 tff(203,plain,
% 79.13/79.29 ((~![A: $i, B: $i] : ((A = B) | (~a_member_of(A, coerce_to_class(S!9))) | (~a_member_of(B, coerce_to_class(S!9))) | (~((~open_in(tptp_fun_G1_2(B, A, S!9), S!9)) | (~open_in(tptp_fun_G2_1(B, A, S!9), S!9)) | (~a_member_of(A, tptp_fun_G1_2(B, A, S!9))) | (~a_member_of(B, tptp_fun_G2_1(B, A, S!9))) | (~disjoint(tptp_fun_G1_2(B, A, S!9), tptp_fun_G2_1(B, A, S!9))))))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), coerce_to_class(S!9))) | (tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.13/79.30 inference(modus_ponens,[status(thm)],[202, 201])).
% 79.13/79.30 tff(204,plain,
% 79.13/79.30 ((tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9) = tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) | (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.13/79.30 inference(unit_resolution,[status(thm)],[203, 194, 173, 150])).
% 79.13/79.30 tff(205,plain,
% 79.13/79.30 (~((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.13/79.30 inference(unit_resolution,[status(thm)],[204, 171])).
% 79.13/79.30 tff(206,plain,
% 79.13/79.30 (((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.13/79.30 inference(tautology,[status(thm)],[])).
% 79.13/79.30 tff(207,plain,
% 79.13/79.30 (a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.13/79.30 inference(unit_resolution,[status(thm)],[206, 205])).
% 79.13/79.30 tff(208,plain,
% 79.13/79.30 (((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.13/79.30 inference(tautology,[status(thm)],[])).
% 79.13/79.30 tff(209,plain,
% 79.13/79.30 (a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.13/79.30 inference(unit_resolution,[status(thm)],[208, 205])).
% 79.13/79.30 tff(210,plain,
% 79.13/79.30 (((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) <=> ((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.13/79.30 inference(rewrite,[status(thm)],[])).
% 79.13/79.30 tff(211,plain,
% 79.13/79.30 (((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | $false) <=> ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.13/79.30 inference(rewrite,[status(thm)],[])).
% 79.13/79.30 tff(212,plain,
% 79.13/79.30 ((~$true) <=> $false),
% 79.13/79.30 inference(rewrite,[status(thm)],[])).
% 79.13/79.30 tff(213,plain,
% 79.13/79.30 ((the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))) <=> $true),
% 79.13/79.30 inference(rewrite,[status(thm)],[])).
% 79.13/79.30 tff(214,plain,
% 79.13/79.30 ((~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))) <=> (~$true)),
% 79.13/79.30 inference(monotonicity,[status(thm)],[213])).
% 79.13/79.30 tff(215,plain,
% 79.13/79.30 ((~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))) <=> $false),
% 79.13/79.30 inference(transitivity,[status(thm)],[214, 212])).
% 79.13/79.30 tff(216,plain,
% 79.13/79.30 (((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))) <=> ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | $false)),
% 79.13/79.30 inference(monotonicity,[status(thm)],[215])).
% 79.13/79.30 tff(217,plain,
% 79.13/79.30 (((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9))))) <=> ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.13/79.30 inference(transitivity,[status(thm)],[216, 211])).
% 79.13/79.30 tff(218,plain,
% 79.13/79.30 (((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))) <=> ((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.13/79.30 inference(monotonicity,[status(thm)],[217])).
% 79.13/79.30 tff(219,plain,
% 79.13/79.30 (((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))) <=> ((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.13/79.31 inference(transitivity,[status(thm)],[218, 210])).
% 79.13/79.31 tff(220,plain,
% 79.13/79.31 ((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | ((~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)))))),
% 79.13/79.31 inference(quant_inst,[status(thm)],[])).
% 79.13/79.31 tff(221,plain,
% 79.13/79.31 ((~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.13/79.31 inference(modus_ponens,[status(thm)],[220, 219])).
