%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP001+6 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:48 AM UTC 2025
% Result : Theorem 14.72s 14.91s
% Output : Proof 14.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP001+6 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 15:29:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 14.72/14.91 % SZS status Theorem
% 14.72/14.91 % SZS output start Proof
% 14.72/14.91 tff(product_type, type, (
% 14.72/14.91 product: ( $i * $i * $i ) > $o)).
% 14.72/14.91 tff(tptp_fun_W_1_type, type, (
% 14.72/14.91 tptp_fun_W_1: $i)).
% 14.72/14.91 tff(tptp_fun_Z_4_type, type, (
% 14.72/14.91 tptp_fun_Z_4: ( $i * $i ) > $i)).
% 14.72/14.91 tff(tptp_fun_V_2_type, type, (
% 14.72/14.91 tptp_fun_V_2: $i)).
% 14.72/14.91 tff(inverse_type, type, (
% 14.72/14.91 inverse: $i > $i)).
% 14.72/14.91 tff(tptp_fun_E_0_type, type, (
% 14.72/14.91 tptp_fun_E_0: $i)).
% 14.72/14.91 tff(tptp_fun_U_3_type, type, (
% 14.72/14.91 tptp_fun_U_3: $i)).
% 14.72/14.91 tff(1,plain,
% 14.72/14.91 (((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0))) <=> ((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & ![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(2,plain,
% 14.72/14.91 ((![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0)) <=> (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(3,plain,
% 14.72/14.91 (((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0))) <=> ((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0)))),
% 14.72/14.91 inference(monotonicity,[status(thm)],[2])).
% 14.72/14.91 tff(4,plain,
% 14.72/14.91 (((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0))) <=> ((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & ![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0))),
% 14.72/14.91 inference(transitivity,[status(thm)],[3, 1])).
% 14.72/14.91 tff(5,plain,
% 14.72/14.91 ((~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E))))) <=> (~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E)))))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(6,plain,
% 14.72/14.91 ((~![E: $i] : (((((((![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (((product(X, Y, U) & product(Y, Z, V)) & product(U, Z, W)) => product(X, V, W))) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (((product(X, Y, U) & product(Y, Z, V)) & product(X, V, W)) => product(U, Z, W))) & ![X: $i] : product(X, E, X)) & ![X: $i] : product(E, X, X)) & ![X: $i] : product(X, inverse(X), E)) & ![X: $i] : product(inverse(X), X, E)) => (![X: $i] : product(X, X, E) => ![U: $i, V: $i, W: $i] : (product(U, V, W) => product(V, U, W))))) <=> (~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E)))))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(7,axiom,(~![E: $i] : (((((((![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (((product(X, Y, U) & product(Y, Z, V)) & product(U, Z, W)) => product(X, V, W))) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (((product(X, Y, U) & product(Y, Z, V)) & product(X, V, W)) => product(U, Z, W))) & ![X: $i] : product(X, E, X)) & ![X: $i] : product(E, X, X)) & ![X: $i] : product(X, inverse(X), E)) & ![X: $i] : product(inverse(X), X, E)) => (![X: $i] : product(X, X, E) => ![U: $i, V: $i, W: $i] : (product(U, V, W) => product(V, U, W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity')).
% 14.72/14.91 tff(8,plain,
% 14.72/14.91 (~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E))))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[7, 6])).
% 14.72/14.91 tff(9,plain,
% 14.72/14.91 (~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E))))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[8, 5])).
% 14.72/14.91 tff(10,plain,
% 14.72/14.91 (~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E))))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[9, 5])).
% 14.72/14.91 tff(11,plain,
% 14.72/14.91 (~![E: $i] : (![U: $i, V: $i, W: $i] : ((~product(U, V, W)) | product(V, U, W)) | (~![X: $i] : product(X, X, E)) | (~(![X: $i, Y: $i] : ?[Z: $i] : product(X, Y, Z) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E, X) & ![X: $i] : product(E, X, X) & ![X: $i] : product(X, inverse(X), E) & ![X: $i] : product(inverse(X), X, E))))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[10, 5])).
% 14.72/14.91 tff(12,plain,
% 14.72/14.91 ((~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))) & ![X: $i] : product(X, X, E!0) & ![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) & ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) & ![X: $i] : product(X, E!0, X) & ![X: $i] : product(E!0, X, X) & ![X: $i] : product(X, inverse(X), E!0) & ![X: $i] : product(inverse(X), X, E!0)),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[11, 4])).
% 14.72/14.91 tff(13,plain,
% 14.72/14.91 (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(14,plain,
% 14.72/14.91 ((~![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))) | product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))),
% 14.72/14.91 inference(quant_inst,[status(thm)],[])).
% 14.72/14.91 tff(15,plain,
% 14.72/14.91 (product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))),
% 14.72/14.91 inference(unit_resolution,[status(thm)],[14, 13])).
