TSTP Solution File: GRP001+6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 22:25:19 EDT 2022
% Result : Theorem 1.02s 0.89s
% Output : Proof 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 14:10:15 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 1.02/0.89 % SZS status Theorem
% 1.02/0.89 % SZS output start Proof
% 1.02/0.89 tff(product_type, type, (
% 1.02/0.89 product: ( $i * $i * $i ) > $o)).
% 1.02/0.89 tff(tptp_fun_W_1_type, type, (
% 1.02/0.89 tptp_fun_W_1: $i)).
% 1.02/0.89 tff(tptp_fun_Z_4_type, type, (
% 1.02/0.89 tptp_fun_Z_4: ( $i * $i ) > $i)).
% 1.02/0.89 tff(tptp_fun_E_0_type, type, (
% 1.02/0.89 tptp_fun_E_0: $i)).
% 1.02/0.89 tff(inverse_type, type, (
% 1.02/0.89 inverse: $i > $i)).
% 1.02/0.89 tff(tptp_fun_V_2_type, type, (
% 1.02/0.89 tptp_fun_V_2: $i)).
% 1.02/0.89 tff(tptp_fun_U_3_type, type, (
% 1.02/0.89 tptp_fun_U_3: $i)).
% 1.02/0.89 tff(1,plain,
% 1.02/0.89 (^[X: $i] : refl(product(X, E!0, X) <=> product(X, E!0, X))),
% 1.02/0.89 inference(bind,[status(th)],[])).
% 1.02/0.89 tff(2,plain,
% 1.02/0.89 (![X: $i] : product(X, E!0, X) <=> ![X: $i] : product(X, E!0, X)),
% 1.02/0.89 inference(quant_intro,[status(thm)],[1])).
% 1.02/0.89 tff(3,plain,
% 1.02/0.89 (((~((~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))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(4,plain,
% 1.02/0.89 ((![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))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(5,plain,
% 1.02/0.89 (((~((~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)))),
% 1.02/0.89 inference(monotonicity,[status(thm)],[4])).
% 1.02/0.89 tff(6,plain,
% 1.02/0.89 (((~((~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))),
% 1.02/0.89 inference(transitivity,[status(thm)],[5, 3])).
% 1.02/0.89 tff(7,plain,
% 1.02/0.89 ((~![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)))))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(8,plain,
% 1.02/0.89 ((~![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)))))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(9,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/sandbox2/benchmark/theBenchmark.p','commutativity')).
% 1.02/0.89 tff(10,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.02/0.89 tff(11,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[10, 7])).
% 1.02/0.89 tff(12,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[11, 7])).
% 1.02/0.89 tff(13,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[12, 7])).
% 1.02/0.89 tff(14,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[13, 7])).
% 1.02/0.89 tff(15,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.02/0.89 tff(16,plain,
% 1.02/0.89 (~![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))))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[15, 7])).
% 1.02/0.89 tff(17,plain,
% 1.02/0.89 ((~((~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)),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[16, 6])).
% 1.02/0.89 tff(18,plain,
% 1.02/0.89 (![X: $i] : product(X, E!0, X)),
% 1.02/0.89 inference(and_elim,[status(thm)],[17])).
% 1.02/0.89 tff(19,plain,
% 1.02/0.89 (![X: $i] : product(X, E!0, X)),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.02/0.89 tff(20,plain,
% 1.02/0.89 ((~![X: $i] : product(X, E!0, X)) | product(V!2, E!0, V!2)),
% 1.02/0.89 inference(quant_inst,[status(thm)],[])).
% 1.02/0.89 tff(21,plain,
% 1.02/0.89 (product(V!2, E!0, V!2)),
% 1.02/0.89 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.02/0.89 tff(22,plain,
% 1.02/0.89 (![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))),
% 1.02/0.89 inference(and_elim,[status(thm)],[17])).
% 1.02/0.89 tff(23,plain,
% 1.02/0.89 ((~![X: $i, Y: $i] : product(X, Y, tptp_fun_Z_4(Y, X))) | product(W!1, E!0, tptp_fun_Z_4(E!0, W!1))),
% 1.02/0.89 inference(quant_inst,[status(thm)],[])).