% 79.13/79.31 tff(222,plain,
% 79.13/79.31 ($false),
% 79.13/79.31 inference(unit_resolution,[status(thm)],[221, 209, 207, 141])).
% 79.13/79.31 tff(223,plain,(~![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))), inference(lemma,lemma(discharge,[]))).
% 79.13/79.31 tff(224,plain,
% 79.13/79.31 ((~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))) | a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B))))),
% 79.13/79.31 inference(tautology,[status(thm)],[])).
% 79.13/79.31 tff(225,plain,
% 79.13/79.31 ((~(a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)) = the_ordered_pair(A, B)))))) | a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.13/79.31 inference(unit_resolution,[status(thm)],[224, 223])).
% 79.13/79.31 tff(226,plain,
% 79.13/79.31 (a_member_of(the_ordered_pair(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.13/79.31 inference(unit_resolution,[status(thm)],[225, 140])).
% 79.13/79.31 tff(227,plain,
% 79.13/79.31 ($false),
% 79.13/79.31 inference(unit_resolution,[status(thm)],[226, 115])).
% 79.13/79.31 tff(228,plain,(a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), inference(lemma,lemma(discharge,[]))).
% 79.13/79.31 tff(229,plain,
% 79.13/79.31 (((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)),
% 79.13/79.31 inference(tautology,[status(thm)],[])).
% 79.13/79.31 tff(230,plain,
% 79.13/79.31 (open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)),
% 79.13/79.31 inference(unit_resolution,[status(thm)],[229, 205])).
% 79.13/79.31 tff(231,plain,
% 79.13/79.31 (((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)),
% 79.13/79.31 inference(tautology,[status(thm)],[])).
% 79.13/79.31 tff(232,plain,
% 79.13/79.31 (open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)),
% 79.13/79.31 inference(unit_resolution,[status(thm)],[231, 205])).
% 79.13/79.31 tff(233,plain,
% 79.13/79.31 (^[A: $i, X: $i, B: $i, Y: $i] : refl((open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y))) <=> (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y))))),
% 79.13/79.31 inference(bind,[status(th)],[])).
% 79.13/79.31 tff(234,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y))) <=> ![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))),
% 79.13/79.31 inference(quant_intro,[status(thm)],[233])).
% 79.13/79.31 tff(235,plain,
% 79.13/79.31 (^[A: $i, X: $i, B: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((open_in(A, X) & open_in(B, Y)) <=> (~((~open_in(A, X)) | (~open_in(B, Y))))), ((~(open_in(A, X) & open_in(B, Y))) <=> (~(~((~open_in(A, X)) | (~open_in(B, Y))))))), rewrite((~(~((~open_in(A, X)) | (~open_in(B, Y))))) <=> ((~open_in(A, X)) | (~open_in(B, Y)))), ((~(open_in(A, X) & open_in(B, Y))) <=> ((~open_in(A, X)) | (~open_in(B, Y))))), (((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> (((~open_in(A, X)) | (~open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))))), rewrite((((~open_in(A, X)) | (~open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))), (((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))))),
% 79.13/79.31 inference(bind,[status(th)],[])).
% 79.13/79.31 tff(236,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> ![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))),
% 79.13/79.31 inference(quant_intro,[status(thm)],[235])).
% 79.13/79.31 tff(237,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> ![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y)))),
% 79.13/79.31 inference(rewrite,[status(thm)],[])).
% 79.13/79.31 tff(238,plain,
% 79.13/79.31 (^[A: $i, X: $i, B: $i, Y: $i] : rewrite(((open_in(A, X) & open_in(B, Y)) => open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y))))),
% 79.13/79.31 inference(bind,[status(th)],[])).
% 79.13/79.31 tff(239,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : ((open_in(A, X) & open_in(B, Y)) => open_in(the_product_of(A, B), the_product_top_space_of(X, Y))) <=> ![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y)))),
% 79.13/79.31 inference(quant_intro,[status(thm)],[238])).
% 79.13/79.31 tff(240,axiom,(![A: $i, X: $i, B: $i, Y: $i] : ((open_in(A, X) & open_in(B, Y)) => open_in(the_product_of(A, B), the_product_top_space_of(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','product_of_open_sets')).
