%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP012+5 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:06:50 AM UTC 2025
% Result : Theorem 50.18s 50.37s
% Output : Proof 50.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP012+5 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:27:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 50.18/50.37 % SZS status Theorem
% 50.18/50.37 % SZS output start Proof
% 50.18/50.37 tff(product_type, type, (
% 50.18/50.37 product: ( $i * $i * $i ) > $o)).
% 50.18/50.37 tff(tptp_fun_X_2_type, type, (
% 50.18/50.37 tptp_fun_X_2: $i)).
% 50.18/50.37 tff(tptp_fun_E_0_type, type, (
% 50.18/50.37 tptp_fun_E_0: $i)).
% 50.18/50.37 tff(inverse_type, type, (
% 50.18/50.37 inverse: $i > $i)).
% 50.18/50.37 tff(tptp_fun_W_3_type, type, (
% 50.18/50.37 tptp_fun_W_3: $i)).
% 50.18/50.37 tff(tptp_fun_Z_1_type, type, (
% 50.18/50.37 tptp_fun_Z_1: ( $i * $i ) > $i)).
% 50.18/50.37 tff(tptp_fun_V_4_type, type, (
% 50.18/50.37 tptp_fun_V_4: $i)).
% 50.18/50.37 tff(tptp_fun_U_5_type, type, (
% 50.18/50.37 tptp_fun_U_5: $i)).
% 50.18/50.37 tff(1,plain,
% 50.18/50.37 (((![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0)))) <=> (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0))))),
% 50.18/50.37 inference(rewrite,[status(thm)],[])).
% 50.18/50.37 tff(2,plain,
% 50.18/50.37 ((![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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_1(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))),
% 50.18/50.37 inference(rewrite,[status(thm)],[])).
% 50.18/50.37 tff(3,plain,
% 50.18/50.37 (((![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0)))) <=> ((![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0))))),
% 50.18/50.37 inference(monotonicity,[status(thm)],[2])).
% 50.18/50.37 tff(4,plain,
% 50.18/50.37 (((![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0)))) <=> (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0))))),
% 50.18/50.37 inference(transitivity,[status(thm)],[3, 1])).
% 50.18/50.37 tff(5,plain,
% 50.18/50.37 ((~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E)))) <=> (~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E))))),
% 50.18/50.37 inference(rewrite,[status(thm)],[])).
% 50.18/50.37 tff(6,plain,
% 50.18/50.37 ((~![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)) => ![U: $i, V: $i, W: $i, X: $i] : ((product(inverse(U), inverse(V), W) & product(V, U, X)) => product(inverse(W), inverse(X), E)))) <=> (~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E))))),
% 50.18/50.37 inference(rewrite,[status(thm)],[])).
% 50.18/50.37 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)) => ![U: $i, V: $i, W: $i, X: $i] : ((product(inverse(U), inverse(V), W) & product(V, U, X)) => product(inverse(W), inverse(X), E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_distribution')).
% 50.18/50.37 tff(8,plain,
% 50.18/50.37 (~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 50.18/50.37 tff(9,plain,
% 50.18/50.37 (~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 50.18/50.37 tff(10,plain,
% 50.18/50.37 (~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 50.18/50.37 tff(11,plain,
% 50.18/50.37 (~![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))) | ![U: $i, V: $i, W: $i, X: $i] : ((~(product(inverse(U), inverse(V), W) & product(V, U, X))) | product(inverse(W), inverse(X), E)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 50.18/50.37 tff(12,plain,
% 50.18/50.37 (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(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(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[11, 4])).
% 50.18/50.37 tff(13,plain,
% 50.18/50.37 (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(Y, X))),
% 50.18/50.37 inference(and_elim,[status(thm)],[12])).
% 50.18/50.37 tff(14,plain,
% 50.18/50.37 ((~![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_1(Y, X))) | product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))),
% 50.18/50.37 inference(quant_inst,[status(thm)],[])).