% 1.02/0.89 tff(24,plain,
% 1.02/0.89 (product(W!1, E!0, tptp_fun_Z_4(E!0, W!1))),
% 1.02/0.89 inference(unit_resolution,[status(thm)],[23, 22])).
% 1.02/0.89 tff(25,plain,
% 1.02/0.89 (^[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))))),
% 1.02/0.89 inference(bind,[status(th)],[])).
% 1.02/0.89 tff(26,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(quant_intro,[status(thm)],[25])).
% 1.02/0.89 tff(27,plain,
% 1.02/0.89 (^[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)))))),
% 1.02/0.89 inference(bind,[status(th)],[])).
% 1.02/0.89 tff(28,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(quant_intro,[status(thm)],[27])).
% 1.02/0.89 tff(29,plain,
% 1.02/0.89 (![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))),
% 1.02/0.89 inference(and_elim,[status(thm)],[17])).
% 1.02/0.89 tff(30,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.02/0.89 tff(31,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.02/0.89 tff(32,plain,
% 1.02/0.89 (~((~product(U!3, V!2, W!1)) | product(V!2, U!3, W!1))),
% 1.02/0.89 inference(and_elim,[status(thm)],[17])).
% 1.02/0.89 tff(33,plain,
% 1.02/0.89 (product(U!3, V!2, W!1)),
% 1.02/0.89 inference(or_elim,[status(thm)],[32])).
% 1.02/0.89 tff(34,plain,
% 1.02/0.89 (((~![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(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(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, V!2, W!1)) | product(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1))))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(35,plain,
% 1.02/0.89 ((product(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1)))) <=> ((~product(U!3, V!2, W!1)) | product(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1))))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(36,plain,
% 1.02/0.89 (((~![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, tptp_fun_Z_4(E!0, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(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, V!2, W!1)) | product(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1)))))),
% 1.02/0.89 inference(monotonicity,[status(thm)],[35])).
% 1.02/0.89 tff(37,plain,
% 1.02/0.89 (((~![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, tptp_fun_Z_4(E!0, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(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, V!2, W!1)) | product(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1))))),
% 1.02/0.89 inference(transitivity,[status(thm)],[36, 34])).
% 1.02/0.89 tff(38,plain,
% 1.02/0.89 ((~![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, tptp_fun_Z_4(E!0, W!1)) | (~product(U!3, V!2, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1))))),
% 1.02/0.89 inference(quant_inst,[status(thm)],[])).
% 1.02/0.89 tff(39,plain,
% 1.02/0.89 ((~![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(U!3, V!2, tptp_fun_Z_4(E!0, W!1)) | (~product(V!2, E!0, V!2)) | (~product(W!1, E!0, tptp_fun_Z_4(E!0, W!1)))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.02/0.89 tff(40,plain,
% 1.02/0.89 (product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))),
% 1.02/0.89 inference(unit_resolution,[status(thm)],[39, 33, 31, 24, 21])).
% 1.02/0.89 tff(41,plain,
% 1.02/0.89 (^[X: $i] : refl(product(X, X, E!0) <=> product(X, X, E!0))),
% 1.02/0.89 inference(bind,[status(th)],[])).
% 1.02/0.89 tff(42,plain,
% 1.02/0.89 (![X: $i] : product(X, X, E!0) <=> ![X: $i] : product(X, X, E!0)),
% 1.02/0.89 inference(quant_intro,[status(thm)],[41])).
% 1.02/0.89 tff(43,plain,
% 1.02/0.89 (![X: $i] : product(X, X, E!0)),
% 1.02/0.89 inference(and_elim,[status(thm)],[17])).
% 1.02/0.89 tff(44,plain,
% 1.02/0.89 (![X: $i] : product(X, X, E!0)),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.02/0.89 tff(45,plain,
% 1.02/0.89 ((~![X: $i] : product(X, X, E!0)) | product(V!2, V!2, E!0)),
% 1.02/0.89 inference(quant_inst,[status(thm)],[])).
% 1.02/0.89 tff(46,plain,
% 1.02/0.89 (product(V!2, V!2, E!0)),
% 1.02/0.89 inference(unit_resolution,[status(thm)],[45, 44])).