% 79.13/79.31 tff(241,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y)))),
% 79.13/79.31 inference(modus_ponens,[status(thm)],[240, 239])).
% 79.13/79.31 tff(242,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y)))),
% 79.13/79.31 inference(modus_ponens,[status(thm)],[241, 237])).
% 79.13/79.31 tff(243,plain,(
% 79.13/79.31 ![A: $i, X: $i, B: $i, Y: $i] : ((~(open_in(A, X) & open_in(B, Y))) | open_in(the_product_of(A, B), the_product_top_space_of(X, Y)))),
% 79.13/79.31 inference(skolemize,[status(sab)],[242])).
% 79.13/79.31 tff(244,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))),
% 79.13/79.31 inference(modus_ponens,[status(thm)],[243, 236])).
% 79.13/79.31 tff(245,plain,
% 79.13/79.31 (![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))),
% 79.13/79.31 inference(modus_ponens,[status(thm)],[244, 234])).
% 79.13/79.31 tff(246,plain,
% 79.13/79.31 (((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | ((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)))) <=> ((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)))),
% 79.13/79.31 inference(rewrite,[status(thm)],[])).
% 79.13/79.31 tff(247,plain,
% 79.13/79.31 ((open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9))) <=> ((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)))),
% 79.13/79.31 inference(rewrite,[status(thm)],[])).
% 79.13/79.31 tff(248,plain,
% 79.13/79.31 (((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | (open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)))) <=> ((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | ((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))))),
% 79.13/79.32 inference(monotonicity,[status(thm)],[247])).
% 79.13/79.32 tff(249,plain,
% 79.13/79.32 (((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | (open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)))) <=> ((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)))),
% 79.13/79.32 inference(transitivity,[status(thm)],[248, 246])).
% 79.13/79.32 tff(250,plain,
% 79.13/79.32 ((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | (open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)))),
% 79.13/79.32 inference(quant_inst,[status(thm)],[])).
% 79.13/79.32 tff(251,plain,
% 79.13/79.32 ((~![A: $i, X: $i, B: $i, Y: $i] : (open_in(the_product_of(A, B), the_product_top_space_of(X, Y)) | (~open_in(A, X)) | (~open_in(B, Y)))) | (~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))),
% 79.13/79.32 inference(modus_ponens,[status(thm)],[250, 249])).
% 79.13/79.32 tff(252,plain,
% 79.13/79.32 (open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))),
% 79.13/79.32 inference(unit_resolution,[status(thm)],[251, 245, 232, 230])).
% 79.13/79.32 tff(253,plain,
% 79.13/79.32 (((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_product_top_space_of(S!9, S!9)))) | a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), coerce_to_class(the_diagonal_top(S!9)))) | ![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))),
% 79.13/79.32 inference(tautology,[status(thm)],[])).
% 79.13/79.32 tff(254,plain,
% 79.13/79.32 (![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))),
% 79.13/79.32 inference(unit_resolution,[status(thm)],[253, 88])).
% 79.13/79.32 tff(255,plain,
% 79.13/79.32 (((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | ((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))))) <=> ((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))))),
% 79.13/79.32 inference(rewrite,[status(thm)],[])).
% 79.13/79.32 tff(256,plain,
% 79.13/79.32 (((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))))) <=> ((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))))),
% 79.13/79.32 inference(rewrite,[status(thm)],[])).
% 79.13/79.32 tff(257,plain,
% 79.13/79.32 (((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))))) <=> ((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | ((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)))))),
% 79.16/79.32 inference(monotonicity,[status(thm)],[256])).
% 79.16/79.32 tff(258,plain,
% 79.16/79.32 (((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))))) <=> ((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))))),
% 79.16/79.32 inference(transitivity,[status(thm)],[257, 255])).
% 79.16/79.32 tff(259,plain,
% 79.16/79.32 ((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))))),
% 79.16/79.32 inference(quant_inst,[status(thm)],[])).