% 50.18/50.37 tff(15,plain,
% 50.18/50.37 (product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))),
% 50.18/50.37 inference(unit_resolution,[status(thm)],[14, 13])).
% 50.18/50.37 tff(16,plain,
% 50.18/50.37 (^[X: $i] : refl(product(X, inverse(X), E!0) <=> product(X, inverse(X), E!0))),
% 50.18/50.37 inference(bind,[status(th)],[])).
% 50.18/50.37 tff(17,plain,
% 50.18/50.37 (![X: $i] : product(X, inverse(X), E!0) <=> ![X: $i] : product(X, inverse(X), E!0)),
% 50.18/50.37 inference(quant_intro,[status(thm)],[16])).
% 50.18/50.37 tff(18,plain,
% 50.18/50.37 (![X: $i] : product(X, inverse(X), E!0)),
% 50.18/50.37 inference(and_elim,[status(thm)],[12])).
% 50.18/50.37 tff(19,plain,
% 50.18/50.37 (![X: $i] : product(X, inverse(X), E!0)),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 50.18/50.37 tff(20,plain,
% 50.18/50.37 ((~![X: $i] : product(X, inverse(X), E!0)) | product(W!3, inverse(W!3), E!0)),
% 50.18/50.37 inference(quant_inst,[status(thm)],[])).
% 50.18/50.37 tff(21,plain,
% 50.18/50.37 (product(W!3, inverse(W!3), E!0)),
% 50.18/50.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 50.18/50.37 tff(22,plain,
% 50.18/50.37 (~((~(product(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2))) | product(inverse(W!3), inverse(X!2), E!0))),
% 50.18/50.37 inference(and_elim,[status(thm)],[12])).
% 50.18/50.37 tff(23,plain,
% 50.18/50.37 (product(inverse(U!5), inverse(V!4), W!3) & product(V!4, U!5, X!2)),
% 50.18/50.37 inference(or_elim,[status(thm)],[22])).
% 50.18/50.37 tff(24,plain,
% 50.18/50.37 (product(inverse(U!5), inverse(V!4), W!3)),
% 50.18/50.37 inference(and_elim,[status(thm)],[23])).
% 50.18/50.37 tff(25,plain,
% 50.18/50.37 (^[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))))),
% 50.18/50.37 inference(bind,[status(th)],[])).
% 50.18/50.37 tff(26,plain,
% 50.18/50.37 (![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)))),
% 50.18/50.37 inference(quant_intro,[status(thm)],[25])).
% 50.18/50.37 tff(27,plain,
% 50.18/50.37 (^[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)))))),
% 50.18/50.37 inference(bind,[status(th)],[])).
% 50.18/50.37 tff(28,plain,
% 50.18/50.37 (![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)))),
% 50.18/50.37 inference(quant_intro,[status(thm)],[27])).
% 50.18/50.37 tff(29,plain,
% 50.18/50.37 (![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))),
% 50.18/50.37 inference(and_elim,[status(thm)],[12])).
% 50.18/50.37 tff(30,plain,
% 50.18/50.37 (![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)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 50.18/50.37 tff(31,plain,
% 50.18/50.37 (![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)))),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 50.18/50.37 tff(32,plain,
% 50.18/50.37 (((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(W!3, inverse(W!3), E!0)) | product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), 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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(W!3, inverse(W!3), E!0)) | product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0))),
% 50.18/50.37 inference(rewrite,[status(thm)],[])).
% 50.18/50.37 tff(33,plain,
% 50.18/50.37 ((product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(W!3, inverse(W!3), E!0))) <=> ((~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(W!3, inverse(W!3), E!0)) | product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0))),
% 50.18/50.37 inference(rewrite,[status(thm)],[])).
% 50.18/50.37 tff(34,plain,
% 50.18/50.37 (((~![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(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(W!3, inverse(W!3), 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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(W!3, inverse(W!3), E!0)) | product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)))),
% 50.18/50.37 inference(monotonicity,[status(thm)],[33])).