% 1.02/0.89 tff(47,plain,
% 1.02/0.89 ((~![X: $i] : product(X, E!0, X)) | product(U!3, E!0, U!3)),
% 1.02/0.89 inference(quant_inst,[status(thm)],[])).
% 1.02/0.89 tff(48,plain,
% 1.02/0.89 (product(U!3, E!0, U!3)),
% 1.02/0.89 inference(unit_resolution,[status(thm)],[47, 19])).
% 1.02/0.89 tff(49,plain,
% 1.02/0.89 (^[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))))),
% 1.02/0.89 inference(bind,[status(th)],[])).
% 1.02/0.89 tff(50,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(quant_intro,[status(thm)],[49])).
% 1.02/0.89 tff(51,plain,
% 1.02/0.89 (^[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)))))),
% 1.02/0.89 inference(bind,[status(th)],[])).
% 1.02/0.89 tff(52,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(quant_intro,[status(thm)],[51])).
% 1.02/0.89 tff(53,plain,
% 1.02/0.89 (![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))),
% 1.02/0.89 inference(and_elim,[status(thm)],[17])).
% 1.02/0.89 tff(54,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.02/0.89 tff(55,plain,
% 1.02/0.89 (![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)))),
% 1.02/0.89 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.02/0.89 tff(56,plain,
% 1.02/0.89 (((~![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!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, E!0, U!3)) | product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(V!2, 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(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, E!0, U!3)) | product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(V!2, V!2, E!0)))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(57,plain,
% 1.02/0.89 ((product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(V!2, V!2, E!0)) | (~product(U!3, E!0, U!3))) <=> ((~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, E!0, U!3)) | product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(V!2, V!2, E!0)))),
% 1.02/0.89 inference(rewrite,[status(thm)],[])).
% 1.02/0.89 tff(58,plain,
% 1.02/0.89 (((~![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(E!0, W!1), V!2, U!3) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(V!2, V!2, E!0)) | (~product(U!3, E!0, U!3)))) <=> ((~![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!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, E!0, U!3)) | product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(V!2, V!2, E!0))))),
% 1.02/0.89 inference(monotonicity,[status(thm)],[57])).
% 1.02/0.89 tff(59,plain,
% 1.02/0.89 (((~![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(E!0, W!1), V!2, U!3) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(V!2, V!2, E!0)) | (~product(U!3, E!0, U!3)))) <=> ((~![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!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, E!0, U!3)) | product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(V!2, V!2, E!0)))),
% 1.02/0.89 inference(transitivity,[status(thm)],[58, 56])).
% 1.02/0.89 tff(60,plain,
% 1.02/0.89 ((~![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(E!0, W!1), V!2, U!3) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(V!2, V!2, E!0)) | (~product(U!3, E!0, U!3)))),
% 1.02/0.89 inference(quant_inst,[status(thm)],[])).
% 1.02/0.89 tff(61,plain,
% 1.02/0.89 ((~![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!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, E!0, U!3)) | product(tptp_fun_Z_4(E!0, W!1), V!2, U!3) | (~product(V!2, V!2, E!0))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.02/0.90 tff(62,plain,
% 1.02/0.90 (product(tptp_fun_Z_4(E!0, W!1), V!2, U!3)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[61, 55, 48, 46, 40])).
% 1.02/0.90 tff(63,plain,
% 1.02/0.90 (^[X: $i] : refl(product(inverse(X), X, E!0) <=> product(inverse(X), X, E!0))),
% 1.02/0.90 inference(bind,[status(th)],[])).
% 1.02/0.90 tff(64,plain,
% 1.02/0.90 (![X: $i] : product(inverse(X), X, E!0) <=> ![X: $i] : product(inverse(X), X, E!0)),
% 1.02/0.90 inference(quant_intro,[status(thm)],[63])).
% 1.02/0.90 tff(65,plain,
% 1.02/0.90 (![X: $i] : product(inverse(X), X, E!0)),
% 1.02/0.90 inference(and_elim,[status(thm)],[17])).
% 1.02/0.90 tff(66,plain,
% 1.02/0.90 (![X: $i] : product(inverse(X), X, E!0)),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.02/0.90 tff(67,plain,
% 1.02/0.90 ((~![X: $i] : product(inverse(X), X, E!0)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(68,plain,
% 1.02/0.90 (product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[67, 66])).