% 79.16/79.32 tff(260,plain,
% 79.16/79.32 ((~![G: $i] : ((~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), G)) | (~open_in(G, the_product_top_space_of(S!9, S!9))) | (~disjoint(G, coerce_to_class(the_diagonal_top(S!9)))))) | (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~open_in(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), the_product_top_space_of(S!9, S!9)))),
% 79.16/79.32 inference(modus_ponens,[status(thm)],[259, 258])).
% 79.16/79.32 tff(261,plain,
% 79.16/79.32 ((~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.16/79.32 inference(unit_resolution,[status(thm)],[260, 254, 252])).
% 79.16/79.32 tff(262,plain,
% 79.16/79.32 (~disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9)))),
% 79.16/79.32 inference(unit_resolution,[status(thm)],[261, 228])).
% 79.16/79.32 tff(263,plain,
% 79.16/79.32 ((~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.16/79.33 inference(tautology,[status(thm)],[])).
% 79.16/79.33 tff(264,plain,
% 79.16/79.33 ((~(disjoint(the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), coerce_to_class(the_diagonal_top(S!9))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.16/79.33 inference(unit_resolution,[status(thm)],[263, 262])).
% 79.16/79.33 tff(265,plain,
% 79.16/79.33 (~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.16/79.33 inference(unit_resolution,[status(thm)],[264, 50])).
% 79.16/79.33 tff(266,plain,
% 79.16/79.33 (((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) | a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))),
% 79.16/79.33 inference(tautology,[status(thm)],[])).
% 79.16/79.33 tff(267,plain,
% 79.16/79.33 (a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))),
% 79.16/79.33 inference(unit_resolution,[status(thm)],[266, 265])).
% 79.16/79.33 tff(268,plain,
% 79.16/79.33 ((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.16/79.33 inference(tautology,[status(thm)],[])).
% 79.16/79.33 tff(269,plain,
% 79.16/79.33 ((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.16/79.33 inference(unit_resolution,[status(thm)],[268, 267])).
% 79.16/79.33 tff(270,plain,
% 79.16/79.33 (~((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))),
% 79.16/79.33 inference(unit_resolution,[status(thm)],[269, 22])).
% 79.16/79.33 tff(271,plain,
% 79.16/79.33 (((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), coerce_to_class(S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | (tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.18/79.33 inference(tautology,[status(thm)],[])).
% 79.18/79.33 tff(272,plain,
% 79.18/79.33 (tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.18/79.34 inference(unit_resolution,[status(thm)],[271, 270])).
% 79.18/79.34 tff(273,plain,
% 79.18/79.34 (((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))))) <=> ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B)))))))))),
% 79.18/79.34 inference(rewrite,[status(thm)],[])).
% 79.18/79.34 tff(274,plain,
% 79.18/79.34 ((~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B)))))))) <=> (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))))),
% 79.18/79.35 inference(rewrite,[status(thm)],[])).
% 79.18/79.35 tff(275,plain,
% 79.18/79.35 (((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))))) <=> ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B)))))))))),
% 79.18/79.35 inference(monotonicity,[status(thm)],[274])).
% 79.18/79.35 tff(276,plain,
% 79.18/79.35 (((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))))) <=> ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B)))))))))),
% 79.18/79.36 inference(transitivity,[status(thm)],[275, 273])).
% 79.18/79.36 tff(277,plain,
% 79.18/79.36 ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))))),
% 79.18/79.36 inference(quant_inst,[status(thm)],[])).
% 79.18/79.36 tff(278,plain,
% 79.18/79.36 ((~![X: $i, S: $i, T: $i] : (~((~((~a_member_of(X, the_product_of(S, T))) | (~((~a_member_of(tptp_fun_A_6(T, S, X), S)) | (~a_member_of(tptp_fun_B_5(T, S, X), T)) | (~(X = the_ordered_pair(tptp_fun_A_6(T, S, X), tptp_fun_B_5(T, S, X)))))))) | (~(a_member_of(X, the_product_of(S, T)) | ![A: $i, B: $i] : ((~a_member_of(A, S)) | (~a_member_of(B, T)) | (~(X = the_ordered_pair(A, B))))))))) | (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))))),
% 79.18/79.37 inference(modus_ponens,[status(thm)],[277, 276])).