% 50.18/50.37 tff(35,plain,
% 50.18/50.37 (((~![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(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(W!3, inverse(W!3), 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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(W!3, inverse(W!3), E!0)) | product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0))),
% 50.18/50.37 inference(transitivity,[status(thm)],[34, 32])).
% 50.18/50.37 tff(36,plain,
% 50.18/50.37 ((~![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(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(W!3, inverse(W!3), E!0)))),
% 50.18/50.37 inference(quant_inst,[status(thm)],[])).
% 50.18/50.37 tff(37,plain,
% 50.18/50.37 ((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(inverse(U!5), inverse(V!4), W!3)) | (~product(W!3, inverse(W!3), E!0)) | product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)),
% 50.18/50.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 50.18/50.37 tff(38,plain,
% 50.18/50.37 (product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)),
% 50.18/50.37 inference(unit_resolution,[status(thm)],[37, 31, 24, 21, 15])).
% 50.18/50.37 tff(39,plain,
% 50.18/50.37 (^[X: $i] : refl(product(X, E!0, X) <=> product(X, E!0, X))),
% 50.18/50.37 inference(bind,[status(th)],[])).
% 50.18/50.37 tff(40,plain,
% 50.18/50.37 (![X: $i] : product(X, E!0, X) <=> ![X: $i] : product(X, E!0, X)),
% 50.18/50.37 inference(quant_intro,[status(thm)],[39])).
% 50.18/50.37 tff(41,plain,
% 50.18/50.37 (![X: $i] : product(X, E!0, X)),
% 50.18/50.38 inference(and_elim,[status(thm)],[12])).
% 50.18/50.38 tff(42,plain,
% 50.18/50.38 (![X: $i] : product(X, E!0, X)),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 50.18/50.38 tff(43,plain,
% 50.18/50.38 ((~![X: $i] : product(X, E!0, X)) | product(U!5, E!0, U!5)),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(44,plain,
% 50.18/50.38 (product(U!5, E!0, U!5)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[43, 42])).
% 50.18/50.38 tff(45,plain,
% 50.18/50.38 ((~![X: $i] : product(X, inverse(X), E!0)) | product(U!5, inverse(U!5), E!0)),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(46,plain,
% 50.18/50.38 (product(U!5, inverse(U!5), E!0)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[45, 19])).
% 50.18/50.38 tff(47,plain,
% 50.18/50.38 (^[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))))),
% 50.18/50.38 inference(bind,[status(th)],[])).
% 50.18/50.38 tff(48,plain,
% 50.18/50.38 (![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)))),
% 50.18/50.38 inference(quant_intro,[status(thm)],[47])).
% 50.18/50.38 tff(49,plain,
% 50.18/50.38 (^[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)))))),
% 50.18/50.38 inference(bind,[status(th)],[])).
% 50.18/50.38 tff(50,plain,
% 50.18/50.38 (![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)))),
% 50.18/50.38 inference(quant_intro,[status(thm)],[49])).
% 50.18/50.38 tff(51,plain,
% 50.18/50.38 (![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))),
% 50.18/50.38 inference(and_elim,[status(thm)],[12])).
% 50.18/50.38 tff(52,plain,
% 50.18/50.38 (![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)))),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 50.18/50.38 tff(53,plain,
% 50.18/50.38 (![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)))),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 50.18/50.38 tff(54,plain,
% 50.18/50.38 (((~![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(U!5, inverse(U!5), E!0)) | (~product(U!5, E!0, U!5)) | product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), 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(U!5, inverse(U!5), E!0)) | (~product(U!5, E!0, U!5)) | product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(55,plain,
% 50.18/50.38 ((product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(U!5, inverse(U!5), E!0)) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)) | (~product(U!5, E!0, U!5))) <=> ((~product(U!5, inverse(U!5), E!0)) | (~product(U!5, E!0, U!5)) | product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(56,plain,
% 50.18/50.38 (((~![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, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(U!5, inverse(U!5), E!0)) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)) | (~product(U!5, E!0, U!5)))) <=> ((~![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(U!5, inverse(U!5), E!0)) | (~product(U!5, E!0, U!5)) | product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0))))),
% 50.18/50.38 inference(monotonicity,[status(thm)],[55])).