% 1.02/0.90 tff(69,plain,
% 1.02/0.90 (^[X: $i] : refl(product(E!0, X, X) <=> product(E!0, X, X))),
% 1.02/0.90 inference(bind,[status(th)],[])).
% 1.02/0.90 tff(70,plain,
% 1.02/0.90 (![X: $i] : product(E!0, X, X) <=> ![X: $i] : product(E!0, X, X)),
% 1.02/0.90 inference(quant_intro,[status(thm)],[69])).
% 1.02/0.90 tff(71,plain,
% 1.02/0.90 (![X: $i] : product(E!0, X, X)),
% 1.02/0.90 inference(and_elim,[status(thm)],[17])).
% 1.02/0.90 tff(72,plain,
% 1.02/0.90 (![X: $i] : product(E!0, X, X)),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.02/0.90 tff(73,plain,
% 1.02/0.90 ((~![X: $i] : product(E!0, X, X)) | product(E!0, V!2, V!2)),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(74,plain,
% 1.02/0.90 (product(E!0, V!2, V!2)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.02/0.90 tff(75,plain,
% 1.02/0.90 (((~![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(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), 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(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(76,plain,
% 1.02/0.90 ((product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2))) <=> ((~product(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(77,plain,
% 1.02/0.90 (((~![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(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~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(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0))))),
% 1.02/0.90 inference(monotonicity,[status(thm)],[76])).
% 1.02/0.90 tff(78,plain,
% 1.02/0.90 (((~![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(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~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(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)))),
% 1.02/0.90 inference(transitivity,[status(thm)],[77, 75])).
% 1.02/0.90 tff(79,plain,
% 1.02/0.90 ((~![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(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)))),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(80,plain,
% 1.02/0.90 ((~![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(E!0, W!1), V!2, U!3)) | (~product(E!0, V!2, V!2)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.02/0.90 tff(81,plain,
% 1.02/0.90 (product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[80, 31, 74, 68, 62])).
% 1.02/0.90 tff(82,plain,
% 1.02/0.90 ((~![X: $i] : product(X, X, E!0)) | product(U!3, U!3, E!0)),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(83,plain,
% 1.02/0.90 (product(U!3, U!3, E!0)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[82, 44])).
% 1.02/0.90 tff(84,plain,
% 1.02/0.90 (~product(V!2, U!3, W!1)),
% 1.02/0.90 inference(or_elim,[status(thm)],[32])).
% 1.02/0.90 tff(85,plain,
% 1.02/0.90 (((~![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(tptp_fun_Z_4(E!0, W!1)), U!3, V!2)) | (~product(U!3, U!3, E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, 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(V!2, U!3, W!1) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), U!3, V!2)) | (~product(U!3, U!3, E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1)))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(86,plain,
% 1.02/0.90 ((~![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(tptp_fun_Z_4(E!0, W!1)), U!3, V!2)) | (~product(U!3, U!3, E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1)))),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(87,plain,
% 1.02/0.90 ((~![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(tptp_fun_Z_4(E!0, W!1)), U!3, V!2)) | (~product(U!3, U!3, E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.02/0.90 tff(88,plain,
% 1.02/0.90 (~product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[87, 84, 55, 83, 81])).
% 1.02/0.90 tff(89,plain,
% 1.02/0.90 ((~![X: $i] : product(X, X, E!0)) | product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(90,plain,
% 1.02/0.90 (product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[89, 44])).
% 1.02/0.90 tff(91,plain,
% 1.02/0.90 (((~![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, tptp_fun_Z_4(E!0, W!1), W!1)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), 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(E!0, tptp_fun_Z_4(E!0, W!1), W!1)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(92,plain,
% 1.02/0.90 ((product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(E!0, tptp_fun_Z_4(E!0, W!1), W!1))) <=> ((~product(E!0, tptp_fun_Z_4(E!0, W!1), W!1)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(93,plain,
% 1.02/0.90 (((~![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(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(E!0, tptp_fun_Z_4(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, tptp_fun_Z_4(E!0, W!1), W!1)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0))))),
% 1.02/0.90 inference(monotonicity,[status(thm)],[92])).
