TSTP Solution File: SYN726+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Thu Sep 29 23:57:06 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN726+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 06:44:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(q_type, type, (
% 0.21/0.42 q: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_X_1_type, type, (
% 0.21/0.42 tptp_fun_X_1: $i)).
% 0.21/0.42 tff(tptp_fun_X_3_type, type, (
% 0.21/0.42 tptp_fun_X_3: $i)).
% 0.21/0.42 tff(p_type, type, (
% 0.21/0.42 p: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.42 tptp_fun_Y_0: $i)).
% 0.21/0.42 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.42 tptp_fun_Y_2: $i)).
% 0.21/0.42 tff(1,assumption,(p(X!3, X!1)), introduced(assumption)).
% 0.21/0.42 tff(2,assumption,(~p(X!1, Y!2)), introduced(assumption)).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl((p(X, Y) | q(X, Y)) <=> (p(X, Y) | q(X, Y)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y)) <=> ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y)) <=> ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 ((~((((![X: $i, Y: $i, Z: $i] : ((p(X, Y) & p(Y, Z)) => p(X, Z)) & ![X: $i, Y: $i, Z: $i] : ((q(X, Y) & q(Y, Z)) => q(X, Z))) & ![X: $i, Y: $i] : (q(X, Y) => q(Y, X))) & ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) => ![X: $i, Y: $i] : p(X, Y))) <=> (~((~(![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z)) & ![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z)) & ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) & ![X: $i, Y: $i] : (p(X, Y) | q(X, Y)))) | ![X: $i, Y: $i] : p(X, Y)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,axiom,(~(((((![X: $i, Y: $i, Z: $i] : ((p(X, Y) & p(Y, Z)) => p(X, Z)) & ![X: $i, Y: $i, Z: $i] : ((q(X, Y) & q(Y, Z)) => q(X, Z))) & ![X: $i, Y: $i] : (q(X, Y) => q(Y, X))) & ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) => ![X: $i, Y: $i] : p(X, Y)) | ![X: $i, Y: $i] : q(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm400')).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (~((((![X: $i, Y: $i, Z: $i] : ((p(X, Y) & p(Y, Z)) => p(X, Z)) & ![X: $i, Y: $i, Z: $i] : ((q(X, Y) & q(Y, Z)) => q(X, Z))) & ![X: $i, Y: $i] : (q(X, Y) => q(Y, X))) & ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) => ![X: $i, Y: $i] : p(X, Y))),
% 0.21/0.42 inference(or_elim,[status(thm)],[7])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (~((~(![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z)) & ![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z)) & ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) & ![X: $i, Y: $i] : (p(X, Y) | q(X, Y)))) | ![X: $i, Y: $i] : p(X, Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[8, 6])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z)) & ![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z)) & ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) & ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(or_elim,[status(thm)],[9])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(and_elim,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.21/0.42 tff(13,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(skolemize,[status(sab)],[12])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!1, Y!2) | q(X!1, Y!2))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!1, Y!2) | q(X!1, Y!2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!1, Y!2) | q(X!1, Y!2))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!1, Y!2) | q(X!1, Y!2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (p(X!1, Y!2) | q(X!1, Y!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (q(X!1, Y!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[18, 2])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl(((~q(X, Y)) | q(Y, X)) <=> ((~q(X, Y)) | q(Y, X)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) <=> ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) <=> ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.21/0.42 inference(and_elim,[status(thm)],[10])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.42 tff(25,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.21/0.42 inference(skolemize,[status(sab)],[24])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!1, Y!2)) | q(Y!2, X!1))) <=> ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!1, Y!2)) | q(Y!2, X!1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!1, Y!2)) | q(Y!2, X!1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!1, Y!2)) | q(Y!2, X!1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (q(Y!2, X!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[29, 26, 19])).