% 50.18/50.38 tff(57,plain,
% 50.18/50.38 (((~![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, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(U!5, inverse(U!5), E!0)) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)) | (~product(U!5, E!0, U!5)))) <=> ((~![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(U!5, inverse(U!5), E!0)) | (~product(U!5, E!0, U!5)) | product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)))),
% 50.18/50.38 inference(transitivity,[status(thm)],[56, 54])).
% 50.18/50.38 tff(58,plain,
% 50.18/50.38 ((~![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, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(U!5, inverse(U!5), E!0)) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0)) | (~product(U!5, E!0, U!5)))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(59,plain,
% 50.18/50.38 ((~![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(U!5, inverse(U!5), E!0)) | (~product(U!5, E!0, U!5)) | product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5) | (~product(inverse(U!5), tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0))),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 50.18/50.38 tff(60,plain,
% 50.18/50.38 (product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[59, 53, 46, 44, 38])).
% 50.18/50.38 tff(61,plain,
% 50.18/50.38 ((~![X: $i] : product(X, E!0, X)) | product(V!4, E!0, V!4)),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(62,plain,
% 50.18/50.38 (product(V!4, E!0, V!4)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[61, 42])).
% 50.18/50.38 tff(63,plain,
% 50.18/50.38 (product(V!4, U!5, X!2)),
% 50.18/50.38 inference(and_elim,[status(thm)],[23])).
% 50.18/50.38 tff(64,plain,
% 50.18/50.38 (((~![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!4, E!0, V!4)) | (~product(V!4, U!5, X!2)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!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!4, E!0, V!4)) | (~product(V!4, U!5, X!2)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(65,plain,
% 50.18/50.38 ((product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2) | (~product(V!4, E!0, V!4)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | (~product(V!4, U!5, X!2))) <=> ((~product(V!4, E!0, V!4)) | (~product(V!4, U!5, X!2)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(66,plain,
% 50.18/50.38 (((~![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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2) | (~product(V!4, E!0, V!4)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | (~product(V!4, U!5, X!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!4, E!0, V!4)) | (~product(V!4, U!5, X!2)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)))),
% 50.18/50.38 inference(monotonicity,[status(thm)],[65])).
% 50.18/50.38 tff(67,plain,
% 50.18/50.38 (((~![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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2) | (~product(V!4, E!0, V!4)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | (~product(V!4, U!5, X!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!4, E!0, V!4)) | (~product(V!4, U!5, X!2)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2))),
% 50.18/50.38 inference(transitivity,[status(thm)],[66, 64])).
% 50.18/50.38 tff(68,plain,
% 50.18/50.38 ((~![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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2) | (~product(V!4, E!0, V!4)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | (~product(V!4, U!5, X!2)))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(69,plain,
% 50.18/50.38 ((~![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!4, E!0, V!4)) | (~product(V!4, U!5, X!2)) | (~product(E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), U!5)) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 50.18/50.38 tff(70,plain,
% 50.18/50.38 (product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[69, 53, 63, 62, 60])).
% 50.18/50.38 tff(71,plain,
% 50.18/50.38 (^[X: $i] : refl(product(E!0, X, X) <=> product(E!0, X, X))),
% 50.18/50.38 inference(bind,[status(th)],[])).
% 50.18/50.38 tff(72,plain,
% 50.18/50.38 (![X: $i] : product(E!0, X, X) <=> ![X: $i] : product(E!0, X, X)),
% 50.18/50.38 inference(quant_intro,[status(thm)],[71])).