% 1.02/0.90 tff(94,plain,
% 1.02/0.90 (((~![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(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(E!0, tptp_fun_Z_4(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, tptp_fun_Z_4(E!0, W!1), W!1)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)))),
% 1.02/0.90 inference(transitivity,[status(thm)],[93, 91])).
% 1.02/0.90 tff(95,plain,
% 1.02/0.90 ((~![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(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(E!0, tptp_fun_Z_4(E!0, W!1), W!1)))),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(96,plain,
% 1.02/0.90 ((~![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, tptp_fun_Z_4(E!0, W!1), W!1)) | product(inverse(tptp_fun_Z_4(E!0, W!1)), E!0, W!1) | (~product(tptp_fun_Z_4(E!0, W!1), tptp_fun_Z_4(E!0, W!1), E!0)) | (~product(inverse(tptp_fun_Z_4(E!0, W!1)), tptp_fun_Z_4(E!0, W!1), E!0))),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.02/0.90 tff(97,plain,
% 1.02/0.90 (~product(E!0, tptp_fun_Z_4(E!0, W!1), W!1)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[96, 31, 90, 68, 88])).
% 1.02/0.90 tff(98,plain,
% 1.02/0.90 ((~![X: $i] : product(E!0, X, X)) | product(E!0, U!3, U!3)),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(99,plain,
% 1.02/0.90 (product(E!0, U!3, U!3)),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[98, 72])).
% 1.02/0.90 tff(100,plain,
% 1.02/0.90 (((~![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(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(E!0, U!3, U!3)) | product(E!0, tptp_fun_Z_4(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(U!3, V!2, W!1)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(E!0, U!3, U!3)) | product(E!0, tptp_fun_Z_4(E!0, W!1), W!1))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(101,plain,
% 1.02/0.90 ((product(E!0, tptp_fun_Z_4(E!0, W!1), W!1) | (~product(E!0, U!3, U!3)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, V!2, W!1))) <=> ((~product(U!3, V!2, W!1)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(E!0, U!3, U!3)) | product(E!0, tptp_fun_Z_4(E!0, W!1), W!1))),
% 1.02/0.90 inference(rewrite,[status(thm)],[])).
% 1.02/0.90 tff(102,plain,
% 1.02/0.90 (((~![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, tptp_fun_Z_4(E!0, W!1), W!1) | (~product(E!0, U!3, U!3)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, 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(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(E!0, U!3, U!3)) | product(E!0, tptp_fun_Z_4(E!0, W!1), W!1)))),
% 1.02/0.90 inference(monotonicity,[status(thm)],[101])).
% 1.02/0.90 tff(103,plain,
% 1.02/0.90 (((~![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, tptp_fun_Z_4(E!0, W!1), W!1) | (~product(E!0, U!3, U!3)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, 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(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(E!0, U!3, U!3)) | product(E!0, tptp_fun_Z_4(E!0, W!1), W!1))),
% 1.02/0.90 inference(transitivity,[status(thm)],[102, 100])).
% 1.02/0.90 tff(104,plain,
% 1.02/0.90 ((~![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, tptp_fun_Z_4(E!0, W!1), W!1) | (~product(E!0, U!3, U!3)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(U!3, V!2, W!1)))),
% 1.02/0.90 inference(quant_inst,[status(thm)],[])).
% 1.02/0.90 tff(105,plain,
% 1.02/0.90 ((~![X: $i, Y: $i, Z: $i, U: $i, V: $i, W: $i] : (product(X, V, W) | (~product(X, Y, U)) | (~product(Y, Z, V)) | (~product(U, Z, W)))) | (~product(U!3, V!2, W!1)) | (~product(U!3, V!2, tptp_fun_Z_4(E!0, W!1))) | (~product(E!0, U!3, U!3)) | product(E!0, tptp_fun_Z_4(E!0, W!1), W!1)),
% 1.02/0.90 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.02/0.90 tff(106,plain,
% 1.02/0.90 ($false),
% 1.02/0.90 inference(unit_resolution,[status(thm)],[105, 33, 31, 99, 40, 97])).
% 1.02/0.90 % SZS output end Proof
%------------------------------------------------------------------------------