% 14.72/14.91 tff(16,plain,
% 14.72/14.91 (^[X: $i] : refl(product(inverse(X), X, E!0) <=> product(inverse(X), X, E!0))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(17,plain,
% 14.72/14.91 (![X: $i] : product(inverse(X), X, E!0) <=> ![X: $i] : product(inverse(X), X, E!0)),
% 14.72/14.91 inference(quant_intro,[status(thm)],[16])).
% 14.72/14.91 tff(18,plain,
% 14.72/14.91 (![X: $i] : product(inverse(X), X, E!0)),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(19,plain,
% 14.72/14.91 (![X: $i] : product(inverse(X), X, E!0)),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[18, 17])).
% 14.72/14.91 tff(20,plain,
% 14.72/14.91 ((~![X: $i] : product(inverse(X), X, E!0)) | product(inverse(V!2), V!2, E!0)),
% 14.72/14.91 inference(quant_inst,[status(thm)],[])).
% 14.72/14.91 tff(21,plain,
% 14.72/14.91 (product(inverse(V!2), V!2, E!0)),
% 14.72/14.91 inference(unit_resolution,[status(thm)],[20, 19])).
% 14.72/14.91 tff(22,plain,
% 14.72/14.91 (^[X: $i] : refl(product(X, inverse(X), E!0) <=> product(X, inverse(X), E!0))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(23,plain,
% 14.72/14.91 (![X: $i] : product(X, inverse(X), E!0) <=> ![X: $i] : product(X, inverse(X), E!0)),
% 14.72/14.91 inference(quant_intro,[status(thm)],[22])).
% 14.72/14.91 tff(24,plain,
% 14.72/14.91 (![X: $i] : product(X, inverse(X), E!0)),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(25,plain,
% 14.72/14.91 (![X: $i] : product(X, inverse(X), E!0)),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[24, 23])).
% 14.72/14.91 tff(26,plain,
% 14.72/14.91 ((~![X: $i] : product(X, inverse(X), E!0)) | product(V!2, inverse(V!2), E!0)),
% 14.72/14.91 inference(quant_inst,[status(thm)],[])).
% 14.72/14.91 tff(27,plain,
% 14.72/14.91 (product(V!2, inverse(V!2), E!0)),
% 14.72/14.91 inference(unit_resolution,[status(thm)],[26, 25])).
% 14.72/14.91 tff(28,plain,
% 14.72/14.91 (^[X: $i] : refl(product(X, E!0, X) <=> product(X, E!0, X))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(29,plain,
% 14.72/14.91 (![X: $i] : product(X, E!0, X) <=> ![X: $i] : product(X, E!0, X)),
% 14.72/14.91 inference(quant_intro,[status(thm)],[28])).
% 14.72/14.91 tff(30,plain,
% 14.72/14.91 (![X: $i] : product(X, E!0, X)),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(31,plain,
% 14.72/14.91 (![X: $i] : product(X, E!0, X)),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[30, 29])).
% 14.72/14.91 tff(32,plain,
% 14.72/14.91 ((~![X: $i] : product(X, E!0, X)) | product(V!2, E!0, V!2)),
% 14.72/14.91 inference(quant_inst,[status(thm)],[])).
% 14.72/14.91 tff(33,plain,
% 14.72/14.91 (product(V!2, E!0, V!2)),
% 14.72/14.91 inference(unit_resolution,[status(thm)],[32, 31])).
% 14.72/14.91 tff(34,plain,
% 14.72/14.91 (^[X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : refl((product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))) <=> (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(35,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))) <=> ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))),
% 14.72/14.91 inference(quant_intro,[status(thm)],[34])).
% 14.72/14.91 tff(36,plain,
% 14.72/14.91 (^[X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((product(X, Y, U) & product(Y, Z, V) & product(X, V, W)) <=> (~((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))))), ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) <=> (~(~((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))))))), rewrite((~(~((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))))) <=> ((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))), ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) <=> ((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))))), (((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) <=> (((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))) | product(U, Z, W)))), rewrite((((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))), (((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(37,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W)) <=> ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))),
% 14.72/14.91 inference(quant_intro,[status(thm)],[36])).
% 14.72/14.91 tff(38,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(X, V, W))) | product(U, Z, W))),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(39,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[38, 37])).
% 14.72/14.91 tff(40,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[39, 35])).
% 14.72/14.91 tff(41,plain,
% 14.72/14.91 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(V!2, E!0, V!2)) | product(E!0, V!2, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, inverse(V!2), E!0)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(V!2, E!0, V!2)) | product(E!0, V!2, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, inverse(V!2), E!0)))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(42,plain,
% 14.72/14.91 ((product(E!0, V!2, V!2) | (~product(V!2, inverse(V!2), E!0)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, E!0, V!2))) <=> ((~product(V!2, E!0, V!2)) | product(E!0, V!2, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, inverse(V!2), E!0)))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(43,plain,
% 14.72/14.91 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(E!0, V!2, V!2) | (~product(V!2, inverse(V!2), E!0)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, E!0, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(V!2, E!0, V!2)) | product(E!0, V!2, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, inverse(V!2), E!0))))),
% 14.72/14.91 inference(monotonicity,[status(thm)],[42])).
