%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA117+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n021.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 : Tue May 5 06:33:05 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA117+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 21:08:11 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(r_type, type, (
% 0.20/0.45 r: ( $i * $i ) > $o)).
% 0.20/0.45 tff(v1_type, type, (
% 0.20/0.45 v1: $i)).
% 0.20/0.45 tff(v0_type, type, (
% 0.20/0.45 v0: $i)).
% 0.20/0.45 tff(v4_type, type, (
% 0.20/0.45 v4: $i)).
% 0.20/0.45 tff(v2_type, type, (
% 0.20/0.45 v2: $i)).
% 0.20/0.45 tff(v5_type, type, (
% 0.20/0.45 v5: $i)).
% 0.20/0.45 tff(v3_type, type, (
% 0.20/0.45 v3: $i)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 ((v5 = v2) <=> (v2 = v5)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 ((v2 = v5) <=> (v5 = v2)),
% 0.20/0.45 inference(symmetry,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 ((~(v2 = v5)) <=> (~(v5 = v2))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 ((~(v2 = v5)) <=> (~(v2 = v5))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(5,axiom,(~(v2 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v2nv5')).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (~(v2 = v5)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (~(v5 = v2)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.20/0.45 tff(8,assumption,(~r(v0, v4)), introduced(assumption)).
% 0.20/0.45 tff(9,assumption,(~r(v2, v1)), introduced(assumption)).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 ((v5 = v4) <=> (v4 = v5)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 ((v4 = v5) <=> (v5 = v4)),
% 0.20/0.45 inference(symmetry,[status(thm)],[10])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 ((~(v4 = v5)) <=> (~(v5 = v4))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 ((~(v4 = v5)) <=> (~(v4 = v5))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,axiom,(~(v4 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v4nv5')).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (~(v4 = v5)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (~(v5 = v4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.45 tff(17,assumption,(~r(v1, v4)), introduced(assumption)).
% 0.20/0.45 tff(18,assumption,(r(v4, v1)), introduced(assumption)).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl(((~r(X, Y)) | r(Y, X)) <=> ((~r(X, Y)) | r(Y, X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(22,axiom,(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rsym')).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.45 tff(24,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[23])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v1)) | r(v1, v4))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v1)) | r(v1, v4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v1)) | r(v1, v4))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v1)) | r(v1, v4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[28, 25, 18, 17])).
% 0.20/0.45 tff(30,plain,((~r(v4, v1)) | r(v1, v4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (~r(v4, v1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[30, 17])).
% 0.20/0.45 tff(32,assumption,(~r(v5, v0)), introduced(assumption)).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 ((v4 = v3) <=> (v3 = v4)),
% 0.20/0.45 inference(commutativity,[status(thm)],[])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 ((v3 = v4) <=> (v4 = v3)),
% 0.20/0.45 inference(symmetry,[status(thm)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 ((~(v3 = v4)) <=> (~(v4 = v3))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 ((~(v3 = v4)) <=> (~(v3 = v4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(37,axiom,(~(v3 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v3nv4')).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (~(v3 = v4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (~(v4 = v3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.20/0.45 tff(40,assumption,(~r(v3, v4)), introduced(assumption)).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v3)) | r(v3, v4))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v3)) | r(v3, v4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v3)) | r(v3, v4))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v3)) | r(v3, v4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (~r(v4, v3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 25, 40])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 ((~(v1 = v4)) <=> (~(v1 = v4))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(46,axiom,(~(v1 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv4')).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (~(v1 = v4)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 ((~(v1 = v3)) <=> (~(v1 = v3))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(49,axiom,(~(v1 = v3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv3')).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (~(v1 = v3)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : refl((r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((X = Y) | (X = Z)) <=> ((X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> (((X = Z) | (X = Y)) | (Y = Z)))), rewrite((((X = Z) | (X = Y)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y)))), (((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) <=> (((Y = Z) | (X = Z) | (X = Y)) | r(X, Y)))), rewrite((((Y = Z) | (X = Z) | (X = Y)) | r(X, Y)) <=> (r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) <=> (r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> ((r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(X, Z)))), rewrite(((r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(X, Z)) <=> (r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> (r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ((r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)))), rewrite(((r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.45 tff(56,axiom,(![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rno3acl')).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.30/0.46 tff(59,plain,(
% 0.30/0.46 ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(skolemize,[status(sab)],[58])).
% 0.30/0.46 tff(60,plain,
% 0.30/0.46 (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.30/0.46 tff(61,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (v3 = v4) | r(v1, v3) | r(v1, v4) | r(v3, v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | r(v1, v3) | r(v1, v4) | r(v3, v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(62,plain,
% 0.30/0.46 ((r(v3, v4) | r(v1, v4) | r(v1, v3) | (v3 = v4) | (v1 = v4) | (v1 = v3)) <=> ((v1 = v3) | (v1 = v4) | (v3 = v4) | r(v1, v3) | r(v1, v4) | r(v3, v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(63,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v1, v4) | r(v1, v3) | (v3 = v4) | (v1 = v4) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (v3 = v4) | r(v1, v3) | r(v1, v4) | r(v3, v4)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[62])).
% 0.30/0.46 tff(64,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v1, v4) | r(v1, v3) | (v3 = v4) | (v1 = v4) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | r(v1, v3) | r(v1, v4) | r(v3, v4))),
% 0.30/0.46 inference(transitivity,[status(thm)],[63, 61])).
% 0.30/0.46 tff(65,plain,
% 0.30/0.46 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v1, v4) | r(v1, v3) | (v3 = v4) | (v1 = v4) | (v1 = v3))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(66,plain,
% 0.30/0.46 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | r(v1, v3) | r(v1, v4) | r(v3, v4)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.30/0.46 tff(67,plain,
% 0.30/0.46 (r(v1, v3)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[66, 60, 50, 47, 38, 40, 17])).
% 0.30/0.46 tff(68,assumption,(~r(v3, v1)), introduced(assumption)).
% 0.30/0.46 tff(69,plain,
% 0.30/0.46 ((v3 = v1) <=> (v1 = v3)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(70,plain,
% 0.30/0.46 ((v1 = v3) <=> (v3 = v1)),
% 0.30/0.46 inference(symmetry,[status(thm)],[69])).
% 0.30/0.46 tff(71,plain,
% 0.30/0.46 ((~(v1 = v3)) <=> (~(v3 = v1))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[70])).
% 0.30/0.46 tff(72,plain,
% 0.30/0.46 (~(v3 = v1)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[50, 71])).
% 0.30/0.46 tff(73,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v3 = v4) | r(v1, v4) | r(v3, v4) | (v3 = v1) | r(v3, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v3 = v4) | r(v1, v4) | r(v3, v4) | (v3 = v1) | r(v3, v1))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(74,plain,
% 0.30/0.46 ((r(v1, v4) | r(v3, v4) | r(v3, v1) | (v1 = v4) | (v3 = v4) | (v3 = v1)) <=> ((v1 = v4) | (v3 = v4) | r(v1, v4) | r(v3, v4) | (v3 = v1) | r(v3, v1))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(75,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v3, v4) | r(v3, v1) | (v1 = v4) | (v3 = v4) | (v3 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v3 = v4) | r(v1, v4) | r(v3, v4) | (v3 = v1) | r(v3, v1)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[74])).
% 0.30/0.46 tff(76,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v3, v4) | r(v3, v1) | (v1 = v4) | (v3 = v4) | (v3 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v3 = v4) | r(v1, v4) | r(v3, v4) | (v3 = v1) | r(v3, v1))),
% 0.30/0.46 inference(transitivity,[status(thm)],[75, 73])).
% 0.30/0.46 tff(77,plain,
% 0.30/0.46 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v3, v4) | r(v3, v1) | (v1 = v4) | (v3 = v4) | (v3 = v1))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(78,plain,
% 0.30/0.46 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v3 = v4) | r(v1, v4) | r(v3, v4) | (v3 = v1) | r(v3, v1)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.30/0.46 tff(79,plain,
% 0.30/0.46 ($false),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[78, 60, 47, 38, 40, 17, 72, 68])).
% 0.30/0.46 tff(80,plain,(r(v3, v1) | r(v3, v4) | r(v1, v4)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.46 tff(81,plain,
% 0.30/0.46 (r(v3, v1)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[80, 40, 17])).
% 0.30/0.46 tff(82,assumption,(~r(v1, v5)), introduced(assumption)).
% 0.30/0.46 tff(83,plain,
% 0.30/0.46 ((v5 = v0) <=> (v0 = v5)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(84,plain,
% 0.30/0.46 ((v0 = v5) <=> (v5 = v0)),
% 0.30/0.46 inference(symmetry,[status(thm)],[83])).
% 0.30/0.46 tff(85,plain,
% 0.30/0.46 ((~(v0 = v5)) <=> (~(v5 = v0))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[84])).
% 0.30/0.46 tff(86,plain,
% 0.30/0.46 ((~(v0 = v5)) <=> (~(v0 = v5))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(87,axiom,(~(v0 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv5')).
% 0.30/0.46 tff(88,plain,
% 0.30/0.46 (~(v0 = v5)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.30/0.46 tff(89,plain,
% 0.30/0.46 (~(v5 = v0)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.30/0.46 tff(90,plain,
% 0.30/0.46 ((v1 = v0) <=> (v0 = v1)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(91,plain,
% 0.30/0.46 ((v0 = v1) <=> (v1 = v0)),
% 0.30/0.46 inference(symmetry,[status(thm)],[90])).
% 0.30/0.46 tff(92,plain,
% 0.30/0.46 ((~(v0 = v1)) <=> (~(v1 = v0))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.30/0.46 tff(93,plain,
% 0.30/0.46 ((~(v0 = v1)) <=> (~(v0 = v1))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(94,axiom,(~(v0 = v1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv1')).
% 0.30/0.46 tff(95,plain,
% 0.30/0.46 (~(v0 = v1)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.30/0.46 tff(96,plain,
% 0.30/0.46 (~(v1 = v0)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.30/0.46 tff(97,plain,
% 0.30/0.46 ((~(v1 = v5)) <=> (~(v1 = v5))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(98,axiom,(~(v1 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv5')).
% 0.30/0.46 tff(99,plain,
% 0.30/0.46 (~(v1 = v5)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.30/0.46 tff(100,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(101,plain,
% 0.30/0.46 ((r(v5, v0) | r(v1, v0) | r(v1, v5) | (v5 = v0) | (v1 = v0) | (v1 = v5)) <=> ((v1 = v5) | r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(102,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v1, v0) | r(v1, v5) | (v5 = v0) | (v1 = v0) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[101])).
% 0.30/0.46 tff(103,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v1, v0) | r(v1, v5) | (v5 = v0) | (v1 = v0) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0))),
% 0.30/0.46 inference(transitivity,[status(thm)],[102, 100])).
% 0.30/0.46 tff(104,plain,
% 0.30/0.46 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v1, v0) | r(v1, v5) | (v5 = v0) | (v1 = v0) | (v1 = v5))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(105,plain,
% 0.30/0.46 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.30/0.46 tff(106,plain,
% 0.30/0.46 (r(v1, v5) | (v5 = v0) | (v1 = v0) | r(v1, v0) | r(v5, v0)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[105, 60, 99])).
