%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN726+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:39:55 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN726+1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:41:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(q_type, type, (
% 0.12/0.39 q: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.39 tptp_fun_Y_2: $i)).
% 0.12/0.39 tff(tptp_fun_X_1_type, type, (
% 0.12/0.39 tptp_fun_X_1: $i)).
% 0.12/0.39 tff(tptp_fun_X_3_type, type, (
% 0.12/0.39 tptp_fun_X_3: $i)).
% 0.12/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.39 tptp_fun_Y_0: $i)).
% 0.12/0.39 tff(p_type, type, (
% 0.12/0.39 p: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~p(X!3, Y!0)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl((p(X, Y) | q(X, Y)) <=> (p(X, Y) | q(X, Y)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y)) <=> ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y)) <=> ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 ((~((((![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,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')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~((((![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))),
% 0.12/0.39 inference(or_elim,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~((~(![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))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(or_elim,[status(thm)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.12/0.39 inference(and_elim,[status(thm)],[9])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.12/0.39 tff(12,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.12/0.39 inference(skolemize,[status(sab)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (p(X, Y) | q(X, Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (((~![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, Y!0) | q(X!3, Y!0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, Y!0) | q(X!3, Y!0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (q(X!3, Y!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[16, 13, 1])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.12/0.39 inference(and_elim,[status(thm)],[9])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.39 tff(24,plain,(
% 0.12/0.39 ![X: $i, Y: $i, Z: $i] : ((~(q(X, Y) & q(Y, Z))) | q(X, Z))),
% 0.12/0.39 inference(skolemize,[status(sab)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : q(X, Y)) <=> (~![X: $i, Y: $i] : q(X, Y))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : q(X, Y)),
% 0.12/0.39 inference(or_elim,[status(thm)],[6])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : q(X, Y)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : q(X, Y)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : q(X, Y)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : q(X, Y)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.39 tff(33,plain,(
% 0.12/0.39 ~q(X!1, Y!0)),
% 0.12/0.39 inference(skolemize,[status(sab)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!1, Y!0) | (~q(X!3, Y!0)) | (~q(X!1, X!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(X!1, Y!0) | (~q(X!3, Y!0)) | (~q(X!1, X!3)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!1, Y!0) | (~q(X!3, Y!0)) | (~q(X!1, X!3)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | q(X!1, Y!0) | (~q(X!3, Y!0)) | (~q(X!1, X!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~q(X!3, Y!0)) | (~q(X!1, X!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 33, 26])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (~q(X!1, X!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[37, 17])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl(((~q(X, Y)) | q(Y, X)) <=> ((~q(X, Y)) | q(Y, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) <=> ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X)) <=> ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.12/0.39 inference(and_elim,[status(thm)],[9])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.39 tff(44,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[43])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!3, X!1)) | q(X!1, X!3))) <=> ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!3, X!1)) | q(X!1, X!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!3, X!1)) | q(X!1, X!3))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!3, X!1)) | q(X!1, X!3)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (~q(X!3, X!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[48, 45, 38])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, X!1) | q(X!3, X!1))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, X!1) | q(X!3, X!1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (p(X!3, X!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[52, 13, 49])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!1, Y!0) | q(X!1, Y!0))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!1, Y!0) | q(X!1, Y!0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (p(X!1, Y!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 33, 13])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.12/0.40 inference(and_elim,[status(thm)],[9])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.40 tff(64,plain,(
% 0.12/0.40 ![X: $i, Y: $i, Z: $i] : ((~(p(X, Y) & p(Y, Z))) | p(X, Z))),
% 0.12/0.40 inference(skolemize,[status(sab)],[63])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(X!1, Y!0)) | p(X!3, Y!0) | (~p(X!3, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | p(X!3, Y!0) | (~p(X!3, X!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 ((p(X!3, Y!0) | (~p(X!3, X!1)) | (~p(X!1, Y!0))) <=> ((~p(X!1, Y!0)) | p(X!3, Y!0) | (~p(X!3, X!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (((~![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, Y!0) | (~p(X!3, X!1))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (((~![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, Y!0) | (~p(X!3, X!1)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[69, 67])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 ((~![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)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(X!1, Y!0)) | p(X!3, Y!0) | (~p(X!3, X!1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[72, 66, 57, 1, 53])).