% 0.21/0.42 tff(31,assumption,(p(Y!0, Y!2)), introduced(assumption)).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : q(X, Y)) <=> (~![X: $i, Y: $i] : q(X, Y))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(or_elim,[status(thm)],[7])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (~![X: $i, Y: $i] : q(X, Y)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.21/0.42 tff(41,plain,(
% 0.21/0.42 ~q(X!1, Y!0)),
% 0.21/0.42 inference(skolemize,[status(sab)],[40])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!1, Y!0) | q(X!1, Y!0))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!1, Y!0) | q(X!1, Y!0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!1, Y!0) | q(X!1, Y!0))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!1, Y!0) | q(X!1, Y!0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (p(X!1, Y!0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[44, 41, 14])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(X, Y) & p(Y, Z)) <=> (~((~p(X, Y)) | (~p(Y, Z))))), ((~(p(X, Y) & p(Y, Z))) <=> (~(~((~p(X, Y)) | (~p(Y, Z))))))), rewrite((~(~((~p(X, Y)) | (~p(Y, Z))))) <=> ((~p(X, Y)) | (~p(Y, Z)))), ((~(p(X, Y) & p(Y, Z))) <=> ((~p(X, Y)) | (~p(Y, Z))))), (((~(p(X, Y) & p(Y, Z))) | p(X, Z)) <=> (((~p(X, Y)) | (~p(Y, Z))) | p(X, Z)))), rewrite((((~p(X, Y)) | (~p(Y, Z))) | p(X, Z)) <=> (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))), (((~(p(X, Y) & p(Y, Z))) | p(X, Z)) <=> (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.21/0.42 inference(and_elim,[status(thm)],[10])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.21/0.43 inference(skolemize,[status(sab)],[51])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(X!1, Y!0)) | p(X!1, Y!2) | (~p(Y!0, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | p(X!1, Y!2) | (~p(Y!0, Y!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((p(X!1, Y!2) | (~p(X!1, Y!0)) | (~p(Y!0, Y!2))) <=> ((~p(X!1, Y!0)) | p(X!1, Y!2) | (~p(Y!0, Y!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!1, Y!2) | (~p(X!1, Y!0)) | (~p(Y!0, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(X!1, Y!0)) | p(X!1, Y!2) | (~p(Y!0, Y!2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!1, Y!2) | (~p(X!1, Y!0)) | (~p(Y!0, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | p(X!1, Y!2) | (~p(Y!0, Y!2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!1, Y!2) | (~p(X!1, Y!0)) | (~p(Y!0, Y!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | p(X!1, Y!2) | (~p(Y!0, Y!2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[60, 54, 45, 2, 31])).
% 0.21/0.43 tff(62,plain,((~p(Y!0, Y!2)) | p(X!1, Y!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (~p(Y!0, Y!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[62, 2])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(Y!0, Y!2) | q(Y!0, Y!2))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(Y!0, Y!2) | q(Y!0, Y!2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(Y!0, Y!2) | q(Y!0, Y!2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(Y!0, Y!2) | q(Y!0, Y!2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (p(Y!0, Y!2) | q(Y!0, Y!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[66, 14])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (q(Y!0, Y!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 63])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(Y!0, X!1)) | q(X!1, Y!0))) <=> ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(Y!0, X!1)) | q(X!1, Y!0))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(Y!0, X!1)) | q(X!1, Y!0))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(Y!0, X!1)) | q(X!1, Y!0)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (~q(Y!0, X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[71, 41, 26])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((q(X, Y) & q(Y, Z)) <=> (~((~q(Y, Z)) | (~q(X, Y))))), ((~(q(X, Y) & q(Y, Z))) <=> (~(~((~q(Y, Z)) | (~q(X, Y))))))), rewrite((~(~((~q(Y, Z)) | (~q(X, Y))))) <=> ((~q(Y, Z)) | (~q(X, Y)))), ((~(q(X, Y) & q(Y, Z))) <=> ((~q(Y, Z)) | (~q(X, Y))))), (((~(q(X, Y) & q(Y, Z))) | q(X, Z)) <=> (((~q(Y, Z)) | (~q(X, Y))) | q(X, Z)))), rewrite((((~q(Y, Z)) | (~q(X, Y))) | q(X, Z)) <=> (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))), (((~(q(X, Y) & q(Y, Z))) | q(X, Z)) <=> (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.21/0.43 inference(and_elim,[status(thm)],[10])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.43 tff(79,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.21/0.43 inference(skolemize,[status(sab)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(Y!2, X!1)) | (~q(Y!0, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(Y!0, X!1) | (~q(Y!2, X!1)) | (~q(Y!0, Y!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(Y!2, X!1)) | (~q(Y!0, Y!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(Y!0, X!1) | (~q(Y!2, X!1)) | (~q(Y!0, Y!2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[84, 81, 72, 68, 30])).
% 0.21/0.43 tff(86,plain,(p(X!1, Y!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(Y!0, X!1) | q(Y!0, X!1))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(Y!0, X!1) | q(Y!0, X!1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(Y!0, X!1) | q(Y!0, X!1))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(Y!0, X!1) | q(Y!0, X!1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (p(Y!0, X!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[89, 14, 72])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(Y!0, X!1)) | p(Y!0, Y!2) | (~p(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(Y!0, X!1)) | p(Y!0, Y!2) | (~p(X!1, Y!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((p(Y!0, Y!2) | (~p(Y!0, X!1)) | (~p(X!1, Y!2))) <=> ((~p(Y!0, X!1)) | p(Y!0, Y!2) | (~p(X!1, Y!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(Y!0, Y!2) | (~p(Y!0, X!1)) | (~p(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(Y!0, X!1)) | p(Y!0, Y!2) | (~p(X!1, Y!2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(Y!0, Y!2) | (~p(Y!0, X!1)) | (~p(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(Y!0, X!1)) | p(Y!0, Y!2) | (~p(X!1, Y!2)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(Y!0, Y!2) | (~p(Y!0, X!1)) | (~p(X!1, Y!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(Y!0, X!1)) | p(Y!0, Y!2) | (~p(X!1, Y!2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (p(Y!0, Y!2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[96, 54, 90, 86])).