% 0.30/0.46 tff(107,plain,
% 0.30/0.46 (r(v1, v5) | r(v1, v0) | r(v5, v0)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[106, 96, 89])).
% 0.30/0.46 tff(108,plain,
% 0.30/0.46 (r(v1, v0)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[107, 82, 32])).
% 0.30/0.46 tff(109,plain,
% 0.30/0.46 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v0)) | r(v0, v1))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v0)) | r(v0, v1))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(110,plain,
% 0.30/0.46 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v0)) | r(v0, v1))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(111,plain,
% 0.30/0.46 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v0)) | r(v0, v1)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.30/0.46 tff(112,plain,
% 0.30/0.46 (r(v0, v1)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[111, 25, 108])).
% 0.30/0.46 tff(113,assumption,(~r(v4, v1)), introduced(assumption)).
% 0.30/0.46 tff(114,plain,
% 0.30/0.46 ((v4 = v2) <=> (v2 = v4)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(115,plain,
% 0.30/0.46 ((v2 = v4) <=> (v4 = v2)),
% 0.30/0.46 inference(symmetry,[status(thm)],[114])).
% 0.30/0.46 tff(116,plain,
% 0.30/0.46 ((~(v2 = v4)) <=> (~(v4 = v2))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[115])).
% 0.30/0.46 tff(117,plain,
% 0.30/0.46 ((~(v2 = v4)) <=> (~(v2 = v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(118,axiom,(~(v2 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v2nv4')).
% 0.30/0.46 tff(119,plain,
% 0.30/0.46 (~(v2 = v4)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.30/0.46 tff(120,plain,
% 0.30/0.46 (~(v4 = v2)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.30/0.46 tff(121,plain,
% 0.30/0.46 ((v2 = v1) <=> (v1 = v2)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(122,plain,
% 0.30/0.46 ((v1 = v2) <=> (v2 = v1)),
% 0.30/0.46 inference(symmetry,[status(thm)],[121])).
% 0.30/0.46 tff(123,plain,
% 0.30/0.46 ((~(v1 = v2)) <=> (~(v2 = v1))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[122])).
% 0.30/0.46 tff(124,plain,
% 0.30/0.46 ((~(v1 = v2)) <=> (~(v1 = v2))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(125,axiom,(~(v1 = v2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv2')).
% 0.30/0.46 tff(126,plain,
% 0.30/0.46 (~(v1 = v2)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.30/0.46 tff(127,plain,
% 0.30/0.46 (~(v2 = v1)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[126, 123])).
% 0.30/0.46 tff(128,plain,
% 0.30/0.46 ((v4 = v1) <=> (v1 = v4)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(129,plain,
% 0.30/0.46 ((v1 = v4) <=> (v4 = v1)),
% 0.30/0.46 inference(symmetry,[status(thm)],[128])).
% 0.30/0.46 tff(130,plain,
% 0.30/0.46 ((~(v1 = v4)) <=> (~(v4 = v1))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[129])).
% 0.30/0.46 tff(131,plain,
% 0.30/0.46 (~(v4 = v1)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[47, 130])).
% 0.30/0.46 tff(132,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v1) | r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v1) | r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(133,plain,
% 0.30/0.46 ((r(v2, v1) | r(v4, v1) | r(v4, v2) | (v2 = v1) | (v4 = v1) | (v4 = v2)) <=> ((v4 = v1) | r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(134,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v4, v1) | r(v4, v2) | (v2 = v1) | (v4 = v1) | (v4 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v1) | r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[133])).
% 0.30/0.46 tff(135,plain,
% 0.30/0.46 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v4, v1) | r(v4, v2) | (v2 = v1) | (v4 = v1) | (v4 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v1) | r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2))),
% 0.30/0.47 inference(transitivity,[status(thm)],[134, 132])).
% 0.30/0.47 tff(136,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v4, v1) | r(v4, v2) | (v2 = v1) | (v4 = v1) | (v4 = v2))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(137,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v1) | r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.30/0.47 tff(138,plain,
% 0.30/0.47 (r(v4, v1) | (v2 = v1) | r(v2, v1) | r(v4, v2) | (v4 = v2)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[137, 60, 131])).
% 0.30/0.47 tff(139,plain,
% 0.30/0.47 (r(v4, v2)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[138, 9, 127, 113, 120])).
% 0.30/0.47 tff(140,plain,
% 0.30/0.47 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v2)) | r(v2, v4))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v2)) | r(v2, v4))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(141,plain,
% 0.30/0.47 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v2)) | r(v2, v4))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(142,plain,
% 0.30/0.47 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v2)) | r(v2, v4)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.30/0.47 tff(143,plain,
% 0.30/0.47 (r(v2, v4)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[142, 25, 139])).
% 0.30/0.47 tff(144,plain,
% 0.30/0.47 ((v5 = v1) <=> (v1 = v5)),
% 0.30/0.47 inference(commutativity,[status(thm)],[])).
% 0.30/0.47 tff(145,plain,
% 0.30/0.47 ((v1 = v5) <=> (v5 = v1)),
% 0.30/0.47 inference(symmetry,[status(thm)],[144])).
% 0.30/0.47 tff(146,plain,
% 0.30/0.47 ((~(v1 = v5)) <=> (~(v5 = v1))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[145])).
% 0.30/0.47 tff(147,plain,
% 0.30/0.47 (~(v5 = v1)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[99, 146])).
% 0.30/0.47 tff(148,plain,
% 0.30/0.47 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v1)) | r(v1, v5))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v1)) | r(v1, v5))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(149,plain,
% 0.30/0.47 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v1)) | r(v1, v5))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(150,plain,
% 0.30/0.47 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v1)) | r(v1, v5)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.30/0.47 tff(151,plain,
% 0.30/0.47 (~r(v5, v1)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[150, 25, 82])).
% 0.30/0.47 tff(152,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v1) | r(v5, v4) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v1) | r(v5, v4) | (v5 = v4))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(153,plain,
% 0.30/0.47 ((r(v4, v1) | r(v5, v1) | r(v5, v4) | (v4 = v1) | (v5 = v1) | (v5 = v4)) <=> (r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v1) | r(v5, v4) | (v5 = v4))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(154,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v5, v1) | r(v5, v4) | (v4 = v1) | (v5 = v1) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v1) | r(v5, v4) | (v5 = v4)))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[153])).
% 0.30/0.47 tff(155,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v5, v1) | r(v5, v4) | (v4 = v1) | (v5 = v1) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v1) | r(v5, v4) | (v5 = v4))),
% 0.30/0.47 inference(transitivity,[status(thm)],[154, 152])).
% 0.30/0.47 tff(156,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v5, v1) | r(v5, v4) | (v4 = v1) | (v5 = v1) | (v5 = v4))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(157,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v1) | r(v5, v4) | (v5 = v4)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.30/0.47 tff(158,plain,
% 0.30/0.47 (r(v5, v4)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[157, 60, 151, 147, 131, 113, 16])).
% 0.30/0.47 tff(159,plain,
% 0.30/0.47 (^[X: $i, Y: $i, Z: $i] : refl(((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) <=> ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.30/0.47 inference(bind,[status(th)],[])).
% 0.30/0.47 tff(160,plain,
% 0.30/0.47 (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(quant_intro,[status(thm)],[159])).
% 0.30/0.47 tff(161,plain,
% 0.30/0.47 (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(162,plain,
% 0.30/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((X = Y) | (X = Z)) <=> ((X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> (((X = Z) | (X = Y)) | (Y = Z)))), rewrite((((X = Z) | (X = Y)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y)))), (((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) <=> (((Y = Z) | (X = Z) | (X = Y)) | (~r(X, Y))))), rewrite((((Y = Z) | (X = Z) | (X = Y)) | (~r(X, Y))) <=> ((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) <=> ((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)))), ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) <=> (((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(X, Z))))), rewrite((((~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(X, Z))) <=> ((~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) <=> ((~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> (((~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(Y, Z))))), rewrite((((~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(Y, Z))) <=> ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.30/0.47 inference(bind,[status(th)],[])).
% 0.30/0.47 tff(163,plain,
% 0.30/0.47 (![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(quant_intro,[status(thm)],[162])).
% 0.30/0.47 tff(164,axiom,(![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rno3cl')).
% 0.30/0.47 tff(165,plain,
% 0.30/0.47 (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.30/0.47 tff(166,plain,
% 0.30/0.47 (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.30/0.47 tff(167,plain,(
% 0.30/0.47 ![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(skolemize,[status(sab)],[166])).
% 0.30/0.47 tff(168,plain,
% 0.30/0.47 (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.30/0.47 tff(169,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (~r(v5, v4)) | (v5 = v4) | (~r(v2, v4)) | (~r(v2, v5)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (~r(v5, v4)) | (v5 = v4) | (~r(v2, v4)) | (~r(v2, v5)))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(170,plain,
% 0.30/0.47 (((~r(v5, v4)) | (~r(v2, v4)) | (~r(v2, v5)) | (v5 = v4) | (v2 = v4) | (v2 = v5)) <=> ((v2 = v4) | (v2 = v5) | (~r(v5, v4)) | (v5 = v4) | (~r(v2, v4)) | (~r(v2, v5)))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(171,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (~r(v2, v4)) | (~r(v2, v5)) | (v5 = v4) | (v2 = v4) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (~r(v5, v4)) | (v5 = v4) | (~r(v2, v4)) | (~r(v2, v5))))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[170])).
% 0.30/0.47 tff(172,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (~r(v2, v4)) | (~r(v2, v5)) | (v5 = v4) | (v2 = v4) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (~r(v5, v4)) | (v5 = v4) | (~r(v2, v4)) | (~r(v2, v5)))),
% 0.30/0.47 inference(transitivity,[status(thm)],[171, 169])).
% 0.30/0.47 tff(173,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (~r(v2, v4)) | (~r(v2, v5)) | (v5 = v4) | (v2 = v4) | (v2 = v5))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(174,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (~r(v5, v4)) | (v5 = v4) | (~r(v2, v4)) | (~r(v2, v5))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.30/0.47 tff(175,plain,
% 0.30/0.47 (~r(v2, v5)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[174, 168, 119, 6, 158, 16, 143])).
% 0.30/0.47 tff(176,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v2 = v5) | r(v1, v5) | (v2 = v1) | r(v2, v1) | r(v2, v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v2 = v5) | r(v1, v5) | (v2 = v1) | r(v2, v1) | r(v2, v5))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(177,plain,
% 0.30/0.47 ((r(v1, v5) | r(v2, v5) | r(v2, v1) | (v1 = v5) | (v2 = v5) | (v2 = v1)) <=> ((v1 = v5) | (v2 = v5) | r(v1, v5) | (v2 = v1) | r(v2, v1) | r(v2, v5))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(178,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v2, v5) | r(v2, v1) | (v1 = v5) | (v2 = v5) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v2 = v5) | r(v1, v5) | (v2 = v1) | r(v2, v1) | r(v2, v5)))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[177])).