% 0.12/0.40 tff(74,plain,(p(X!3, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : p(X, Y)) <=> (~![X: $i, Y: $i] : p(X, Y))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (~![X: $i, Y: $i] : p(X, Y)),
% 0.12/0.40 inference(or_elim,[status(thm)],[8])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (~![X: $i, Y: $i] : p(X, Y)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (~![X: $i, Y: $i] : p(X, Y)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (~![X: $i, Y: $i] : p(X, Y)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.12/0.40 tff(80,plain,(
% 0.12/0.40 ~p(X!3, Y!2)),
% 0.12/0.40 inference(skolemize,[status(sab)],[79])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (((~![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 ((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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (((~![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))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (((~![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)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 ((~![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)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 ((~![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))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 ((~p(Y!0, Y!2)) | (~p(X!3, Y!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[86, 66, 80])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (~p(Y!0, Y!2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[87, 74])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(Y!0, Y!2) | q(Y!0, Y!2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(Y!0, Y!2) | q(Y!0, Y!2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (q(Y!0, Y!2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[91, 13, 88])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(Y!0, Y!2)) | q(Y!2, Y!0))) <=> ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(Y!0, Y!2)) | q(Y!2, Y!0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(Y!0, Y!2)) | q(Y!2, Y!0))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(Y!0, Y!2)) | q(Y!2, Y!0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (q(Y!2, Y!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[95, 45, 92])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, Y!2) | q(X!3, Y!2))) <=> ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, Y!2) | q(X!3, Y!2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!3, Y!2) | q(X!3, Y!2))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!3, Y!2) | q(X!3, Y!2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (q(X!3, Y!2)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[99, 13, 80])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | ((~q(X!3, Y!2)) | q(X!3, Y!0) | (~q(Y!2, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (~q(X!3, Y!2)) | q(X!3, Y!0) | (~q(Y!2, Y!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 ((q(X!3, Y!0) | (~q(Y!2, Y!0)) | (~q(X!3, Y!2))) <=> ((~q(X!3, Y!2)) | q(X!3, Y!0) | (~q(Y!2, Y!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!3, Y!0) | (~q(Y!2, Y!0)) | (~q(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | ((~q(X!3, Y!2)) | q(X!3, Y!0) | (~q(Y!2, Y!0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[102])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!3, Y!0) | (~q(Y!2, Y!0)) | (~q(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (~q(X!3, Y!2)) | q(X!3, Y!0) | (~q(Y!2, Y!0)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[103, 101])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!3, Y!0) | (~q(Y!2, Y!0)) | (~q(X!3, Y!2)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (~q(X!3, Y!2)) | q(X!3, Y!0) | (~q(Y!2, Y!0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (q(X!3, Y!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[106, 26, 100, 96])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (~q(X!1, X!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[37, 107])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!3, Y!2)) | q(Y!2, X!3))) <=> ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!3, Y!2)) | q(Y!2, X!3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(X!3, Y!2)) | q(Y!2, X!3))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(X!3, Y!2)) | q(Y!2, X!3)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 (q(Y!2, X!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[111, 45, 100])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | ((~q(Y!2, X!3)) | q(X!1, X!3) | (~q(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (~q(Y!2, X!3)) | q(X!1, X!3) | (~q(X!1, Y!2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 ((q(X!1, X!3) | (~q(Y!2, X!3)) | (~q(X!1, Y!2))) <=> ((~q(Y!2, X!3)) | q(X!1, X!3) | (~q(X!1, Y!2)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!1, X!3) | (~q(Y!2, X!3)) | (~q(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | ((~q(Y!2, X!3)) | q(X!1, X!3) | (~q(X!1, Y!2))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[114])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!1, X!3) | (~q(Y!2, X!3)) | (~q(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (~q(Y!2, X!3)) | q(X!1, X!3) | (~q(X!1, Y!2)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (q(X!1, X!3) | (~q(Y!2, X!3)) | (~q(X!1, Y!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (q(X, Z) | (~q(Y, Z)) | (~q(X, Y)))) | (~q(Y!2, X!3)) | q(X!1, X!3) | (~q(X!1, Y!2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (~q(X!1, Y!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[118, 26, 112, 108])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | ((~q(Y!0, X!1)) | q(X!1, Y!0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~q(X, Y)) | q(Y, X))) | (~q(Y!0, X!1)) | q(X!1, Y!0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (~q(Y!0, X!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[122, 33, 45])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(Y!0, X!1) | q(Y!0, X!1))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(Y!0, X!1) | q(Y!0, X!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 (p(Y!0, X!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[126, 13, 123])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(Y!0, X!1)) | (~p(X!3, Y!0)) | p(X!3, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(Y!0, X!1)) | (~p(X!3, Y!0)) | p(X!3, X!1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 ((p(X!3, X!1) | (~p(X!3, Y!0)) | (~p(Y!0, X!1))) <=> ((~p(Y!0, X!1)) | (~p(X!3, Y!0)) | p(X!3, X!1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, X!1) | (~p(X!3, Y!0)) | (~p(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | ((~p(Y!0, X!1)) | (~p(X!3, Y!0)) | p(X!3, X!1)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, X!1) | (~p(X!3, Y!0)) | (~p(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(Y!0, X!1)) | (~p(X!3, Y!0)) | p(X!3, X!1))),
% 0.21/0.41 inference(transitivity,[status(thm)],[130, 128])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, X!1) | (~p(X!3, Y!0)) | (~p(Y!0, X!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (~p(Y!0, X!1)) | (~p(X!3, Y!0)) | p(X!3, X!1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (p(X!3, X!1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[133, 66, 127, 74])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(X!3, X!1)) | (~p(X!1, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | p(X!3, Y!2) | (~p(X!3, X!1)) | (~p(X!1, Y!2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | (p(X!3, Y!2) | (~p(X!3, X!1)) | (~p(X!1, Y!2)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : (p(X, Z) | (~p(X, Y)) | (~p(Y, Z)))) | p(X!3, Y!2) | (~p(X!3, X!1)) | (~p(X!1, Y!2))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 (~p(X!1, Y!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[137, 66, 80, 134])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | (p(X!1, Y!2) | q(X!1, Y!2))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (p(X, Y) | q(X, Y))) | p(X!1, Y!2) | q(X!1, Y!2)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[141, 13, 138, 119])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------