% 14.72/14.91 tff(44,plain,
% 14.72/14.91 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(E!0, V!2, V!2) | (~product(V!2, inverse(V!2), E!0)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, E!0, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(V!2, E!0, V!2)) | product(E!0, V!2, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, inverse(V!2), E!0)))),
% 14.72/14.91 inference(transitivity,[status(thm)],[43, 41])).
% 14.72/14.91 tff(45,plain,
% 14.72/14.91 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(E!0, V!2, V!2) | (~product(V!2, inverse(V!2), E!0)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, E!0, V!2)))),
% 14.72/14.91 inference(quant_inst,[status(thm)],[])).
% 14.72/14.91 tff(46,plain,
% 14.72/14.91 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(V!2, E!0, V!2)) | product(E!0, V!2, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, inverse(V!2), E!0))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[45, 44])).
% 14.72/14.91 tff(47,plain,
% 14.72/14.91 (product(E!0, V!2, V!2)),
% 14.72/14.91 inference(unit_resolution,[status(thm)],[46, 40, 33, 27, 21])).
% 14.72/14.91 tff(48,plain,
% 14.72/14.91 (^[X: $i] : refl(product(X, X, E!0) <=> product(X, X, E!0))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(49,plain,
% 14.72/14.91 (![X: $i] : product(X, X, E!0) <=> ![X: $i] : product(X, X, E!0)),
% 14.72/14.91 inference(quant_intro,[status(thm)],[48])).
% 14.72/14.91 tff(50,plain,
% 14.72/14.91 (![X: $i] : product(X, X, E!0)),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(51,plain,
% 14.72/14.91 (![X: $i] : product(X, X, E!0)),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[50, 49])).
% 14.72/14.91 tff(52,plain,
% 14.72/14.91 ((~![X: $i] : product(X, X, E!0)) | product(V!2, V!2, E!0)),
% 14.72/14.91 inference(quant_inst,[status(thm)],[])).
% 14.72/14.91 tff(53,plain,
% 14.72/14.91 (product(V!2, V!2, E!0)),
% 14.72/14.91 inference(unit_resolution,[status(thm)],[52, 51])).
% 14.72/14.91 tff(54,plain,
% 14.72/14.91 (^[X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : refl((product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))) <=> (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(55,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))) <=> ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))),
% 14.72/14.91 inference(quant_intro,[status(thm)],[54])).
% 14.72/14.91 tff(56,plain,
% 14.72/14.91 (^[X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((product(X, Y, U) & product(Y, Z, V) & product(U, Z, W)) <=> (~((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))))), ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) <=> (~(~((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))))))), rewrite((~(~((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))))) <=> ((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))), ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) <=> ((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))))), (((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) <=> (((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))) | product(X, V, W)))), rewrite((((~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W))) | product(X, V, W)) <=> (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))), (((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) <=> (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))))),
% 14.72/14.91 inference(bind,[status(th)],[])).
% 14.72/14.91 tff(57,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W)) <=> ![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))),
% 14.72/14.91 inference(quant_intro,[status(thm)],[56])).
% 14.72/14.91 tff(58,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : ((~(product(X, Y, U) & product(Y, Z, V) & product(U, Z, W))) | product(X, V, W))),
% 14.72/14.91 inference(and_elim,[status(thm)],[12])).
% 14.72/14.91 tff(59,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[58, 57])).
% 14.72/14.91 tff(60,plain,
% 14.72/14.91 (![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))),
% 14.72/14.91 inference(modus_ponens,[status(thm)],[59, 55])).
% 14.72/14.91 tff(61,plain,
% 14.72/14.91 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(inverse(V!2), V!2, E!0)) | (~product(E!0, V!2, V!2)) | (~product(V!2, V!2, E!0)) | product(inverse(V!2), E!0, V!2))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(V!2), V!2, E!0)) | (~product(E!0, V!2, V!2)) | (~product(V!2, V!2, E!0)) | product(inverse(V!2), E!0, V!2))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(62,plain,
% 14.72/14.91 ((product(inverse(V!2), E!0, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)) | (~product(E!0, V!2, V!2))) <=> ((~product(inverse(V!2), V!2, E!0)) | (~product(E!0, V!2, V!2)) | (~product(V!2, V!2, E!0)) | product(inverse(V!2), E!0, V!2))),
% 14.72/14.91 inference(rewrite,[status(thm)],[])).