% 79.18/79.37 tff(279,plain,
% 79.18/79.37 (~((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B)))))))),
% 79.18/79.37 inference(unit_resolution,[status(thm)],[278, 131])).
% 79.18/79.37 tff(280,plain,
% 79.18/79.37 (((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~(a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![A: $i, B: $i] : ((~a_member_of(B, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(A, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(A, B))))))) | ((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.18/79.37 inference(tautology,[status(thm)],[])).
% 79.18/79.37 tff(281,plain,
% 79.18/79.37 ((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.18/79.38 inference(unit_resolution,[status(thm)],[280, 279])).
% 79.18/79.38 tff(282,plain,
% 79.18/79.38 (((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), coerce_to_class(the_diagonal_top(S!9)))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) | a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.18/79.38 inference(tautology,[status(thm)],[])).
% 79.18/79.38 tff(283,plain,
% 79.18/79.38 (a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.18/79.38 inference(unit_resolution,[status(thm)],[282, 265])).
% 79.18/79.38 tff(284,plain,
% 79.18/79.38 ((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.18/79.38 inference(tautology,[status(thm)],[])).
% 79.18/79.38 tff(285,plain,
% 79.18/79.38 ((~((~a_member_of(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))) | (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.18/79.39 inference(unit_resolution,[status(thm)],[284, 283])).
% 79.18/79.39 tff(286,plain,
% 79.18/79.39 (~((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))),
% 79.18/79.39 inference(unit_resolution,[status(thm)],[285, 281])).
% 79.18/79.39 tff(287,plain,
% 79.18/79.39 (((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | (tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))),
% 79.18/79.39 inference(tautology,[status(thm)],[])).
% 79.18/79.39 tff(288,plain,
% 79.18/79.39 (tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.18/79.39 inference(unit_resolution,[status(thm)],[287, 286])).
% 79.18/79.39 tff(289,plain,
% 79.18/79.39 (the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) = tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.18/79.39 inference(symmetry,[status(thm)],[288])).
% 79.18/79.39 tff(290,plain,
% 79.18/79.39 (the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.18/79.39 inference(transitivity,[status(thm)],[289, 272])).
% 79.18/79.39 tff(291,plain,
% 79.18/79.39 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 79.18/79.39 inference(bind,[status(th)],[])).
% 79.18/79.39 tff(292,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 79.18/79.39 inference(quant_intro,[status(thm)],[291])).
% 79.18/79.39 tff(293,plain,
% 79.18/79.39 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 79.18/79.39 inference(bind,[status(th)],[])).
% 79.18/79.39 tff(294,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 79.18/79.39 inference(quant_intro,[status(thm)],[293])).
% 79.18/79.39 tff(295,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 79.18/79.39 inference(rewrite,[status(thm)],[])).
% 79.18/79.39 tff(296,plain,
% 79.18/79.39 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((the_ordered_pair(A, B) = the_ordered_pair(C, D)) => ((A = C) & (B = D))) <=> ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D))))),
% 79.18/79.39 inference(bind,[status(th)],[])).
% 79.18/79.39 tff(297,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((the_ordered_pair(A, B) = the_ordered_pair(C, D)) => ((A = C) & (B = D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 79.18/79.39 inference(quant_intro,[status(thm)],[296])).
% 79.18/79.39 tff(298,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((the_ordered_pair(A, B) = the_ordered_pair(C, D)) => ((A = C) & (B = D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ordered_pair')).
% 79.18/79.39 tff(299,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 79.18/79.39 inference(modus_ponens,[status(thm)],[298, 297])).
% 79.18/79.39 tff(300,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 79.18/79.39 inference(modus_ponens,[status(thm)],[299, 295])).