% 50.18/50.38 tff(73,plain,
% 50.18/50.38 (![X: $i] : product(E!0, X, X)),
% 50.18/50.38 inference(and_elim,[status(thm)],[12])).
% 50.18/50.38 tff(74,plain,
% 50.18/50.38 (![X: $i] : product(E!0, X, X)),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[73, 72])).
% 50.18/50.38 tff(75,plain,
% 50.18/50.38 ((~![X: $i] : product(E!0, X, X)) | product(E!0, inverse(W!3), inverse(W!3))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(76,plain,
% 50.18/50.38 (product(E!0, inverse(W!3), inverse(W!3))),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[75, 74])).
% 50.18/50.38 tff(77,plain,
% 50.18/50.38 ((~![X: $i] : product(X, inverse(X), E!0)) | product(V!4, inverse(V!4), E!0)),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(78,plain,
% 50.18/50.38 (product(V!4, inverse(V!4), E!0)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[77, 19])).
% 50.18/50.38 tff(79,plain,
% 50.18/50.38 (((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, inverse(V!4), E!0)) | (~product(E!0, inverse(W!3), inverse(W!3))) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)))) <=> ((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, inverse(V!4), E!0)) | (~product(E!0, inverse(W!3), inverse(W!3))) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(80,plain,
% 50.18/50.38 ((product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)) | (~product(V!4, inverse(V!4), E!0)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(E!0, inverse(W!3), inverse(W!3)))) <=> ((~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, inverse(V!4), E!0)) | (~product(E!0, inverse(W!3), inverse(W!3))) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(81,plain,
% 50.18/50.38 (((~![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(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)) | (~product(V!4, inverse(V!4), E!0)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(E!0, inverse(W!3), inverse(W!3))))) <=> ((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, inverse(V!4), E!0)) | (~product(E!0, inverse(W!3), inverse(W!3))) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))))),
% 50.18/50.38 inference(monotonicity,[status(thm)],[80])).
% 50.18/50.38 tff(82,plain,
% 50.18/50.38 (((~![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(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)) | (~product(V!4, inverse(V!4), E!0)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(E!0, inverse(W!3), inverse(W!3))))) <=> ((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, inverse(V!4), E!0)) | (~product(E!0, inverse(W!3), inverse(W!3))) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)))),
% 50.18/50.38 inference(transitivity,[status(thm)],[81, 79])).
% 50.18/50.38 tff(83,plain,
% 50.18/50.38 ((~![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(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3)) | (~product(V!4, inverse(V!4), E!0)) | (~product(inverse(V!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(E!0, inverse(W!3), inverse(W!3))))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(84,plain,
% 50.18/50.38 ((~![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!4), inverse(W!3), tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, inverse(V!4), E!0)) | (~product(E!0, inverse(W!3), inverse(W!3))) | product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 50.18/50.38 tff(85,plain,
% 50.18/50.38 (product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[84, 31, 78, 15, 76])).
% 50.18/50.38 tff(86,plain,
% 50.18/50.38 ((~![X: $i] : product(X, E!0, X)) | product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(87,plain,
% 50.18/50.38 (product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[86, 42])).
% 50.18/50.38 tff(88,plain,
% 50.18/50.38 (((~![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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(89,plain,
% 50.18/50.38 ((product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2))) <=> ((~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(90,plain,
% 50.18/50.38 (((~![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(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2))))),
% 50.18/50.38 inference(monotonicity,[status(thm)],[89])).
% 50.18/50.38 tff(91,plain,
% 50.18/50.38 (((~![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(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)))),
% 50.18/50.38 inference(transitivity,[status(thm)],[90, 88])).