% 14.72/14.91 tff(63,plain,
% 14.72/14.91 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(V!2), E!0, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)) | (~product(E!0, V!2, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(inverse(V!2), V!2, E!0)) | (~product(E!0, V!2, V!2)) | (~product(V!2, V!2, E!0)) | product(inverse(V!2), E!0, V!2)))),
% 14.72/14.91 inference(monotonicity,[status(thm)],[62])).
% 14.72/14.91 tff(64,plain,
% 14.72/14.91 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(V!2), E!0, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)) | (~product(E!0, V!2, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(V!2), V!2, E!0)) | (~product(E!0, V!2, V!2)) | (~product(V!2, V!2, E!0)) | product(inverse(V!2), E!0, V!2))),
% 14.72/14.92 inference(transitivity,[status(thm)],[63, 61])).
% 14.72/14.92 tff(65,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(V!2), E!0, V!2) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)) | (~product(E!0, V!2, V!2)))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(66,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(V!2), V!2, E!0)) | (~product(E!0, V!2, V!2)) | (~product(V!2, V!2, E!0)) | product(inverse(V!2), E!0, V!2)),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[65, 64])).
% 14.72/14.92 tff(67,plain,
% 14.72/14.92 (product(inverse(V!2), E!0, V!2)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[66, 60, 21, 53, 47])).
% 14.72/14.92 tff(68,plain,
% 14.72/14.92 (^[X: $i] : refl(product(E!0, X, X) <=> product(E!0, X, X))),
% 14.72/14.92 inference(bind,[status(th)],[])).
% 14.72/14.92 tff(69,plain,
% 14.72/14.92 (![X: $i] : product(E!0, X, X) <=> ![X: $i] : product(E!0, X, X)),
% 14.72/14.92 inference(quant_intro,[status(thm)],[68])).
% 14.72/14.92 tff(70,plain,
% 14.72/14.92 (![X: $i] : product(E!0, X, X)),
% 14.72/14.92 inference(and_elim,[status(thm)],[12])).
% 14.72/14.92 tff(71,plain,
% 14.72/14.92 (![X: $i] : product(E!0, X, X)),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[70, 69])).
% 14.72/14.92 tff(72,plain,
% 14.72/14.92 ((~![X: $i] : product(E!0, X, X)) | product(E!0, U!3, U!3)),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(73,plain,
% 14.72/14.92 (product(E!0, U!3, U!3)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[72, 71])).
% 14.72/14.92 tff(74,plain,
% 14.72/14.92 (~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))),
% 14.72/14.92 inference(and_elim,[status(thm)],[12])).
% 14.72/14.92 tff(75,plain,
% 14.72/14.92 (~product(V!2, U!3, W!1)),
% 14.72/14.92 inference(or_elim,[status(thm)],[74])).
% 14.72/14.92 tff(76,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), E!0, V!2)) | (~product(inverse(V!2), U!3, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | product(V!2, U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), E!0, V!2)) | (~product(inverse(V!2), U!3, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(77,plain,
% 14.72/14.92 ((product(V!2, U!3, W!1) | (~product(inverse(V!2), E!0, V!2)) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), U!3, W!1))) <=> (product(V!2, U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), E!0, V!2)) | (~product(inverse(V!2), U!3, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(78,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, U!3, W!1) | (~product(inverse(V!2), E!0, V!2)) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), U!3, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), E!0, V!2)) | (~product(inverse(V!2), U!3, W!1))))),
% 14.72/14.92 inference(monotonicity,[status(thm)],[77])).
% 14.72/14.92 tff(79,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, U!3, W!1) | (~product(inverse(V!2), E!0, V!2)) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), U!3, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | product(V!2, U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), E!0, V!2)) | (~product(inverse(V!2), U!3, W!1)))),
% 14.72/14.92 inference(transitivity,[status(thm)],[78, 76])).
% 14.72/14.92 tff(80,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, U!3, W!1) | (~product(inverse(V!2), E!0, V!2)) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), U!3, W!1)))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(81,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | product(V!2, U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(V!2), E!0, V!2)) | (~product(inverse(V!2), U!3, W!1))),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[80, 79])).
% 14.72/14.92 tff(82,plain,
% 14.72/14.92 (~product(inverse(V!2), U!3, W!1)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[81, 75, 40, 73, 67])).
% 14.72/14.92 tff(83,plain,
% 14.72/14.92 ((~![X: $i] : product(inverse(X), X, E!0)) | product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(84,plain,
% 14.72/14.92 (product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[83, 19])).
% 14.72/14.92 tff(85,plain,
% 14.72/14.92 ((~![X: $i] : product(inverse(X), X, E!0)) | product(inverse(inverse(V!2)), inverse(V!2), E!0)),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(86,plain,
% 14.72/14.92 (product(inverse(inverse(V!2)), inverse(V!2), E!0)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[85, 19])).
% 14.72/14.92 tff(87,plain,
% 14.72/14.92 ((~![X: $i] : product(E!0, X, X)) | product(E!0, inverse(V!2), inverse(V!2))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(88,plain,
% 14.72/14.92 (product(E!0, inverse(V!2), inverse(V!2))),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[87, 71])).