% 0.30/0.47 tff(179,plain,
% 0.30/0.47 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v2, v5) | r(v2, v1) | (v1 = v5) | (v2 = v5) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v2 = v5) | r(v1, v5) | (v2 = v1) | r(v2, v1) | r(v2, v5))),
% 0.30/0.47 inference(transitivity,[status(thm)],[178, 176])).
% 0.30/0.47 tff(180,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v2, v5) | r(v2, v1) | (v1 = v5) | (v2 = v5) | (v2 = v1))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(181,plain,
% 0.30/0.47 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v2 = v5) | r(v1, v5) | (v2 = v1) | r(v2, v1) | r(v2, v5)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.30/0.47 tff(182,plain,
% 0.30/0.47 ($false),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[181, 60, 99, 6, 82, 127, 9, 175])).
% 0.30/0.47 tff(183,plain,(r(v2, v1) | r(v1, v5) | r(v4, v1)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47 tff(184,plain,
% 0.30/0.47 (r(v2, v1)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[183, 82, 113])).
% 0.30/0.48 tff(185,plain,
% 0.30/0.48 ((~(v0 = v2)) <=> (~(v0 = v2))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(186,axiom,(~(v0 = v2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv2')).
% 0.30/0.48 tff(187,plain,
% 0.30/0.48 (~(v0 = v2)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.30/0.48 tff(188,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v1)) | (~r(v2, v1)) | (~r(v0, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v1)) | (~r(v2, v1)) | (~r(v0, v2)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(189,plain,
% 0.30/0.48 (((~r(v2, v1)) | (~r(v0, v1)) | (~r(v0, v2)) | (v2 = v1) | (v0 = v1) | (v0 = v2)) <=> ((v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v1)) | (~r(v2, v1)) | (~r(v0, v2)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(190,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v0, v1)) | (~r(v0, v2)) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v1)) | (~r(v2, v1)) | (~r(v0, v2))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[189])).
% 0.30/0.48 tff(191,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v0, v1)) | (~r(v0, v2)) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v1)) | (~r(v2, v1)) | (~r(v0, v2)))),
% 0.30/0.48 inference(transitivity,[status(thm)],[190, 188])).
% 0.30/0.48 tff(192,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v0, v1)) | (~r(v0, v2)) | (v2 = v1) | (v0 = v1) | (v0 = v2))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(193,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v1)) | (~r(v2, v1)) | (~r(v0, v2))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.30/0.48 tff(194,plain,
% 0.30/0.48 (~r(v0, v2)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[193, 168, 95, 187, 127, 184, 112])).
% 0.30/0.48 tff(195,assumption,(r(v3, v1)), introduced(assumption)).
% 0.30/0.48 tff(196,plain,
% 0.30/0.48 ((~(v2 = v3)) <=> (~(v2 = v3))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(197,axiom,(~(v2 = v3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v2nv3')).
% 0.30/0.48 tff(198,plain,
% 0.30/0.48 (~(v2 = v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.30/0.48 tff(199,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v1) | (v3 = v1) | (~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v1) | (v3 = v1) | (~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(200,plain,
% 0.30/0.48 (((~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)) | (v3 = v1) | (v2 = v1) | (v2 = v3)) <=> ((v2 = v3) | (v2 = v1) | (v3 = v1) | (~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(201,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)) | (v3 = v1) | (v2 = v1) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v1) | (v3 = v1) | (~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[200])).
% 0.30/0.48 tff(202,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)) | (v3 = v1) | (v2 = v1) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v1) | (v3 = v1) | (~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)))),
% 0.30/0.48 inference(transitivity,[status(thm)],[201, 199])).
% 0.30/0.48 tff(203,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3)) | (v3 = v1) | (v2 = v1) | (v2 = v3))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(204,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v1) | (v3 = v1) | (~r(v3, v1)) | (~r(v2, v1)) | (~r(v2, v3))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.30/0.48 tff(205,plain,
% 0.30/0.48 (~r(v2, v3)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[204, 168, 198, 72, 195, 127, 184])).
% 0.30/0.48 tff(206,plain,
% 0.30/0.48 ((~(v0 = v3)) <=> (~(v0 = v3))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(207,axiom,(~(v0 = v3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv3')).
% 0.30/0.48 tff(208,plain,
% 0.30/0.48 (~(v0 = v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.30/0.48 tff(209,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v3 = v1) | (~r(v3, v1)) | (~r(v0, v3)) | (~r(v0, v1)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v3 = v1) | (~r(v3, v1)) | (~r(v0, v3)) | (~r(v0, v1)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(210,plain,
% 0.30/0.48 (((~r(v3, v1)) | (~r(v0, v1)) | (~r(v0, v3)) | (v3 = v1) | (v0 = v1) | (v0 = v3)) <=> ((v0 = v1) | (v0 = v3) | (v3 = v1) | (~r(v3, v1)) | (~r(v0, v3)) | (~r(v0, v1)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(211,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v1)) | (~r(v0, v1)) | (~r(v0, v3)) | (v3 = v1) | (v0 = v1) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v3 = v1) | (~r(v3, v1)) | (~r(v0, v3)) | (~r(v0, v1))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[210])).
% 0.30/0.48 tff(212,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v1)) | (~r(v0, v1)) | (~r(v0, v3)) | (v3 = v1) | (v0 = v1) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v3 = v1) | (~r(v3, v1)) | (~r(v0, v3)) | (~r(v0, v1)))),
% 0.30/0.48 inference(transitivity,[status(thm)],[211, 209])).
% 0.30/0.48 tff(213,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v1)) | (~r(v0, v1)) | (~r(v0, v3)) | (v3 = v1) | (v0 = v1) | (v0 = v3))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(214,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v3 = v1) | (~r(v3, v1)) | (~r(v0, v3)) | (~r(v0, v1))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.30/0.48 tff(215,plain,
% 0.30/0.48 (~r(v0, v3)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[214, 168, 95, 208, 72, 195, 112])).
% 0.30/0.48 tff(216,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v0, v2) | r(v2, v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v0, v2) | r(v2, v3))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(217,plain,
% 0.30/0.48 ((r(v2, v3) | r(v0, v3) | r(v0, v2) | (v2 = v3) | (v0 = v3) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v0, v2) | r(v2, v3))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(218,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v3) | r(v0, v3) | r(v0, v2) | (v2 = v3) | (v0 = v3) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v0, v2) | r(v2, v3)))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[217])).
% 0.30/0.48 tff(219,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v3) | r(v0, v3) | r(v0, v2) | (v2 = v3) | (v0 = v3) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v0, v2) | r(v2, v3))),
% 0.30/0.48 inference(transitivity,[status(thm)],[218, 216])).
% 0.30/0.48 tff(220,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v3) | r(v0, v3) | r(v0, v2) | (v2 = v3) | (v0 = v3) | (v0 = v2))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(221,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v0, v2) | r(v2, v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.30/0.48 tff(222,plain,
% 0.30/0.48 ($false),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[221, 60, 187, 208, 198, 215, 205, 194])).
% 0.30/0.48 tff(223,plain,(r(v1, v5) | (~r(v3, v1)) | r(v4, v1) | r(v5, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48 tff(224,plain,
% 0.30/0.48 (r(v1, v5)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[223, 81, 31, 32])).
% 0.30/0.48 tff(225,plain,
% 0.30/0.48 ((v5 = v3) <=> (v3 = v5)),
% 0.30/0.48 inference(commutativity,[status(thm)],[])).
% 0.30/0.48 tff(226,plain,
% 0.30/0.48 ((v3 = v5) <=> (v5 = v3)),
% 0.30/0.48 inference(symmetry,[status(thm)],[225])).
% 0.30/0.48 tff(227,plain,
% 0.30/0.48 ((~(v3 = v5)) <=> (~(v5 = v3))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[226])).
% 0.30/0.48 tff(228,plain,
% 0.30/0.48 ((~(v3 = v5)) <=> (~(v3 = v5))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(229,axiom,(~(v3 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v3nv5')).
% 0.30/0.48 tff(230,plain,
% 0.30/0.48 (~(v3 = v5)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.30/0.48 tff(231,plain,
% 0.30/0.48 (~(v5 = v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[230, 227])).
% 0.30/0.48 tff(232,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(233,plain,
% 0.30/0.48 (((~r(v5, v3)) | (~r(v1, v3)) | (~r(v1, v5)) | (v5 = v3) | (v1 = v3) | (v1 = v5)) <=> ((v1 = v3) | (v1 = v5) | (v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(234,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v1, v3)) | (~r(v1, v5)) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[233])).
% 0.30/0.48 tff(235,plain,
% 0.30/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v1, v3)) | (~r(v1, v5)) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)))),
% 0.30/0.48 inference(transitivity,[status(thm)],[234, 232])).
% 0.30/0.48 tff(236,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v1, v3)) | (~r(v1, v5)) | (v5 = v3) | (v1 = v3) | (v1 = v5))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(237,plain,
% 0.30/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.30/0.49 tff(238,plain,
% 0.30/0.49 ((v5 = v3) | (~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[237, 168, 50, 99])).
% 0.30/0.49 tff(239,plain,
% 0.30/0.49 ((~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[238, 231])).
% 0.30/0.49 tff(240,plain,
% 0.30/0.49 (~r(v5, v3)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[239, 224, 67])).
% 0.30/0.49 tff(241,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v5 = v3) | r(v5, v3) | r(v4, v3) | r(v5, v4) | (v5 = v4) | (v4 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v3) | r(v5, v3) | r(v4, v3) | r(v5, v4) | (v5 = v4) | (v4 = v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(242,plain,
% 0.30/0.49 ((r(v4, v3) | r(v5, v3) | r(v5, v4) | (v4 = v3) | (v5 = v3) | (v5 = v4)) <=> ((v5 = v3) | r(v5, v3) | r(v4, v3) | r(v5, v4) | (v5 = v4) | (v4 = v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(243,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v5, v3) | r(v5, v4) | (v4 = v3) | (v5 = v3) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v5 = v3) | r(v5, v3) | r(v4, v3) | r(v5, v4) | (v5 = v4) | (v4 = v3)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[242])).
% 0.30/0.49 tff(244,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v5, v3) | r(v5, v4) | (v4 = v3) | (v5 = v3) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v3) | r(v5, v3) | r(v4, v3) | r(v5, v4) | (v5 = v4) | (v4 = v3))),
% 0.30/0.49 inference(transitivity,[status(thm)],[243, 241])).
% 0.30/0.49 tff(245,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v5, v3) | r(v5, v4) | (v4 = v3) | (v5 = v3) | (v5 = v4))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(246,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v3) | r(v5, v3) | r(v4, v3) | r(v5, v4) | (v5 = v4) | (v4 = v3)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.30/0.49 tff(247,plain,
% 0.30/0.49 (r(v5, v4)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[246, 60, 231, 240, 44, 39, 16])).
% 0.30/0.49 tff(248,plain,
% 0.30/0.49 ((~(v0 = v4)) <=> (~(v0 = v4))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(249,axiom,(~(v0 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv4')).
% 0.30/0.49 tff(250,plain,
% 0.30/0.49 (~(v0 = v4)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.30/0.49 tff(251,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v0, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v0, v1))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(252,plain,
% 0.30/0.49 ((r(v1, v4) | r(v0, v4) | r(v0, v1) | (v1 = v4) | (v0 = v4) | (v0 = v1)) <=> ((v0 = v1) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v0, v1))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(253,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v0, v4) | r(v0, v1) | (v1 = v4) | (v0 = v4) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v0, v1)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[252])).