% 50.18/50.38 tff(92,plain,
% 50.18/50.38 ((~![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(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2)))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(93,plain,
% 50.18/50.38 ((~![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!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), inverse(W!3))) | (~product(tptp_fun_Z_1(inverse(W!3), inverse(V!4)), E!0, tptp_fun_Z_1(inverse(W!3), inverse(V!4)))) | product(inverse(W!3), E!0, X!2) | (~product(V!4, tptp_fun_Z_1(inverse(W!3), inverse(V!4)), X!2))),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 50.18/50.38 tff(94,plain,
% 50.18/50.38 (product(inverse(W!3), E!0, X!2)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[93, 53, 87, 85, 70])).
% 50.18/50.38 tff(95,plain,
% 50.18/50.38 (^[X: $i] : refl(product(inverse(X), X, E!0) <=> product(inverse(X), X, E!0))),
% 50.18/50.38 inference(bind,[status(th)],[])).
% 50.18/50.38 tff(96,plain,
% 50.18/50.38 (![X: $i] : product(inverse(X), X, E!0) <=> ![X: $i] : product(inverse(X), X, E!0)),
% 50.18/50.38 inference(quant_intro,[status(thm)],[95])).
% 50.18/50.38 tff(97,plain,
% 50.18/50.38 (![X: $i] : product(inverse(X), X, E!0)),
% 50.18/50.38 inference(and_elim,[status(thm)],[12])).
% 50.18/50.38 tff(98,plain,
% 50.18/50.38 (![X: $i] : product(inverse(X), X, E!0)),
% 50.18/50.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 50.18/50.38 tff(99,plain,
% 50.18/50.38 ((~![X: $i] : product(inverse(X), X, E!0)) | product(inverse(inverse(X!2)), inverse(X!2), E!0)),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(100,plain,
% 50.18/50.38 (product(inverse(inverse(X!2)), inverse(X!2), E!0)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[99, 98])).
% 50.18/50.38 tff(101,plain,
% 50.18/50.38 ((~![X: $i] : product(X, inverse(X), E!0)) | product(inverse(X!2), inverse(inverse(X!2)), E!0)),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(102,plain,
% 50.18/50.38 (product(inverse(X!2), inverse(inverse(X!2)), E!0)),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[101, 19])).
% 50.18/50.38 tff(103,plain,
% 50.18/50.38 ((~![X: $i] : product(X, E!0, X)) | product(inverse(X!2), E!0, inverse(X!2))),
% 50.18/50.38 inference(quant_inst,[status(thm)],[])).
% 50.18/50.38 tff(104,plain,
% 50.18/50.38 (product(inverse(X!2), E!0, inverse(X!2))),
% 50.18/50.38 inference(unit_resolution,[status(thm)],[103, 42])).
% 50.18/50.38 tff(105,plain,
% 50.18/50.38 (((~![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(X!2), E!0, inverse(X!2))) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(inverse(X!2)), inverse(X!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(X!2), E!0, inverse(X!2))) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(106,plain,
% 50.18/50.38 ((product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)) | (~product(inverse(X!2), E!0, inverse(X!2)))) <=> ((~product(inverse(X!2), E!0, inverse(X!2))) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)))),
% 50.18/50.38 inference(rewrite,[status(thm)],[])).
% 50.18/50.38 tff(107,plain,
% 50.18/50.38 (((~![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(X!2), inverse(X!2)) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)) | (~product(inverse(X!2), E!0, inverse(X!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(X!2), E!0, inverse(X!2))) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0))))),
% 50.18/50.38 inference(monotonicity,[status(thm)],[106])).
% 50.18/50.38 tff(108,plain,
% 50.18/50.38 (((~![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(X!2), inverse(X!2)) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)) | (~product(inverse(X!2), E!0, inverse(X!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(X!2), E!0, inverse(X!2))) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)))),
% 50.18/50.39 inference(transitivity,[status(thm)],[107, 105])).
% 50.18/50.39 tff(109,plain,
% 50.18/50.39 ((~![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(X!2), inverse(X!2)) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0)) | (~product(inverse(X!2), E!0, inverse(X!2))))),
% 50.18/50.39 inference(quant_inst,[status(thm)],[])).