% 14.72/14.92 tff(89,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(90,plain,
% 14.72/14.92 ((product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2)))) <=> ((~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(91,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0))))),
% 14.72/14.92 inference(monotonicity,[status(thm)],[90])).
% 14.72/14.92 tff(92,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))),
% 14.72/14.92 inference(transitivity,[status(thm)],[91, 89])).
% 14.72/14.92 tff(93,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(94,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2)) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0))),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[93, 92])).
% 14.72/14.92 tff(95,plain,
% 14.72/14.92 (product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[94, 60, 88, 86, 84])).
% 14.72/14.92 tff(96,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(V!2), U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | product(inverse(V!2), U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(97,plain,
% 14.72/14.92 ((product(inverse(V!2), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1))) <=> (product(inverse(V!2), U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(98,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(V!2), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(V!2), U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1))))),
% 14.72/14.92 inference(monotonicity,[status(thm)],[97])).
% 14.72/14.92 tff(99,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(V!2), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | product(inverse(V!2), U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))),
% 14.72/14.92 inference(transitivity,[status(thm)],[98, 96])).
% 14.72/14.92 tff(100,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(V!2), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1)))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(101,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | product(inverse(V!2), U!3, W!1) | (~product(E!0, U!3, U!3)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(V!2))) | (~product(inverse(inverse(inverse(V!2))), U!3, W!1))),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[100, 99])).
% 14.72/14.92 tff(102,plain,
% 14.72/14.92 (~product(inverse(inverse(inverse(V!2))), U!3, W!1)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[101, 40, 73, 95, 82])).
% 14.72/14.92 tff(103,plain,
% 14.72/14.92 ((~![X: $i] : product(X, E!0, X)) | product(U!3, E!0, U!3)),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(104,plain,
% 14.72/14.92 (product(U!3, E!0, U!3)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[103, 31])).
% 14.72/14.92 tff(105,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(U!3, E!0, U!3)) | product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, E!0, U!3)) | product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(106,plain,
% 14.72/14.92 ((product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, U!3)) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))) <=> ((~product(U!3, E!0, U!3)) | product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(107,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, U!3)) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(U!3, E!0, U!3)) | product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))))),
% 14.72/14.92 inference(monotonicity,[status(thm)],[106])).
% 14.72/14.92 tff(108,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, U!3)) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, E!0, U!3)) | product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))),
% 14.72/14.92 inference(transitivity,[status(thm)],[107, 105])).
% 14.72/14.92 tff(109,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, U!3)) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(110,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, E!0, U!3)) | product(inverse(inverse(inverse(V!2))), U!3, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[109, 108])).
% 14.72/14.92 tff(111,plain,
% 14.72/14.92 (~product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[110, 60, 104, 102, 15])).
% 14.72/14.92 tff(112,plain,
% 14.72/14.92 ((~![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))) | product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(113,plain,
% 14.72/14.92 (product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[112, 13])).
% 14.72/14.92 tff(114,plain,
% 14.72/14.92 (product(U!3, V!2, W!1)),
% 14.72/14.92 inference(or_elim,[status(thm)],[74])).
% 14.72/14.92 tff(115,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(U!3, V!2, W!1)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(V!2, V!2, E!0)) | product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, V!2, W!1)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(V!2, V!2, E!0)) | product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(116,plain,
% 14.72/14.92 ((product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, V!2, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1)))) <=> ((~product(U!3, V!2, W!1)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(V!2, V!2, E!0)) | product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(117,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, V!2, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(U!3, V!2, W!1)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(V!2, V!2, E!0)) | product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))))),
% 14.72/14.92 inference(monotonicity,[status(thm)],[116])).
% 14.72/14.92 tff(118,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, V!2, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, V!2, W!1)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(V!2, V!2, E!0)) | product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)))),
% 14.72/14.92 inference(transitivity,[status(thm)],[117, 115])).
% 14.72/14.92 tff(119,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(U!3, E!0, tptp_fun_Z_4(V!2, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, V!2, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))))),
% 14.72/14.92 inference(quant_inst,[status(thm)],[])).
% 14.72/14.92 tff(120,plain,
% 14.72/14.92 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, V!2, W!1)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(V!2, V!2, E!0)) | product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))),
% 14.72/14.92 inference(modus_ponens,[status(thm)],[119, 118])).
% 14.72/14.92 tff(121,plain,
% 14.72/14.92 (product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))),
% 14.72/14.92 inference(unit_resolution,[status(thm)],[120, 114, 60, 113, 53])).
% 14.72/14.92 tff(122,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)) | product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)) | product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(123,plain,
% 14.72/14.92 ((product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1))) <=> ((~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)) | product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))),
% 14.72/14.92 inference(rewrite,[status(thm)],[])).
% 14.72/14.92 tff(124,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)) | product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)))),
% 14.72/14.92 inference(monotonicity,[status(thm)],[123])).