% 0.30/0.49 tff(254,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v0, v4) | r(v0, v1) | (v1 = v4) | (v0 = v4) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v0, v1))),
% 0.30/0.49 inference(transitivity,[status(thm)],[253, 251])).
% 0.30/0.49 tff(255,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v0, v4) | r(v0, v1) | (v1 = v4) | (v0 = v4) | (v0 = v1))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(256,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v0, v1)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.30/0.49 tff(257,plain,
% 0.30/0.49 (r(v0, v1)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[256, 60, 95, 250, 47, 17, 8])).
% 0.30/0.49 tff(258,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | r(v3, v4) | r(v0, v4) | r(v0, v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | r(v3, v4) | r(v0, v4) | r(v0, v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(259,plain,
% 0.30/0.49 ((r(v3, v4) | r(v0, v4) | r(v0, v3) | (v3 = v4) | (v0 = v4) | (v0 = v3)) <=> ((v0 = v3) | (v0 = v4) | (v3 = v4) | r(v3, v4) | r(v0, v4) | r(v0, v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(260,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v0, v4) | r(v0, v3) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | r(v3, v4) | r(v0, v4) | r(v0, v3)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[259])).
% 0.30/0.49 tff(261,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v0, v4) | r(v0, v3) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | r(v3, v4) | r(v0, v4) | r(v0, v3))),
% 0.30/0.49 inference(transitivity,[status(thm)],[260, 258])).
% 0.30/0.49 tff(262,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v0, v4) | r(v0, v3) | (v3 = v4) | (v0 = v4) | (v0 = v3))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(263,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | r(v3, v4) | r(v0, v4) | r(v0, v3)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.30/0.49 tff(264,plain,
% 0.30/0.49 (r(v0, v3)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[263, 60, 208, 250, 38, 40, 8])).
% 0.30/0.49 tff(265,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v1 = v3) | (~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v1 = v3) | (~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(266,plain,
% 0.30/0.49 (((~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)) | (v1 = v3) | (v0 = v3) | (v0 = v1)) <=> ((v0 = v1) | (v0 = v3) | (v1 = v3) | (~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(267,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)) | (v1 = v3) | (v0 = v3) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v1 = v3) | (~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[266])).
% 0.30/0.49 tff(268,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)) | (v1 = v3) | (v0 = v3) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v1 = v3) | (~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)))),
% 0.30/0.49 inference(transitivity,[status(thm)],[267, 265])).
% 0.30/0.49 tff(269,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1)) | (v1 = v3) | (v0 = v3) | (v0 = v1))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(270,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v1 = v3) | (~r(v1, v3)) | (~r(v0, v3)) | (~r(v0, v1))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.30/0.49 tff(271,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[270, 168, 95, 208, 50, 67, 264, 257])).
% 0.30/0.49 tff(272,plain,(r(v0, v4) | r(v1, v4) | r(v3, v4)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(273,plain,
% 0.30/0.49 (r(v0, v4)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[272, 40, 17])).
% 0.30/0.49 tff(274,plain,
% 0.30/0.49 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v5)) | r(v5, v0))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v5)) | r(v5, v0))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(275,plain,
% 0.30/0.49 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v5)) | r(v5, v0))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(276,plain,
% 0.30/0.49 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v5)) | r(v5, v0)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.30/0.49 tff(277,plain,
% 0.30/0.49 (~r(v0, v5)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[276, 25, 32])).
% 0.30/0.49 tff(278,assumption,(r(v2, v4)), introduced(assumption)).
% 0.30/0.49 tff(279,assumption,(r(v0, v4)), introduced(assumption)).
% 0.30/0.49 tff(280,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | (v2 = v4) | (~r(v0, v4)) | (~r(v2, v4)) | (~r(v0, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | (~r(v0, v4)) | (~r(v2, v4)) | (~r(v0, v2)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(281,plain,
% 0.30/0.49 (((~r(v2, v4)) | (~r(v0, v4)) | (~r(v0, v2)) | (v2 = v4) | (v0 = v4) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v4) | (v2 = v4) | (~r(v0, v4)) | (~r(v2, v4)) | (~r(v0, v2)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(282,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v4)) | (~r(v0, v4)) | (~r(v0, v2)) | (v2 = v4) | (v0 = v4) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | (v2 = v4) | (~r(v0, v4)) | (~r(v2, v4)) | (~r(v0, v2))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[281])).
% 0.30/0.49 tff(283,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v4)) | (~r(v0, v4)) | (~r(v0, v2)) | (v2 = v4) | (v0 = v4) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | (~r(v0, v4)) | (~r(v2, v4)) | (~r(v0, v2)))),
% 0.30/0.49 inference(transitivity,[status(thm)],[282, 280])).
% 0.30/0.49 tff(284,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v4)) | (~r(v0, v4)) | (~r(v0, v2)) | (v2 = v4) | (v0 = v4) | (v0 = v2))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(285,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | (~r(v0, v4)) | (~r(v2, v4)) | (~r(v0, v2))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.30/0.49 tff(286,plain,
% 0.30/0.49 (~r(v0, v2)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[285, 168, 187, 250, 119, 279, 278])).
% 0.30/0.49 tff(287,assumption,(r(v5, v4)), introduced(assumption)).
% 0.30/0.49 tff(288,plain,
% 0.30/0.49 (~r(v2, v5)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[174, 168, 119, 6, 287, 16, 278])).
% 0.30/0.49 tff(289,assumption,(~r(v0, v5)), introduced(assumption)).
% 0.30/0.49 tff(290,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v2, v5) | r(v0, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v2, v5) | r(v0, v2))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(291,plain,
% 0.30/0.49 ((r(v2, v5) | r(v0, v5) | r(v0, v2) | (v2 = v5) | (v0 = v5) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v2, v5) | r(v0, v2))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(292,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v5) | r(v0, v5) | r(v0, v2) | (v2 = v5) | (v0 = v5) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v2, v5) | r(v0, v2)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[291])).
% 0.30/0.49 tff(293,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v5) | r(v0, v5) | r(v0, v2) | (v2 = v5) | (v0 = v5) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v2, v5) | r(v0, v2))),
% 0.30/0.49 inference(transitivity,[status(thm)],[292, 290])).
% 0.30/0.49 tff(294,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v5) | r(v0, v5) | r(v0, v2) | (v2 = v5) | (v0 = v5) | (v0 = v2))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(295,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v2, v5) | r(v0, v2)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.30/0.49 tff(296,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[295, 60, 187, 88, 6, 289, 288, 286])).
% 0.30/0.49 tff(297,plain,((~r(v2, v4)) | r(v0, v5) | (~r(v0, v4)) | (~r(v5, v4))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(298,plain,
% 0.30/0.49 (~r(v2, v4)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[297, 277, 273, 247])).
% 0.30/0.49 tff(299,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | (v3 = v4) | r(v3, v4) | r(v2, v4) | r(v2, v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (v3 = v4) | r(v3, v4) | r(v2, v4) | r(v2, v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(300,plain,
% 0.30/0.49 ((r(v3, v4) | r(v2, v4) | r(v2, v3) | (v3 = v4) | (v2 = v4) | (v2 = v3)) <=> ((v2 = v3) | (v2 = v4) | (v3 = v4) | r(v3, v4) | r(v2, v4) | r(v2, v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(301,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v2, v4) | r(v2, v3) | (v3 = v4) | (v2 = v4) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | (v3 = v4) | r(v3, v4) | r(v2, v4) | r(v2, v3)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[300])).
% 0.30/0.49 tff(302,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v2, v4) | r(v2, v3) | (v3 = v4) | (v2 = v4) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (v3 = v4) | r(v3, v4) | r(v2, v4) | r(v2, v3))),
% 0.30/0.49 inference(transitivity,[status(thm)],[301, 299])).
% 0.30/0.49 tff(303,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v2, v4) | r(v2, v3) | (v3 = v4) | (v2 = v4) | (v2 = v3))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(304,plain,
% 0.30/0.49 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (v3 = v4) | r(v3, v4) | r(v2, v4) | r(v2, v3)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.30/0.49 tff(305,plain,
% 0.30/0.49 (r(v2, v3)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[304, 60, 198, 119, 38, 40, 298])).
% 0.30/0.49 tff(306,plain,
% 0.30/0.49 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v2 = v4) | r(v1, v4) | (v2 = v1) | r(v2, v1) | r(v2, v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | r(v1, v4) | (v2 = v1) | r(v2, v1) | r(v2, v4))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(307,plain,
% 0.30/0.50 ((r(v1, v4) | r(v2, v4) | r(v2, v1) | (v1 = v4) | (v2 = v4) | (v2 = v1)) <=> ((v1 = v4) | (v2 = v4) | r(v1, v4) | (v2 = v1) | r(v2, v1) | r(v2, v4))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(308,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v2, v4) | r(v2, v1) | (v1 = v4) | (v2 = v4) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v2 = v4) | r(v1, v4) | (v2 = v1) | r(v2, v1) | r(v2, v4)))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[307])).
% 0.30/0.50 tff(309,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v2, v4) | r(v2, v1) | (v1 = v4) | (v2 = v4) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | r(v1, v4) | (v2 = v1) | r(v2, v1) | r(v2, v4))),
% 0.30/0.50 inference(transitivity,[status(thm)],[308, 306])).
% 0.30/0.50 tff(310,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v2, v4) | r(v2, v1) | (v1 = v4) | (v2 = v4) | (v2 = v1))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(311,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | r(v1, v4) | (v2 = v1) | r(v2, v1) | r(v2, v4)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.30/0.50 tff(312,plain,
% 0.30/0.50 (r(v2, v1)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[311, 60, 47, 119, 17, 127, 298])).
% 0.30/0.50 tff(313,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v2 = v3) | (~r(v1, v3)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v2 = v3) | (~r(v1, v3)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v3)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(314,plain,
% 0.30/0.50 (((~r(v1, v3)) | (~r(v2, v3)) | (~r(v2, v1)) | (v1 = v3) | (v2 = v3) | (v2 = v1)) <=> ((v1 = v3) | (v2 = v3) | (~r(v1, v3)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v3)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(315,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v2, v3)) | (~r(v2, v1)) | (v1 = v3) | (v2 = v3) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v2 = v3) | (~r(v1, v3)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v3))))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[314])).
% 0.30/0.50 tff(316,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v2, v3)) | (~r(v2, v1)) | (v1 = v3) | (v2 = v3) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v2 = v3) | (~r(v1, v3)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v3)))),
% 0.30/0.50 inference(transitivity,[status(thm)],[315, 313])).
% 0.30/0.50 tff(317,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v2, v3)) | (~r(v2, v1)) | (v1 = v3) | (v2 = v3) | (v2 = v1))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(318,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v2 = v3) | (~r(v1, v3)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v3))),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.30/0.50 tff(319,plain,
% 0.30/0.50 ($false),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[318, 168, 50, 198, 67, 127, 312, 305])).