% 0.21/0.44 tff(98,assumption,(p(X!3, Y!0)), introduced(assumption)).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : p(X, Y)) <=> (~![X: $i, Y: $i] : p(X, Y))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(or_elim,[status(thm)],[9])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (~![X: $i, Y: $i] : p(X, Y)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[105, 99])).
% 0.21/0.44 tff(107,plain,(
% 0.21/0.44 ~p(X!3, Y!2)),
% 0.21/0.44 inference(skolemize,[status(sab)],[106])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(Y!0, Y!2)) | (~p(X!3, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | p(X!3, Y!2) | (~p(Y!0, Y!2)) | (~p(X!3, Y!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((p(X!3, Y!2) | (~p(X!3, Y!0)) | (~p(Y!0, Y!2))) <=> (p(X!3, Y!2) | (~p(Y!0, Y!2)) | (~p(X!3, Y!0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(X!3, Y!0)) | (~p(Y!0, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(Y!0, Y!2)) | (~p(X!3, Y!0))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(X!3, Y!0)) | (~p(Y!0, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | p(X!3, Y!2) | (~p(Y!0, Y!2)) | (~p(X!3, Y!0)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[110, 108])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(X!3, Y!0)) | (~p(Y!0, Y!2)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | p(X!3, Y!2) | (~p(Y!0, Y!2)) | (~p(X!3, Y!0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[113, 54, 107, 98, 97])).
% 0.21/0.44 tff(115,plain,(~p(X!3, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(X!1, Y!0)) | (~p(X!3, X!1)) | p(X!3, Y!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | (~p(X!3, X!1)) | p(X!3, Y!0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 ((p(X!3, Y!0) | (~p(X!3, X!1)) | (~p(X!1, Y!0))) <=> ((~p(X!1, Y!0)) | (~p(X!3, X!1)) | p(X!3, Y!0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!0) | (~p(X!3, X!1)) | (~p(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(X!1, Y!0)) | (~p(X!3, X!1)) | p(X!3, Y!0)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!0) | (~p(X!3, X!1)) | (~p(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | (~p(X!3, X!1)) | p(X!3, Y!0))),
% 0.21/0.44 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!0) | (~p(X!3, X!1)) | (~p(X!1, Y!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | (~p(X!3, X!1)) | p(X!3, Y!0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[121, 54, 45, 115, 1])).
% 0.21/0.44 tff(123,plain,(~p(X!3, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, X!1) | q(X!3, X!1))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, X!1) | q(X!3, X!1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, X!1) | q(X!3, X!1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, X!1) | q(X!3, X!1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (p(X!3, X!1) | q(X!3, X!1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[126, 14])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (q(X!3, X!1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, Y!0) | q(X!3, Y!0))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, Y!0) | q(X!3, Y!0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, Y!0) | q(X!3, Y!0))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, Y!0) | q(X!3, Y!0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (p(X!3, Y!0) | q(X!3, Y!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 14])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (q(X!3, Y!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[132, 115])).
% 0.21/0.44 tff(134,assumption,(q(X!3, Y!0)), introduced(assumption)).
% 0.21/0.44 tff(135,assumption,(~q(Y!0, X!3)), introduced(assumption)).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!3, Y!0)) | q(Y!0, X!3))) <=> ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!3, Y!0)) | q(Y!0, X!3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!3, Y!0)) | q(Y!0, X!3))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!3, Y!0)) | q(Y!0, X!3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 26, 135, 134])).
% 0.21/0.44 tff(140,plain,((~q(X!3, Y!0)) | q(Y!0, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 (q(Y!0, X!3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[140, 133])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(Y!0, X!3)) | (~q(X!3, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(Y!0, X!1) | (~q(Y!0, X!3)) | (~q(X!3, X!1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 ((q(Y!0, X!1) | (~q(X!3, X!1)) | (~q(Y!0, X!3))) <=> (q(Y!0, X!1) | (~q(Y!0, X!3)) | (~q(X!3, X!1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(X!3, X!1)) | (~q(Y!0, X!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(Y!0, X!3)) | (~q(X!3, X!1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(X!3, X!1)) | (~q(Y!0, X!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(Y!0, X!1) | (~q(Y!0, X!3)) | (~q(X!3, X!1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[144, 142])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(Y!0, X!1) | (~q(X!3, X!1)) | (~q(Y!0, X!3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(Y!0, X!1) | (~q(Y!0, X!3)) | (~q(X!3, X!1))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[147, 81, 72, 141, 128])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------