% 14.72/14.92 tff(125,plain,
% 14.72/14.92 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)) | product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1))),
% 14.72/14.93 inference(transitivity,[status(thm)],[124, 122])).
% 14.72/14.93 tff(126,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(127,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(inverse(inverse(V!2))), U!3, tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))))) | (~product(U!3, E!0, tptp_fun_Z_4(V!2, W!1))) | (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)) | product(tptp_fun_Z_4(U!3, inverse(inverse(inverse(V!2)))), E!0, W!1)),
% 14.72/14.93 inference(modus_ponens,[status(thm)],[126, 125])).
% 14.72/14.93 tff(128,plain,
% 14.72/14.93 (~product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1)),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[127, 40, 15, 121, 111])).
% 14.72/14.93 tff(129,plain,
% 14.72/14.93 ((~![X: $i] : product(X, E!0, X)) | product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(130,plain,
% 14.72/14.93 (product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[129, 31])).
% 14.72/14.93 tff(131,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(132,plain,
% 14.72/14.93 ((product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2)))))) <=> ((~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(133,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0))))),
% 14.72/14.93 inference(monotonicity,[status(thm)],[132])).
% 14.72/14.93 tff(134,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)))),
% 14.72/14.93 inference(transitivity,[status(thm)],[133, 131])).
% 14.72/14.93 tff(135,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0)) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(136,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(inverse(V!2)), inverse(V!2), E!0)) | product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(inverse(inverse(inverse(V!2))), E!0, inverse(inverse(inverse(V!2))))) | (~product(inverse(inverse(inverse(V!2))), inverse(inverse(V!2)), E!0))),
% 14.72/14.93 inference(modus_ponens,[status(thm)],[135, 134])).
% 14.72/14.93 tff(137,plain,
% 14.72/14.93 (product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[136, 40, 86, 84, 130])).
% 14.72/14.93 tff(138,plain,
% 14.72/14.93 ((~![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))) | product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(139,plain,
% 14.72/14.93 (product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[138, 13])).
% 14.72/14.93 tff(140,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, E!0, V!2)) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, inverse(V!2), E!0)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, E!0, V!2)) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, inverse(V!2), E!0)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(141,plain,
% 14.72/14.93 ((product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, inverse(V!2), E!0)) | (~product(V!2, E!0, V!2))) <=> ((~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, E!0, V!2)) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, inverse(V!2), E!0)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(142,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, inverse(V!2), E!0)) | (~product(V!2, E!0, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, E!0, V!2)) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, inverse(V!2), E!0))))),
% 14.72/14.93 inference(monotonicity,[status(thm)],[141])).
% 14.72/14.93 tff(143,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, inverse(V!2), E!0)) | (~product(V!2, E!0, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, E!0, V!2)) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, inverse(V!2), E!0)))),
% 14.72/14.93 inference(transitivity,[status(thm)],[142, 140])).
% 14.72/14.93 tff(144,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, inverse(V!2), E!0)) | (~product(V!2, E!0, V!2)))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(145,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(V!2, V!2, tptp_fun_Z_4(V!2, V!2))) | (~product(V!2, E!0, V!2)) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2) | (~product(V!2, inverse(V!2), E!0))),
% 14.72/14.93 inference(modus_ponens,[status(thm)],[144, 143])).
% 14.72/14.93 tff(146,plain,
% 14.72/14.93 (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[145, 40, 139, 33, 27])).
% 14.72/14.93 tff(147,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(inverse(V!2), V!2, E!0)) | product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(V!2, V!2, E!0)) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(V!2), V!2, E!0)) | product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(V!2, V!2, E!0)) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(148,plain,
% 14.72/14.93 ((product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0))) <=> ((~product(inverse(V!2), V!2, E!0)) | product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(V!2, V!2, E!0)) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(149,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(inverse(V!2), V!2, E!0)) | product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(V!2, V!2, E!0)) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2))))),
% 14.72/14.93 inference(monotonicity,[status(thm)],[148])).
% 14.72/14.93 tff(150,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(V!2), V!2, E!0)) | product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(V!2, V!2, E!0)) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)))),
% 14.72/14.93 inference(transitivity,[status(thm)],[149, 147])).
% 14.72/14.93 tff(151,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), V!2, E!0)) | (~product(V!2, V!2, E!0)))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(152,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(inverse(V!2), V!2, E!0)) | product(tptp_fun_Z_4(V!2, V!2), E!0, E!0) | (~product(V!2, V!2, E!0)) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2))),
% 14.72/14.93 inference(modus_ponens,[status(thm)],[151, 150])).
% 14.72/14.93 tff(153,plain,
% 14.72/14.93 (product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[152, 60, 21, 53, 146])).