% 0.30/0.50 tff(320,plain,(r(v3, v4) | r(v1, v4) | r(v5, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50 tff(321,plain,
% 0.30/0.50 (r(v3, v4)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[320, 32, 17])).
% 0.30/0.50 tff(322,assumption,(~r(v0, v3)), introduced(assumption)).
% 0.30/0.50 tff(323,assumption,(r(v3, v4)), introduced(assumption)).
% 0.30/0.50 tff(324,plain,
% 0.30/0.50 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v4)) | r(v4, v3))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v4)) | r(v4, v3))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(325,plain,
% 0.30/0.50 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v4)) | r(v4, v3))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(326,plain,
% 0.30/0.50 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v4)) | r(v4, v3)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.30/0.50 tff(327,plain,
% 0.30/0.50 (r(v4, v3)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[326, 25, 323])).
% 0.30/0.50 tff(328,plain,
% 0.30/0.50 (~r(v3, v1)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[223, 82, 113, 32])).
% 0.30/0.50 tff(329,assumption,(r(v4, v3)), introduced(assumption)).
% 0.30/0.50 tff(330,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v5, v3)) | (~r(v5, v4)) | (v4 = v3) | (v5 = v3) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v3)) | (~r(v5, v3)) | (~r(v5, v4)) | (v4 = v3) | (v5 = v3) | (v5 = v4))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(331,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v5, v3)) | (~r(v5, v4)) | (v4 = v3) | (v5 = v3) | (v5 = v4))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(332,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v3)) | (~r(v5, v3)) | (~r(v5, v4)) | (v4 = v3) | (v5 = v3) | (v5 = v4)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.30/0.50 tff(333,plain,
% 0.30/0.50 ((~r(v4, v3)) | (~r(v5, v3)) | (~r(v5, v4)) | (v4 = v3) | (v5 = v4)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[332, 168, 231])).
% 0.30/0.50 tff(334,plain,
% 0.30/0.50 ((~r(v4, v3)) | (~r(v5, v3)) | (~r(v5, v4))),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[333, 39, 16])).
% 0.30/0.50 tff(335,plain,
% 0.30/0.50 (~r(v5, v3)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[334, 158, 329])).
% 0.30/0.50 tff(336,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (v5 = v3) | r(v5, v3) | r(v1, v3) | r(v1, v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v5 = v3) | r(v5, v3) | r(v1, v3) | r(v1, v5))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(337,plain,
% 0.30/0.50 ((r(v5, v3) | r(v1, v3) | r(v1, v5) | (v5 = v3) | (v1 = v3) | (v1 = v5)) <=> ((v1 = v3) | (v1 = v5) | (v5 = v3) | r(v5, v3) | r(v1, v3) | r(v1, v5))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(338,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v1, v3) | r(v1, v5) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (v5 = v3) | r(v5, v3) | r(v1, v3) | r(v1, v5)))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[337])).
% 0.30/0.50 tff(339,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v1, v3) | r(v1, v5) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v5 = v3) | r(v5, v3) | r(v1, v3) | r(v1, v5))),
% 0.30/0.50 inference(transitivity,[status(thm)],[338, 336])).
% 0.30/0.50 tff(340,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v1, v3) | r(v1, v5) | (v5 = v3) | (v1 = v3) | (v1 = v5))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(341,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v5 = v3) | r(v5, v3) | r(v1, v3) | r(v1, v5)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.30/0.50 tff(342,plain,
% 0.30/0.50 (r(v5, v3) | r(v1, v3) | r(v1, v5)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[341, 60, 50, 99, 231])).
% 0.30/0.50 tff(343,plain,
% 0.30/0.50 (r(v1, v3)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[342, 335, 82])).
% 0.30/0.50 tff(344,plain,
% 0.30/0.50 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v3)) | r(v3, v1))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v3)) | r(v3, v1))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(345,plain,
% 0.30/0.50 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v3)) | r(v3, v1))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(346,plain,
% 0.30/0.50 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v3)) | r(v3, v1)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.30/0.50 tff(347,plain,
% 0.30/0.50 ($false),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[346, 25, 343, 328])).
% 0.30/0.50 tff(348,plain,(r(v1, v5) | (~r(v4, v3)) | r(v4, v1) | r(v5, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50 tff(349,plain,
% 0.30/0.50 (r(v1, v5)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[348, 327, 113, 32])).
% 0.30/0.50 tff(350,plain,
% 0.30/0.50 ((v3 = v0) <=> (v0 = v3)),
% 0.30/0.50 inference(commutativity,[status(thm)],[])).
% 0.30/0.50 tff(351,plain,
% 0.30/0.50 ((v0 = v3) <=> (v3 = v0)),
% 0.30/0.50 inference(symmetry,[status(thm)],[350])).
% 0.30/0.50 tff(352,plain,
% 0.30/0.50 ((~(v0 = v3)) <=> (~(v3 = v0))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[351])).
% 0.30/0.50 tff(353,plain,
% 0.30/0.50 (~(v3 = v0)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[208, 352])).
% 0.30/0.50 tff(354,plain,
% 0.30/0.50 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v0)) | r(v0, v3))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v0)) | r(v0, v3))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(355,plain,
% 0.30/0.50 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v0)) | r(v0, v3))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(356,plain,
% 0.30/0.50 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v0)) | r(v0, v3)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.30/0.50 tff(357,plain,
% 0.30/0.50 (~r(v3, v0)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[356, 25, 322])).
% 0.30/0.50 tff(358,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v5 = v3) | r(v5, v3) | (v5 = v0) | r(v5, v0) | (v3 = v0) | r(v3, v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v3) | r(v5, v3) | (v5 = v0) | r(v5, v0) | (v3 = v0) | r(v3, v0))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(359,plain,
% 0.30/0.50 ((r(v3, v0) | r(v5, v0) | r(v5, v3) | (v3 = v0) | (v5 = v0) | (v5 = v3)) <=> ((v5 = v3) | r(v5, v3) | (v5 = v0) | r(v5, v0) | (v3 = v0) | r(v3, v0))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(360,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v5, v0) | r(v5, v3) | (v3 = v0) | (v5 = v0) | (v5 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v5 = v3) | r(v5, v3) | (v5 = v0) | r(v5, v0) | (v3 = v0) | r(v3, v0)))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[359])).
% 0.30/0.50 tff(361,plain,
% 0.30/0.50 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v5, v0) | r(v5, v3) | (v3 = v0) | (v5 = v0) | (v5 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v3) | r(v5, v3) | (v5 = v0) | r(v5, v0) | (v3 = v0) | r(v3, v0))),
% 0.30/0.50 inference(transitivity,[status(thm)],[360, 358])).
% 0.30/0.50 tff(362,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v5, v0) | r(v5, v3) | (v3 = v0) | (v5 = v0) | (v5 = v3))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(363,plain,
% 0.30/0.50 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v3) | r(v5, v3) | (v5 = v0) | r(v5, v0) | (v3 = v0) | r(v3, v0)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.30/0.50 tff(364,plain,
% 0.30/0.50 (r(v5, v3)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[363, 60, 231, 89, 32, 357, 353])).
% 0.30/0.51 tff(365,plain,
% 0.30/0.51 (~r(v1, v3)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[239, 364, 349])).
% 0.30/0.51 tff(366,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v1 = v3) | r(v1, v3) | r(v0, v3) | r(v0, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v1 = v3) | r(v1, v3) | r(v0, v3) | r(v0, v1))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(367,plain,
% 0.30/0.51 ((r(v1, v3) | r(v0, v3) | r(v0, v1) | (v1 = v3) | (v0 = v3) | (v0 = v1)) <=> ((v0 = v1) | (v0 = v3) | (v1 = v3) | r(v1, v3) | r(v0, v3) | r(v0, v1))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(368,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v0, v3) | r(v0, v1) | (v1 = v3) | (v0 = v3) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v1 = v3) | r(v1, v3) | r(v0, v3) | r(v0, v1)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[367])).
% 0.30/0.51 tff(369,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v0, v3) | r(v0, v1) | (v1 = v3) | (v0 = v3) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v1 = v3) | r(v1, v3) | r(v0, v3) | r(v0, v1))),
% 0.30/0.51 inference(transitivity,[status(thm)],[368, 366])).
% 0.30/0.51 tff(370,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v0, v3) | r(v0, v1) | (v1 = v3) | (v0 = v3) | (v0 = v1))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(371,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v1 = v3) | r(v1, v3) | r(v0, v3) | r(v0, v1)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.30/0.51 tff(372,plain,
% 0.30/0.51 (r(v0, v1)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[371, 60, 95, 208, 50, 365, 322])).
% 0.30/0.51 tff(373,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(374,plain,
% 0.30/0.51 (((~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)) | (v3 = v4) | (v2 = v4) | (v2 = v3)) <=> ((v2 = v3) | (v2 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(375,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)) | (v3 = v4) | (v2 = v4) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[374])).
% 0.30/0.51 tff(376,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)) | (v3 = v4) | (v2 = v4) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[375, 373])).
% 0.30/0.51 tff(377,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3)) | (v3 = v4) | (v2 = v4) | (v2 = v3))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(378,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v2, v4)) | (~r(v2, v3))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.30/0.51 tff(379,plain,
% 0.30/0.51 (~r(v2, v3)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[378, 168, 198, 119, 38, 323, 143])).
% 0.30/0.51 tff(380,assumption,(~r(v1, v3)), introduced(assumption)).
% 0.30/0.51 tff(381,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v2 = v3) | r(v1, v3) | (v2 = v1) | r(v2, v1) | r(v2, v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v2 = v3) | r(v1, v3) | (v2 = v1) | r(v2, v1) | r(v2, v3))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(382,plain,
% 0.30/0.51 ((r(v1, v3) | r(v2, v3) | r(v2, v1) | (v1 = v3) | (v2 = v3) | (v2 = v1)) <=> ((v1 = v3) | (v2 = v3) | r(v1, v3) | (v2 = v1) | r(v2, v1) | r(v2, v3))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(383,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v2, v3) | r(v2, v1) | (v1 = v3) | (v2 = v3) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v2 = v3) | r(v1, v3) | (v2 = v1) | r(v2, v1) | r(v2, v3)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[382])).
% 0.30/0.51 tff(384,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v2, v3) | r(v2, v1) | (v1 = v3) | (v2 = v3) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v2 = v3) | r(v1, v3) | (v2 = v1) | r(v2, v1) | r(v2, v3))),
% 0.30/0.51 inference(transitivity,[status(thm)],[383, 381])).
% 0.30/0.51 tff(385,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v2, v3) | r(v2, v1) | (v1 = v3) | (v2 = v3) | (v2 = v1))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(386,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v2 = v3) | r(v1, v3) | (v2 = v1) | r(v2, v1) | r(v2, v3)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.30/0.51 tff(387,plain,
% 0.30/0.51 ($false),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[386, 60, 50, 198, 380, 127, 9, 379])).
% 0.30/0.51 tff(388,plain,(r(v2, v1) | r(v1, v3) | (~r(v3, v4)) | r(v4, v1)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51 tff(389,plain,
% 0.30/0.51 (r(v2, v1)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[388, 365, 323, 113])).