% 79.18/79.39 tff(301,plain,(
% 79.18/79.39 ![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | ((A = C) & (B = D)))),
% 79.18/79.39 inference(skolemize,[status(sab)],[300])).
% 79.18/79.39 tff(302,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 79.18/79.39 inference(modus_ponens,[status(thm)],[301, 294])).
% 79.18/79.39 tff(303,plain,
% 79.18/79.39 (![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))),
% 79.18/79.39 inference(modus_ponens,[status(thm)],[302, 292])).
% 79.18/79.39 tff(304,plain,
% 79.18/79.39 (((~![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((~(the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (~(the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.18/79.40 inference(rewrite,[status(thm)],[])).
% 79.18/79.40 tff(305,plain,
% 79.18/79.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | ((~(the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.18/79.40 inference(quant_inst,[status(thm)],[])).
% 79.18/79.40 tff(306,plain,
% 79.18/79.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(the_ordered_pair(A, B) = the_ordered_pair(C, D))) | (~((~(A = C)) | (~(B = D)))))) | (~(the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) = the_ordered_pair(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))),
% 79.18/79.40 inference(modus_ponens,[status(thm)],[305, 304])).
% 79.18/79.40 tff(307,plain,
% 79.18/79.40 (~((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))),
% 79.18/79.41 inference(unit_resolution,[status(thm)],[306, 303, 290])).
% 79.18/79.41 tff(308,plain,
% 79.18/79.41 (((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.18/79.41 inference(tautology,[status(thm)],[])).
% 79.18/79.41 tff(309,plain,
% 79.18/79.41 (tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.18/79.41 inference(unit_resolution,[status(thm)],[308, 307])).
% 79.18/79.41 tff(310,plain,
% 79.18/79.41 (a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) <=> a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.18/79.41 inference(monotonicity,[status(thm)],[309])).
% 79.18/79.41 tff(311,plain,
% 79.18/79.41 (a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) <=> a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.18/79.41 inference(symmetry,[status(thm)],[310])).
% 79.18/79.41 tff(312,plain,
% 79.18/79.41 ((~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) <=> (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.18/79.41 inference(monotonicity,[status(thm)],[311])).
% 79.18/79.41 tff(313,plain,
% 79.18/79.41 (((~(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.18/79.41 inference(tautology,[status(thm)],[])).
% 79.18/79.41 tff(314,plain,
% 79.18/79.41 (tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) = tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.18/79.41 inference(unit_resolution,[status(thm)],[313, 307])).
% 79.18/79.41 tff(315,plain,
% 79.18/79.41 (a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) <=> a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.18/79.41 inference(monotonicity,[status(thm)],[314])).
% 79.18/79.41 tff(316,plain,
% 79.18/79.41 ((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) <=> (~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.18/79.41 inference(monotonicity,[status(thm)],[315])).
% 79.18/79.41 tff(317,plain,
% 79.18/79.41 (((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.18/79.42 inference(tautology,[status(thm)],[])).
% 79.18/79.42 tff(318,plain,
% 79.18/79.42 (a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.18/79.42 inference(unit_resolution,[status(thm)],[317, 286])).
% 79.18/79.42 tff(319,plain,
% 79.18/79.42 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.18/79.42 inference(rewrite,[status(thm)],[])).
% 79.18/79.42 tff(320,plain,
% 79.18/79.42 ((~((~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) <=> (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.18/79.42 inference(rewrite,[status(thm)],[])).
% 79.18/79.42 tff(321,plain,
% 79.18/79.42 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.27/79.43 inference(monotonicity,[status(thm)],[320])).
% 79.27/79.43 tff(322,plain,
% 79.27/79.43 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))))),
% 79.27/79.43 inference(transitivity,[status(thm)],[321, 319])).
% 79.27/79.43 tff(323,plain,
% 79.27/79.43 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))) | (~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))),
% 79.27/79.43 inference(quant_inst,[status(thm)],[])).