% 50.18/50.39 tff(110,plain,
% 50.18/50.39 ((~![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(X!2), E!0, inverse(X!2))) | (~product(inverse(X!2), inverse(inverse(X!2)), E!0)) | product(E!0, inverse(X!2), inverse(X!2)) | (~product(inverse(inverse(X!2)), inverse(X!2), E!0))),
% 50.18/50.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 50.18/50.39 tff(111,plain,
% 50.18/50.39 (product(E!0, inverse(X!2), inverse(X!2))),
% 50.18/50.39 inference(unit_resolution,[status(thm)],[110, 53, 104, 102, 100])).
% 50.18/50.39 tff(112,plain,
% 50.18/50.39 ((~![X: $i] : product(X, inverse(X), E!0)) | product(X!2, inverse(X!2), E!0)),
% 50.18/50.39 inference(quant_inst,[status(thm)],[])).
% 50.18/50.39 tff(113,plain,
% 50.18/50.39 (product(X!2, inverse(X!2), E!0)),
% 50.18/50.39 inference(unit_resolution,[status(thm)],[112, 19])).
% 50.18/50.39 tff(114,plain,
% 50.18/50.39 (~product(inverse(W!3), inverse(X!2), E!0)),
% 50.18/50.39 inference(or_elim,[status(thm)],[22])).
% 50.18/50.39 tff(115,plain,
% 50.18/50.39 (((~![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(W!3), inverse(X!2), E!0) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)) | (~product(inverse(W!3), E!0, X!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(W!3), inverse(X!2), E!0) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)) | (~product(inverse(W!3), E!0, X!2)))),
% 50.18/50.39 inference(rewrite,[status(thm)],[])).
% 50.18/50.39 tff(116,plain,
% 50.18/50.39 ((product(inverse(W!3), inverse(X!2), E!0) | (~product(inverse(W!3), E!0, X!2)) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0))) <=> (product(inverse(W!3), inverse(X!2), E!0) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)) | (~product(inverse(W!3), E!0, X!2)))),
% 50.18/50.39 inference(rewrite,[status(thm)],[])).
% 50.18/50.39 tff(117,plain,
% 50.18/50.39 (((~![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(W!3), inverse(X!2), E!0) | (~product(inverse(W!3), E!0, X!2)) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!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(W!3), inverse(X!2), E!0) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)) | (~product(inverse(W!3), E!0, X!2))))),
% 50.18/50.39 inference(monotonicity,[status(thm)],[116])).
% 50.18/50.39 tff(118,plain,
% 50.18/50.39 (((~![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(W!3), inverse(X!2), E!0) | (~product(inverse(W!3), E!0, X!2)) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!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(W!3), inverse(X!2), E!0) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)) | (~product(inverse(W!3), E!0, X!2)))),
% 50.18/50.39 inference(transitivity,[status(thm)],[117, 115])).
% 50.18/50.39 tff(119,plain,
% 50.18/50.39 ((~![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(W!3), inverse(X!2), E!0) | (~product(inverse(W!3), E!0, X!2)) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)))),
% 50.18/50.41 inference(quant_inst,[status(thm)],[])).
% 50.18/50.41 tff(120,plain,
% 50.18/50.41 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | product(inverse(W!3), inverse(X!2), E!0) | (~product(E!0, inverse(X!2), inverse(X!2))) | (~product(X!2, inverse(X!2), E!0)) | (~product(inverse(W!3), E!0, X!2))),
% 50.18/50.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 50.18/50.41 tff(121,plain,
% 50.18/50.41 ($false),
% 50.18/50.41 inference(unit_resolution,[status(thm)],[120, 31, 114, 113, 111, 94])).
% 50.18/50.41 % SZS output end Proof
% 50.18/50.42 % E exiting
%------------------------------------------------------------------------------