% 14.72/14.93 tff(154,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(E!0, inverse(V!2), inverse(V!2))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(155,plain,
% 14.72/14.93 ((product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2)))))) <=> ((~product(E!0, inverse(V!2), inverse(V!2))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(156,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(E!0, inverse(V!2), inverse(V!2))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))))),
% 14.72/14.93 inference(monotonicity,[status(thm)],[155])).
% 14.72/14.93 tff(157,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))))),
% 14.72/14.93 inference(transitivity,[status(thm)],[156, 154])).
% 14.72/14.93 tff(158,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(159,plain,
% 14.72/14.93 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(E!0, inverse(V!2), inverse(V!2))) | (~product(tptp_fun_Z_4(V!2, V!2), E!0, E!0)) | (~product(E!0, inverse(V!2), inverse(inverse(inverse(V!2))))) | product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))),
% 14.72/14.93 inference(modus_ponens,[status(thm)],[158, 157])).
% 14.72/14.93 tff(160,plain,
% 14.72/14.93 (product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[159, 60, 88, 153, 137])).
% 14.72/14.93 tff(161,plain,
% 14.72/14.93 ((~![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))) | product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))),
% 14.72/14.93 inference(quant_inst,[status(thm)],[])).
% 14.72/14.93 tff(162,plain,
% 14.72/14.93 (product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))),
% 14.72/14.93 inference(unit_resolution,[status(thm)],[161, 13])).
% 14.72/14.93 tff(163,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(164,plain,
% 14.72/14.93 ((product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1))) <=> ((~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))),
% 14.72/14.93 inference(rewrite,[status(thm)],[])).
% 14.72/14.93 tff(165,plain,
% 14.72/14.93 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1))))),
% 14.72/14.93 inference(monotonicity,[status(thm)],[164])).
% 14.72/14.94 tff(166,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))),
% 14.72/14.94 inference(transitivity,[status(thm)],[165, 163])).
% 14.72/14.94 tff(167,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)))),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(168,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(inverse(inverse(inverse(V!2))), tptp_fun_Z_4(V!2, W!1), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), inverse(inverse(inverse(V!2))))) | (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1))),
% 14.72/14.94 inference(modus_ponens,[status(thm)],[167, 166])).
% 14.72/14.94 tff(169,plain,
% 14.72/14.94 (~product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[168, 40, 162, 160, 128])).
% 14.72/14.94 tff(170,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(171,plain,
% 14.72/14.94 ((product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))) <=> ((~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(172,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))))),
% 14.72/14.94 inference(monotonicity,[status(thm)],[171])).
% 14.72/14.94 tff(173,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))),
% 14.72/14.94 inference(transitivity,[status(thm)],[172, 170])).
% 14.72/14.94 tff(174,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(175,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(tptp_fun_Z_4(V!2, V!2), inverse(V!2), V!2)) | (~product(inverse(V!2), tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)))) | product(tptp_fun_Z_4(V!2, V!2), tptp_fun_Z_4(tptp_fun_Z_4(V!2, W!1), inverse(V!2)), W!1) | (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))),
% 14.72/14.94 inference(modus_ponens,[status(thm)],[174, 173])).
% 14.72/14.94 tff(176,plain,
% 14.72/14.94 (~product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[175, 60, 146, 162, 169])).
% 14.72/14.94 tff(177,plain,
% 14.72/14.94 ((~![X: $i] : product(X, X, E!0)) | product(W!1, W!1, E!0)),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(178,plain,
% 14.72/14.94 (product(W!1, W!1, E!0)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[177, 51])).
% 14.72/14.94 tff(179,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(W!1, W!1, E!0)) | product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(E!0, V!2, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(W!1, W!1, E!0)) | product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(E!0, V!2, V!2)))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(180,plain,
% 14.72/14.94 ((product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(W!1, W!1, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(E!0, V!2, V!2))) <=> ((~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(W!1, W!1, E!0)) | product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(E!0, V!2, V!2)))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(181,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(W!1, W!1, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(E!0, V!2, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(W!1, W!1, E!0)) | product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(E!0, V!2, V!2))))),
% 14.72/14.94 inference(monotonicity,[status(thm)],[180])).
% 14.72/14.94 tff(182,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(W!1, W!1, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(E!0, V!2, V!2)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(W!1, W!1, E!0)) | product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(E!0, V!2, V!2)))),
% 14.72/14.94 inference(transitivity,[status(thm)],[181, 179])).
% 14.72/14.94 tff(183,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(W!1, W!1, E!0)) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(E!0, V!2, V!2)))),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(184,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(W!1, V!2, tptp_fun_Z_4(V!2, W!1))) | (~product(W!1, W!1, E!0)) | product(W!1, tptp_fun_Z_4(V!2, W!1), V!2) | (~product(E!0, V!2, V!2))),
% 14.72/14.94 inference(modus_ponens,[status(thm)],[183, 182])).
% 14.72/14.94 tff(185,plain,
% 14.72/14.94 (product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[184, 60, 178, 113, 47])).