% 79.27/79.43 tff(324,plain,
% 79.27/79.43 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~a_member_of(tptp_fun_Y_7(B, A), A)) | (~a_member_of(tptp_fun_Y_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![Y: $i] : ((~a_member_of(Y, B)) | (~a_member_of(Y, A)))))))) | (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))))),
% 79.27/79.43 inference(modus_ponens,[status(thm)],[323, 322])).
% 79.27/79.43 tff(325,plain,
% 79.27/79.43 (~((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))))))),
% 79.27/79.43 inference(unit_resolution,[status(thm)],[324, 41])).
% 79.27/79.43 tff(326,plain,
% 79.27/79.43 (((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~(disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)) | (~((~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_Y_7(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | ((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))),
% 79.27/79.43 inference(tautology,[status(thm)],[])).
% 79.27/79.43 tff(327,plain,
% 79.27/79.43 ((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.27/79.43 inference(unit_resolution,[status(thm)],[326, 325])).
% 79.27/79.43 tff(328,plain,
% 79.27/79.43 (((~open_in(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~open_in(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), S!9)) | (~a_member_of(tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))) | disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.43 inference(tautology,[status(thm)],[])).
% 79.27/79.43 tff(329,plain,
% 79.27/79.43 (disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.43 inference(unit_resolution,[status(thm)],[328, 205])).
% 79.27/79.43 tff(330,plain,
% 79.27/79.43 ((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | (~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.27/79.43 inference(tautology,[status(thm)],[])).
% 79.27/79.43 tff(331,plain,
% 79.27/79.43 ((~((~disjoint(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))) | ![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.27/79.44 inference(unit_resolution,[status(thm)],[330, 329])).
% 79.27/79.44 tff(332,plain,
% 79.27/79.44 (![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.27/79.44 inference(unit_resolution,[status(thm)],[331, 327])).
% 79.27/79.44 tff(333,plain,
% 79.27/79.44 (((~![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) | ((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) <=> ((~![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) | (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.27/79.44 inference(rewrite,[status(thm)],[])).
% 79.27/79.44 tff(334,plain,
% 79.27/79.44 ((~![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) | ((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))),
% 79.27/79.44 inference(quant_inst,[status(thm)],[])).
% 79.27/79.44 tff(335,plain,
% 79.27/79.44 ((~![Y: $i] : ((~a_member_of(Y, tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(Y, tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))))) | (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))),
% 79.27/79.44 inference(modus_ponens,[status(thm)],[334, 333])).
% 79.27/79.44 tff(336,plain,
% 79.27/79.44 (~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.44 inference(unit_resolution,[status(thm)],[335, 332, 318])).
% 79.27/79.44 tff(337,plain,
% 79.27/79.44 (~a_member_of(tptp_fun_A_8(S!9, tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.44 inference(modus_ponens,[status(thm)],[336, 316])).
% 79.27/79.44 tff(338,plain,
% 79.27/79.44 (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.44 inference(modus_ponens,[status(thm)],[337, 312])).
% 79.27/79.44 tff(339,plain,
% 79.27/79.44 (((~a_member_of(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) | (~(tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))) = the_ordered_pair(tptp_fun_A_6(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))))))) | a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.46 inference(tautology,[status(thm)],[])).
% 79.27/79.46 tff(340,plain,
% 79.27/79.46 (a_member_of(tptp_fun_B_5(tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_Y_7(coerce_to_class(the_diagonal_top(S!9)), the_product_of(tptp_fun_G2_1(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9)))), tptp_fun_G1_2(tptp_fun_A_4(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), tptp_fun_B_3(tptp_fun_Y_0(coerce_to_class(the_diagonal_top(S!9)), the_product_top_space_of(S!9, S!9)), S!9, S!9), S!9))),
% 79.27/79.46 inference(unit_resolution,[status(thm)],[339, 286])).
% 79.27/79.46 tff(341,plain,
% 79.27/79.46 ($false),
% 79.27/79.46 inference(unit_resolution,[status(thm)],[340, 338])).
% 79.27/79.46 % SZS output end Proof
% 79.27/79.46 % E exiting
%------------------------------------------------------------------------------