% 0.30/0.51 tff(390,plain,
% 0.30/0.51 (~r(v0, v2)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[193, 168, 95, 187, 127, 389, 372])).
% 0.30/0.51 tff(391,plain,
% 0.30/0.51 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v5)) | r(v5, v1))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v5)) | r(v5, v1))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(392,plain,
% 0.30/0.51 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v5)) | r(v5, v1))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(393,plain,
% 0.30/0.51 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v5)) | r(v5, v1)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.30/0.51 tff(394,plain,
% 0.30/0.51 (r(v5, v1)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[393, 25, 349])).
% 0.30/0.51 tff(395,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v5 = v1) | (~r(v5, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v5)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v5 = v1) | (~r(v5, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v5)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(396,plain,
% 0.30/0.51 (((~r(v5, v1)) | (~r(v2, v1)) | (~r(v2, v5)) | (v5 = v1) | (v2 = v1) | (v2 = v5)) <=> ((v2 = v5) | (v5 = v1) | (~r(v5, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v5)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(397,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v1)) | (~r(v2, v1)) | (~r(v2, v5)) | (v5 = v1) | (v2 = v1) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v5 = v1) | (~r(v5, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v5))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[396])).
% 0.30/0.51 tff(398,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v1)) | (~r(v2, v1)) | (~r(v2, v5)) | (v5 = v1) | (v2 = v1) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v5 = v1) | (~r(v5, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v5)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[397, 395])).
% 0.30/0.51 tff(399,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v1)) | (~r(v2, v1)) | (~r(v2, v5)) | (v5 = v1) | (v2 = v1) | (v2 = v5))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(400,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v5 = v1) | (~r(v5, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v5))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.30/0.51 tff(401,plain,
% 0.30/0.51 (~r(v2, v5)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[400, 168, 6, 394, 147, 127, 389])).
% 0.30/0.51 tff(402,plain,
% 0.30/0.51 ($false),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[295, 60, 187, 88, 6, 277, 401, 390])).
% 0.30/0.51 tff(403,plain,(r(v0, v3) | (~r(v3, v4)) | r(v4, v1) | r(v5, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51 tff(404,plain,
% 0.30/0.51 (r(v0, v3)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[403, 321, 31, 32])).
% 0.30/0.51 tff(405,plain,
% 0.30/0.51 (r(v4, v3)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[326, 25, 321])).
% 0.30/0.51 tff(406,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v0, v4)) | (~r(v0, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v0, v4)) | (~r(v0, v3)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(407,plain,
% 0.30/0.51 (((~r(v4, v3)) | (~r(v0, v3)) | (~r(v0, v4)) | (v4 = v3) | (v0 = v3) | (v0 = v4)) <=> ((v0 = v3) | (v0 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v0, v4)) | (~r(v0, v3)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(408,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v0, v3)) | (~r(v0, v4)) | (v4 = v3) | (v0 = v3) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v0, v4)) | (~r(v0, v3))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[407])).
% 0.30/0.51 tff(409,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v0, v3)) | (~r(v0, v4)) | (v4 = v3) | (v0 = v3) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v0, v4)) | (~r(v0, v3)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[408, 406])).
% 0.30/0.51 tff(410,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v0, v3)) | (~r(v0, v4)) | (v4 = v3) | (v0 = v3) | (v0 = v4))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(411,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v0, v4)) | (~r(v0, v3))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.30/0.51 tff(412,plain,
% 0.30/0.51 (~r(v0, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[411, 168, 208, 250, 405, 39, 404])).
% 0.30/0.51 tff(413,plain,
% 0.30/0.51 (r(v0, v1)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[256, 60, 95, 250, 47, 17, 412])).
% 0.30/0.51 tff(414,plain,
% 0.30/0.51 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v3)) | r(v3, v0))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v3)) | r(v3, v0))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(415,plain,
% 0.30/0.51 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v3)) | r(v3, v0))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(416,plain,
% 0.30/0.51 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v3)) | r(v3, v0)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.30/0.51 tff(417,plain,
% 0.30/0.51 (r(v3, v0)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[416, 25, 404])).
% 0.30/0.51 tff(418,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v1 = v4) | r(v1, v4) | (v1 = v0) | r(v1, v0) | r(v0, v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | r(v1, v4) | (v1 = v0) | r(v1, v0) | r(v0, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(419,plain,
% 0.30/0.51 ((r(v0, v4) | r(v1, v4) | r(v1, v0) | (v0 = v4) | (v1 = v4) | (v1 = v0)) <=> ((v0 = v4) | (v1 = v4) | r(v1, v4) | (v1 = v0) | r(v1, v0) | r(v0, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(420,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v1, v4) | r(v1, v0) | (v0 = v4) | (v1 = v4) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v1 = v4) | r(v1, v4) | (v1 = v0) | r(v1, v0) | r(v0, v4)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[419])).
% 0.30/0.51 tff(421,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v1, v4) | r(v1, v0) | (v0 = v4) | (v1 = v4) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | r(v1, v4) | (v1 = v0) | r(v1, v0) | r(v0, v4))),
% 0.30/0.51 inference(transitivity,[status(thm)],[420, 418])).
% 0.30/0.51 tff(422,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v1, v4) | r(v1, v0) | (v0 = v4) | (v1 = v4) | (v1 = v0))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(423,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | r(v1, v4) | (v1 = v0) | r(v1, v0) | r(v0, v4)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.30/0.51 tff(424,plain,
% 0.30/0.51 (r(v1, v0)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[423, 60, 250, 47, 17, 96, 412])).
% 0.30/0.51 tff(425,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (~r(v1, v3)) | (v1 = v0) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (~r(v1, v3)) | (v1 = v0) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(426,plain,
% 0.30/0.51 (((~r(v3, v0)) | (~r(v1, v0)) | (~r(v1, v3)) | (v3 = v0) | (v1 = v0) | (v1 = v3)) <=> ((v1 = v3) | (~r(v1, v3)) | (v1 = v0) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(427,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v1, v0)) | (~r(v1, v3)) | (v3 = v0) | (v1 = v0) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (~r(v1, v3)) | (v1 = v0) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[426])).
% 0.30/0.51 tff(428,plain,
% 0.30/0.51 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v1, v0)) | (~r(v1, v3)) | (v3 = v0) | (v1 = v0) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (~r(v1, v3)) | (v1 = v0) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[427, 425])).
% 0.30/0.51 tff(429,plain,
% 0.30/0.51 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v1, v0)) | (~r(v1, v3)) | (v3 = v0) | (v1 = v0) | (v1 = v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(430,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (~r(v1, v3)) | (v1 = v0) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.30/0.52 tff(431,plain,
% 0.30/0.52 ((~r(v1, v3)) | (v3 = v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[430, 168, 50, 96, 424, 417])).
% 0.30/0.52 tff(432,plain,
% 0.30/0.52 (~r(v1, v3)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[431, 353])).
% 0.30/0.52 tff(433,plain,
% 0.30/0.52 (r(v2, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[388, 432, 321, 31])).
% 0.30/0.52 tff(434,plain,
% 0.30/0.52 (~r(v0, v2)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[193, 168, 95, 187, 127, 433, 413])).
% 0.30/0.52 tff(435,plain,
% 0.30/0.52 (r(v1, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[348, 405, 31, 32])).
% 0.30/0.52 tff(436,plain,
% 0.30/0.52 (r(v5, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[393, 25, 435])).
% 0.30/0.52 tff(437,plain,
% 0.30/0.52 (~r(v2, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[400, 168, 6, 436, 147, 127, 433])).
% 0.30/0.52 tff(438,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[295, 60, 187, 88, 6, 277, 437, 434])).
% 0.30/0.52 tff(439,plain,(r(v5, v0) | r(v1, v4)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(440,plain,
% 0.30/0.52 (r(v5, v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[439, 17])).
% 0.30/0.52 tff(441,plain,
% 0.30/0.52 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v0)) | r(v0, v5))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v0)) | r(v0, v5))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(442,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v0)) | r(v0, v5))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(443,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v0)) | r(v0, v5)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.30/0.52 tff(444,plain,
% 0.30/0.52 (r(v0, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[443, 25, 440])).
% 0.30/0.52 tff(445,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v5) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(446,plain,
% 0.30/0.52 ((r(v5, v1) | r(v4, v1) | r(v4, v5) | (v5 = v1) | (v4 = v1) | (v4 = v5)) <=> ((v4 = v5) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(447,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v4, v1) | r(v4, v5) | (v5 = v1) | (v4 = v1) | (v4 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v5) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[446])).
% 0.30/0.52 tff(448,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v4, v1) | r(v4, v5) | (v5 = v1) | (v4 = v1) | (v4 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1))),
% 0.30/0.52 inference(transitivity,[status(thm)],[447, 445])).
% 0.30/0.52 tff(449,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v4, v1) | r(v4, v5) | (v5 = v1) | (v4 = v1) | (v4 = v5))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(450,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.30/0.52 tff(451,plain,
% 0.30/0.52 (r(v5, v1) | (v5 = v1) | (v4 = v1) | r(v4, v5) | r(v4, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[450, 60, 15])).
% 0.30/0.52 tff(452,plain,
% 0.30/0.52 (r(v5, v1) | r(v4, v5) | r(v4, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[451, 131, 147])).
% 0.30/0.52 tff(453,plain,
% 0.30/0.52 (r(v4, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[452, 151, 31])).
% 0.30/0.52 tff(454,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v0 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v0 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(455,plain,
% 0.30/0.52 (((~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)) | (v4 = v5) | (v0 = v5) | (v0 = v4)) <=> ((v0 = v4) | (v0 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(456,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)) | (v4 = v5) | (v0 = v5) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v0 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4))))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[455])).
% 0.30/0.52 tff(457,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)) | (v4 = v5) | (v0 = v5) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v0 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)))),
% 0.30/0.52 inference(transitivity,[status(thm)],[456, 454])).
% 0.30/0.52 tff(458,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4)) | (v4 = v5) | (v0 = v5) | (v0 = v4))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(459,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v0 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v0, v5)) | (~r(v0, v4))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.30/0.52 tff(460,plain,
% 0.30/0.52 (~r(v0, v4)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[459, 168, 250, 88, 15, 453, 444])).
% 0.30/0.52 tff(461,plain,
% 0.30/0.52 (r(v0, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[256, 60, 95, 250, 47, 17, 460])).
% 0.30/0.52 tff(462,plain,
% 0.30/0.52 (r(v2, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[183, 82, 31])).
% 0.30/0.52 tff(463,plain,
% 0.30/0.52 (~r(v0, v2)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[193, 168, 95, 187, 127, 462, 461])).
% 0.30/0.52 tff(464,plain,
% 0.30/0.52 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v0)) | r(v0, v2))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v0)) | r(v0, v2))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(465,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v0)) | r(v0, v2))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(466,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v0)) | r(v0, v2)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.30/0.52 tff(467,plain,
% 0.30/0.52 (~r(v2, v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[466, 25, 463])).
% 0.30/0.52 tff(468,plain,
% 0.30/0.52 ((v2 = v0) <=> (v0 = v2)),
% 0.30/0.52 inference(commutativity,[status(thm)],[])).