% 14.72/14.94 tff(186,plain,
% 14.72/14.94 ((~![X: $i] : product(E!0, X, X)) | product(E!0, W!1, W!1)),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(187,plain,
% 14.72/14.94 (product(E!0, W!1, W!1)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[186, 71])).
% 14.72/14.94 tff(188,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(E!0, W!1, W!1)) | (~product(W!1, W!1, E!0)) | product(W!1, E!0, W!1))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(E!0, W!1, W!1)) | (~product(W!1, W!1, E!0)) | product(W!1, E!0, W!1))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(189,plain,
% 14.72/14.94 ((product(W!1, E!0, W!1) | (~product(W!1, W!1, E!0)) | (~product(W!1, W!1, E!0)) | (~product(E!0, W!1, W!1))) <=> ((~product(E!0, W!1, W!1)) | (~product(W!1, W!1, E!0)) | product(W!1, E!0, W!1))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(190,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(W!1, E!0, W!1) | (~product(W!1, W!1, E!0)) | (~product(W!1, W!1, E!0)) | (~product(E!0, W!1, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | ((~product(E!0, W!1, W!1)) | (~product(W!1, W!1, E!0)) | product(W!1, E!0, W!1)))),
% 14.72/14.94 inference(monotonicity,[status(thm)],[189])).
% 14.72/14.94 tff(191,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(W!1, E!0, W!1) | (~product(W!1, W!1, E!0)) | (~product(W!1, W!1, E!0)) | (~product(E!0, W!1, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(E!0, W!1, W!1)) | (~product(W!1, W!1, E!0)) | product(W!1, E!0, W!1))),
% 14.72/14.94 inference(transitivity,[status(thm)],[190, 188])).
% 14.72/14.94 tff(192,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (product(W!1, E!0, W!1) | (~product(W!1, W!1, E!0)) | (~product(W!1, W!1, E!0)) | (~product(E!0, W!1, W!1)))),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(193,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(E!0, W!1, W!1)) | (~product(W!1, W!1, E!0)) | product(W!1, E!0, W!1)),
% 14.72/14.94 inference(modus_ponens,[status(thm)],[192, 191])).
% 14.72/14.94 tff(194,plain,
% 14.72/14.94 (product(W!1, E!0, W!1)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[193, 60, 178, 187])).
% 14.72/14.94 tff(195,plain,
% 14.72/14.94 ((~![X: $i] : product(X, X, E!0)) | product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)),
% 14.72/14.94 inference(quant_inst,[status(thm)],[])).
% 14.72/14.94 tff(196,plain,
% 14.72/14.94 (product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)),
% 14.72/14.94 inference(unit_resolution,[status(thm)],[195, 51])).
% 14.72/14.94 tff(197,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(W!1, E!0, W!1)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(W!1, E!0, W!1)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(198,plain,
% 14.72/14.94 ((product(V!2, tptp_fun_Z_4(V!2, W!1), W!1) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | (~product(W!1, E!0, W!1))) <=> ((~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(W!1, E!0, W!1)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))),
% 14.72/14.94 inference(rewrite,[status(thm)],[])).
% 14.72/14.94 tff(199,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, tptp_fun_Z_4(V!2, W!1), W!1) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | (~product(W!1, E!0, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | ((~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(W!1, E!0, W!1)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)))),
% 14.72/14.94 inference(monotonicity,[status(thm)],[198])).
% 14.72/14.94 tff(200,plain,
% 14.72/14.94 (((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, tptp_fun_Z_4(V!2, W!1), W!1) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | (~product(W!1, E!0, W!1)))) <=> ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(W!1, E!0, W!1)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | product(V!2, tptp_fun_Z_4(V!2, W!1), W!1))),
% 14.72/14.94 inference(transitivity,[status(thm)],[199, 197])).
% 14.72/14.94 tff(201,plain,
% 14.72/14.94 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (product(V!2, tptp_fun_Z_4(V!2, W!1), W!1) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | (~product(W!1, E!0, W!1)))),
% 14.72/14.95 inference(quant_inst,[status(thm)],[])).
% 14.72/14.95 tff(202,plain,
% 14.72/14.95 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(U, Z, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(X, V, W)))) | (~product(W!1, tptp_fun_Z_4(V!2, W!1), V!2)) | (~product(W!1, E!0, W!1)) | (~product(tptp_fun_Z_4(V!2, W!1), tptp_fun_Z_4(V!2, W!1), E!0)) | product(V!2, tptp_fun_Z_4(V!2, W!1), W!1)),
% 14.72/14.95 inference(modus_ponens,[status(thm)],[201, 200])).
% 14.72/14.95 tff(203,plain,
% 14.72/14.95 ($false),
% 14.72/14.95 inference(unit_resolution,[status(thm)],[202, 40, 196, 194, 185, 176])).
% 14.72/14.95 % SZS output end Proof
% 14.72/14.96 % E exiting
%------------------------------------------------------------------------------