% 0.30/0.52 tff(469,plain,
% 0.30/0.52 ((v0 = v2) <=> (v2 = v0)),
% 0.30/0.52 inference(symmetry,[status(thm)],[468])).
% 0.30/0.52 tff(470,plain,
% 0.30/0.52 ((~(v0 = v2)) <=> (~(v2 = v0))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[469])).
% 0.30/0.52 tff(471,plain,
% 0.30/0.52 (~(v2 = v0)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[187, 470])).
% 0.30/0.52 tff(472,plain,
% 0.30/0.52 ((v4 = v0) <=> (v0 = v4)),
% 0.30/0.52 inference(commutativity,[status(thm)],[])).
% 0.30/0.52 tff(473,plain,
% 0.30/0.52 ((v0 = v4) <=> (v4 = v0)),
% 0.30/0.52 inference(symmetry,[status(thm)],[472])).
% 0.30/0.52 tff(474,plain,
% 0.30/0.52 ((~(v0 = v4)) <=> (~(v4 = v0))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[473])).
% 0.30/0.52 tff(475,plain,
% 0.30/0.52 (~(v4 = v0)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[250, 474])).
% 0.30/0.52 tff(476,plain,
% 0.30/0.52 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v0)) | r(v0, v4))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v0)) | r(v0, v4))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(477,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v0)) | r(v0, v4))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(478,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v0)) | r(v0, v4)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.30/0.52 tff(479,plain,
% 0.30/0.52 (~r(v4, v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[478, 25, 460])).
% 0.30/0.52 tff(480,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v4, v0) | (v4 = v0) | r(v2, v4) | (v2 = v0) | r(v2, v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v4, v0) | (v4 = v0) | r(v2, v4) | (v2 = v0) | r(v2, v0))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(481,plain,
% 0.30/0.52 ((r(v4, v0) | r(v2, v0) | r(v2, v4) | (v4 = v0) | (v2 = v0) | (v2 = v4)) <=> ((v2 = v4) | r(v4, v0) | (v4 = v0) | r(v2, v4) | (v2 = v0) | r(v2, v0))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(482,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v0) | r(v2, v0) | r(v2, v4) | (v4 = v0) | (v2 = v0) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v4, v0) | (v4 = v0) | r(v2, v4) | (v2 = v0) | r(v2, v0)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[481])).
% 0.30/0.52 tff(483,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v0) | r(v2, v0) | r(v2, v4) | (v4 = v0) | (v2 = v0) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v4, v0) | (v4 = v0) | r(v2, v4) | (v2 = v0) | r(v2, v0))),
% 0.30/0.52 inference(transitivity,[status(thm)],[482, 480])).
% 0.30/0.52 tff(484,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v0) | r(v2, v0) | r(v2, v4) | (v4 = v0) | (v2 = v0) | (v2 = v4))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(485,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v4, v0) | (v4 = v0) | r(v2, v4) | (v2 = v0) | r(v2, v0)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.30/0.52 tff(486,plain,
% 0.30/0.52 (r(v2, v4)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[485, 60, 119, 479, 475, 471, 467])).
% 0.30/0.52 tff(487,plain,
% 0.30/0.52 (r(v3, v4)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[272, 460, 17])).
% 0.30/0.52 tff(488,plain,
% 0.30/0.52 (~r(v2, v3)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[378, 168, 198, 119, 38, 487, 486])).
% 0.30/0.52 tff(489,plain,
% 0.30/0.52 (r(v5, v4)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[157, 60, 151, 147, 131, 31, 16])).
% 0.30/0.52 tff(490,assumption,(~r(v4, v3)), introduced(assumption)).
% 0.30/0.52 tff(491,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[326, 25, 323, 490])).
% 0.30/0.52 tff(492,plain,(r(v4, v3) | (~r(v3, v4))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(493,plain,
% 0.30/0.52 (r(v4, v3)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[492, 487])).
% 0.30/0.52 tff(494,plain,
% 0.30/0.52 (~r(v5, v3)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[334, 493, 489])).
% 0.30/0.52 tff(495,plain,
% 0.30/0.52 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v5)) | r(v5, v3))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v5)) | r(v5, v3))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(496,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v5)) | r(v5, v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(497,plain,
% 0.30/0.52 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v5)) | r(v5, v3)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.30/0.52 tff(498,plain,
% 0.30/0.52 (~r(v3, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[497, 25, 494])).
% 0.30/0.52 tff(499,plain,
% 0.30/0.52 (~r(v2, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[174, 168, 119, 6, 489, 16, 486])).
% 0.30/0.52 tff(500,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v3 = v5) | r(v3, v5) | r(v2, v5) | r(v2, v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | r(v3, v5) | r(v2, v5) | r(v2, v3))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(501,plain,
% 0.30/0.52 ((r(v3, v5) | r(v2, v5) | r(v2, v3) | (v3 = v5) | (v2 = v5) | (v2 = v3)) <=> ((v2 = v3) | (v2 = v5) | (v3 = v5) | r(v3, v5) | r(v2, v5) | r(v2, v3))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(502,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v5) | r(v2, v5) | r(v2, v3) | (v3 = v5) | (v2 = v5) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v3 = v5) | r(v3, v5) | r(v2, v5) | r(v2, v3)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[501])).
% 0.30/0.52 tff(503,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v5) | r(v2, v5) | r(v2, v3) | (v3 = v5) | (v2 = v5) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | r(v3, v5) | r(v2, v5) | r(v2, v3))),
% 0.30/0.52 inference(transitivity,[status(thm)],[502, 500])).
% 0.30/0.52 tff(504,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v5) | r(v2, v5) | r(v2, v3) | (v3 = v5) | (v2 = v5) | (v2 = v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(505,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | r(v3, v5) | r(v2, v5) | r(v2, v3)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.30/0.52 tff(506,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[505, 60, 198, 6, 230, 499, 498, 488])).
% 0.30/0.52 tff(507,plain,(r(v1, v5) | r(v1, v4)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(508,plain,
% 0.30/0.52 (r(v1, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[507, 17])).
% 0.30/0.52 tff(509,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(510,plain,
% 0.30/0.52 (((~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)) | (v1 = v5) | (v0 = v5) | (v0 = v1)) <=> ((v0 = v1) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(511,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)) | (v1 = v5) | (v0 = v5) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1))))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[510])).
% 0.30/0.52 tff(512,plain,
% 0.30/0.52 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)) | (v1 = v5) | (v0 = v5) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)))),
% 0.30/0.52 inference(transitivity,[status(thm)],[511, 509])).
% 0.30/0.52 tff(513,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1)) | (v1 = v5) | (v0 = v5) | (v0 = v1))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(514,plain,
% 0.30/0.52 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (~r(v0, v5)) | (~r(v0, v1))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.30/0.52 tff(515,plain,
% 0.30/0.52 (~r(v0, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[514, 168, 95, 88, 99, 508, 444])).
% 0.30/0.52 tff(516,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (v4 = v1) | r(v4, v1) | r(v0, v4) | r(v0, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v4 = v1) | r(v4, v1) | r(v0, v4) | r(v0, v1))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(517,plain,
% 0.30/0.53 ((r(v4, v1) | r(v0, v1) | r(v0, v4) | (v4 = v1) | (v0 = v1) | (v0 = v4)) <=> ((v0 = v1) | (v0 = v4) | (v4 = v1) | r(v4, v1) | r(v0, v4) | r(v0, v1))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(518,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v0, v1) | r(v0, v4) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (v4 = v1) | r(v4, v1) | r(v0, v4) | r(v0, v1)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[517])).
% 0.30/0.53 tff(519,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v0, v1) | r(v0, v4) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v4 = v1) | r(v4, v1) | r(v0, v4) | r(v0, v1))),
% 0.30/0.53 inference(transitivity,[status(thm)],[518, 516])).
% 0.30/0.53 tff(520,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v0, v1) | r(v0, v4) | (v4 = v1) | (v0 = v1) | (v0 = v4))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(521,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v4 = v1) | r(v4, v1) | r(v0, v4) | r(v0, v1)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.30/0.53 tff(522,plain,
% 0.30/0.53 (r(v0, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[521, 60, 95, 250, 131, 31, 515])).
% 0.30/0.53 tff(523,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (v1 = v0) | (~r(v0, v5)) | (~r(v1, v0)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (v1 = v0) | (~r(v0, v5)) | (~r(v1, v0)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(524,plain,
% 0.30/0.53 (((~r(v0, v5)) | (~r(v1, v5)) | (~r(v1, v0)) | (v0 = v5) | (v1 = v5) | (v1 = v0)) <=> ((v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (v1 = v0) | (~r(v0, v5)) | (~r(v1, v0)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(525,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v1, v5)) | (~r(v1, v0)) | (v0 = v5) | (v1 = v5) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (v1 = v0) | (~r(v0, v5)) | (~r(v1, v0))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[524])).
% 0.30/0.53 tff(526,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v1, v5)) | (~r(v1, v0)) | (v0 = v5) | (v1 = v5) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (v1 = v0) | (~r(v0, v5)) | (~r(v1, v0)))),
% 0.30/0.53 inference(transitivity,[status(thm)],[525, 523])).
% 0.30/0.53 tff(527,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v1, v5)) | (~r(v1, v0)) | (v0 = v5) | (v1 = v5) | (v1 = v0))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(528,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | (~r(v1, v5)) | (v1 = v0) | (~r(v0, v5)) | (~r(v1, v0))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.30/0.53 tff(529,plain,
% 0.30/0.53 (~r(v1, v0)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[528, 168, 88, 99, 508, 96, 444])).
% 0.30/0.53 tff(530,plain,
% 0.30/0.53 (~r(v0, v2)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[285, 168, 187, 250, 119, 279, 143])).
% 0.30/0.53 tff(531,plain,
% 0.30/0.53 (~r(v2, v0)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[466, 25, 530])).
% 0.30/0.53 tff(532,assumption,(~r(v1, v0)), introduced(assumption)).
% 0.30/0.53 tff(533,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v1) | r(v2, v1) | (v1 = v0) | r(v1, v0) | (v2 = v0) | r(v2, v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | r(v2, v1) | (v1 = v0) | r(v1, v0) | (v2 = v0) | r(v2, v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(534,plain,
% 0.30/0.53 ((r(v1, v0) | r(v2, v0) | r(v2, v1) | (v1 = v0) | (v2 = v0) | (v2 = v1)) <=> ((v2 = v1) | r(v2, v1) | (v1 = v0) | r(v1, v0) | (v2 = v0) | r(v2, v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(535,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v2, v0) | r(v2, v1) | (v1 = v0) | (v2 = v0) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v1) | r(v2, v1) | (v1 = v0) | r(v1, v0) | (v2 = v0) | r(v2, v0)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[534])).
% 0.30/0.53 tff(536,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v2, v0) | r(v2, v1) | (v1 = v0) | (v2 = v0) | (v2 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | r(v2, v1) | (v1 = v0) | r(v1, v0) | (v2 = v0) | r(v2, v0))),
% 0.30/0.53 inference(transitivity,[status(thm)],[535, 533])).
% 0.30/0.53 tff(537,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v2, v0) | r(v2, v1) | (v1 = v0) | (v2 = v0) | (v2 = v1))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(538,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | r(v2, v1) | (v1 = v0) | r(v1, v0) | (v2 = v0) | r(v2, v0)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.30/0.53 tff(539,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[538, 60, 96, 532, 127, 9, 471, 531])).
% 0.30/0.53 tff(540,plain,(r(v2, v1) | r(v1, v0) | (~r(v0, v4)) | r(v4, v1)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(541,plain,
% 0.30/0.53 (r(v2, v1)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[540, 529, 522, 31])).
% 0.30/0.53 tff(542,plain,
% 0.30/0.53 (r(v5, v1)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[393, 25, 508])).
% 0.30/0.53 tff(543,plain,
% 0.30/0.53 (~r(v2, v5)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[400, 168, 6, 542, 147, 127, 541])).
% 0.30/0.53 tff(544,plain,
% 0.30/0.53 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v4)) | r(v4, v0))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v4)) | r(v4, v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(545,plain,
% 0.30/0.53 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v4)) | r(v4, v0))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(546,plain,
% 0.30/0.53 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v4)) | r(v4, v0)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.30/0.53 tff(547,plain,
% 0.30/0.53 (r(v4, v0)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[546, 25, 522])).
% 0.30/0.53 tff(548,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v5) | (~r(v5, v0)) | (v5 = v0) | (~r(v4, v5)) | (~r(v4, v0)) | (v4 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | (~r(v5, v0)) | (v5 = v0) | (~r(v4, v5)) | (~r(v4, v0)) | (v4 = v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(549,plain,
% 0.30/0.53 (((~r(v5, v0)) | (~r(v4, v0)) | (~r(v4, v5)) | (v5 = v0) | (v4 = v0) | (v4 = v5)) <=> ((v4 = v5) | (~r(v5, v0)) | (v5 = v0) | (~r(v4, v5)) | (~r(v4, v0)) | (v4 = v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(550,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v0)) | (~r(v4, v0)) | (~r(v4, v5)) | (v5 = v0) | (v4 = v0) | (v4 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v5) | (~r(v5, v0)) | (v5 = v0) | (~r(v4, v5)) | (~r(v4, v0)) | (v4 = v0)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[549])).
% 0.30/0.53 tff(551,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v0)) | (~r(v4, v0)) | (~r(v4, v5)) | (v5 = v0) | (v4 = v0) | (v4 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | (~r(v5, v0)) | (v5 = v0) | (~r(v4, v5)) | (~r(v4, v0)) | (v4 = v0))),
% 0.30/0.53 inference(transitivity,[status(thm)],[550, 548])).
% 0.30/0.53 tff(552,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v0)) | (~r(v4, v0)) | (~r(v4, v5)) | (v5 = v0) | (v4 = v0) | (v4 = v5))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(553,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | (~r(v5, v0)) | (v5 = v0) | (~r(v4, v5)) | (~r(v4, v0)) | (v4 = v0)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.30/0.53 tff(554,plain,
% 0.30/0.53 (~r(v4, v5)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[553, 168, 15, 89, 440, 547, 475])).
% 0.30/0.53 tff(555,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (v4 = v5) | r(v4, v5) | r(v2, v4) | r(v2, v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | r(v4, v5) | r(v2, v4) | r(v2, v5))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(556,plain,
% 0.30/0.53 ((r(v4, v5) | r(v2, v5) | r(v2, v4) | (v4 = v5) | (v2 = v5) | (v2 = v4)) <=> ((v2 = v4) | (v2 = v5) | (v4 = v5) | r(v4, v5) | r(v2, v4) | r(v2, v5))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(557,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v2, v5) | r(v2, v4) | (v4 = v5) | (v2 = v5) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (v4 = v5) | r(v4, v5) | r(v2, v4) | r(v2, v5)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[556])).
% 0.30/0.53 tff(558,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v2, v5) | r(v2, v4) | (v4 = v5) | (v2 = v5) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | r(v4, v5) | r(v2, v4) | r(v2, v5))),
% 0.30/0.53 inference(transitivity,[status(thm)],[557, 555])).
% 0.30/0.53 tff(559,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v2, v5) | r(v2, v4) | (v4 = v5) | (v2 = v5) | (v2 = v4))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(560,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | r(v4, v5) | r(v2, v4) | r(v2, v5)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.30/0.53 tff(561,plain,
% 0.30/0.53 (r(v2, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[560, 60, 119, 6, 15, 554, 543])).
% 0.30/0.53 tff(562,plain,
% 0.30/0.53 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v1)) | r(v1, v3))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v1)) | r(v1, v3))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(563,plain,
% 0.30/0.53 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v1)) | r(v1, v3))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(564,plain,
% 0.30/0.53 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v1)) | r(v1, v3)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.30/0.53 tff(565,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[564, 25, 380, 195])).
% 0.30/0.53 tff(566,plain,(r(v1, v3) | (~r(v3, v1))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(567,plain,
% 0.30/0.53 (r(v1, v3)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[566, 81])).
% 0.30/0.53 tff(568,plain,
% 0.30/0.53 (~r(v5, v3)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[239, 567, 508])).
% 0.30/0.53 tff(569,plain,
% 0.30/0.53 (~r(v3, v5)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[497, 25, 568])).
% 0.30/0.53 tff(570,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v3 = v5) | (v4 = v5) | r(v4, v5) | r(v3, v4) | r(v3, v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v3 = v5) | (v4 = v5) | r(v4, v5) | r(v3, v4) | r(v3, v5))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(571,plain,
% 0.30/0.53 ((r(v4, v5) | r(v3, v5) | r(v3, v4) | (v4 = v5) | (v3 = v5) | (v3 = v4)) <=> ((v3 = v4) | (v3 = v5) | (v4 = v5) | r(v4, v5) | r(v3, v4) | r(v3, v5))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(572,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v3, v5) | r(v3, v4) | (v4 = v5) | (v3 = v5) | (v3 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v3 = v5) | (v4 = v5) | r(v4, v5) | r(v3, v4) | r(v3, v5)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[571])).
% 0.30/0.53 tff(573,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v3, v5) | r(v3, v4) | (v4 = v5) | (v3 = v5) | (v3 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v3 = v5) | (v4 = v5) | r(v4, v5) | r(v3, v4) | r(v3, v5))),
% 0.30/0.53 inference(transitivity,[status(thm)],[572, 570])).
% 0.30/0.53 tff(574,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v3, v5) | r(v3, v4) | (v4 = v5) | (v3 = v5) | (v3 = v4))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(575,plain,
% 0.30/0.53 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v3 = v5) | (v4 = v5) | r(v4, v5) | r(v3, v4) | r(v3, v5)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.30/0.53 tff(576,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[575, 60, 38, 230, 15, 554, 40, 569])).
% 0.30/0.53 tff(577,plain,(r(v3, v4) | r(v1, v4)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(578,plain,
% 0.30/0.53 (r(v3, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[577, 17])).
% 0.30/0.53 tff(579,plain,
% 0.30/0.53 (~r(v2, v3)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[378, 168, 198, 119, 38, 578, 561])).
% 0.30/0.53 tff(580,plain,
% 0.30/0.53 (~r(v0, v2)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[285, 168, 187, 250, 119, 522, 561])).
% 0.30/0.53 tff(581,plain,
% 0.30/0.53 (~r(v2, v0)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[466, 25, 580])).
% 0.30/0.53 tff(582,assumption,(r(v0, v3)), introduced(assumption)).
% 0.30/0.53 tff(583,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(584,plain,
% 0.30/0.53 (((~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)) | (v3 = v4) | (v0 = v4) | (v0 = v3)) <=> ((v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(585,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[584])).
% 0.30/0.53 tff(586,plain,
% 0.30/0.53 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)))),
% 0.30/0.54 inference(transitivity,[status(thm)],[585, 583])).
% 0.30/0.54 tff(587,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3)) | (v3 = v4) | (v0 = v4) | (v0 = v3))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(588,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v0, v4)) | (~r(v0, v3))),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.30/0.54 tff(589,plain,
% 0.30/0.54 ($false),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[588, 168, 208, 250, 38, 323, 279, 582])).
% 0.30/0.54 tff(590,plain,((~r(v0, v3)) | (~r(v3, v4)) | (~r(v0, v4))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54 tff(591,plain,
% 0.30/0.54 (~r(v0, v3)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[590, 578, 522])).
% 0.30/0.54 tff(592,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v2 = v3) | r(v0, v3) | r(v2, v3) | (v2 = v0) | r(v2, v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v2, v3) | (v2 = v0) | r(v2, v0))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(593,plain,
% 0.30/0.54 ((r(v0, v3) | r(v2, v3) | r(v2, v0) | (v0 = v3) | (v2 = v3) | (v2 = v0)) <=> ((v0 = v3) | (v2 = v3) | r(v0, v3) | r(v2, v3) | (v2 = v0) | r(v2, v0))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(594,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v2, v3) | r(v2, v0) | (v0 = v3) | (v2 = v3) | (v2 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v2 = v3) | r(v0, v3) | r(v2, v3) | (v2 = v0) | r(v2, v0)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[593])).
% 0.30/0.54 tff(595,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v2, v3) | r(v2, v0) | (v0 = v3) | (v2 = v3) | (v2 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v2, v3) | (v2 = v0) | r(v2, v0))),
% 0.30/0.54 inference(transitivity,[status(thm)],[594, 592])).
% 0.30/0.54 tff(596,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v2, v3) | r(v2, v0) | (v0 = v3) | (v2 = v3) | (v2 = v0))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(597,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v2 = v3) | r(v0, v3) | r(v2, v3) | (v2 = v0) | r(v2, v0)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.30/0.54 tff(598,plain,
% 0.30/0.54 ($false),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[597, 60, 208, 198, 591, 471, 581, 579])).
% 0.30/0.54 tff(599,plain,(r(v1, v4)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54 tff(600,plain,
% 0.30/0.54 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v4)) | r(v4, v1))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v4)) | r(v4, v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(601,plain,
% 0.30/0.54 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v4)) | r(v4, v1))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(602,plain,
% 0.30/0.54 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v4)) | r(v4, v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.30/0.54 tff(603,plain,
% 0.30/0.54 (r(v4, v1)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[602, 25, 599])).
% 0.30/0.54 tff(604,assumption,(r(v1, v2)), introduced(assumption)).
% 0.30/0.54 tff(605,plain,
% 0.30/0.54 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v2)) | r(v2, v1))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v2)) | r(v2, v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(606,plain,
% 0.30/0.54 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v2)) | r(v2, v1))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(607,plain,
% 0.30/0.54 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v2)) | r(v2, v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[606, 605])).
% 0.30/0.54 tff(608,plain,
% 0.30/0.54 ($false),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[607, 25, 9, 604])).
% 0.30/0.54 tff(609,plain,((~r(v1, v2)) | r(v2, v1)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54 tff(610,plain,
% 0.30/0.54 (~r(v1, v2)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[609, 9])).
% 0.30/0.54 tff(611,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v5) | r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(612,plain,
% 0.30/0.54 ((r(v5, v2) | r(v1, v2) | r(v1, v5) | (v5 = v2) | (v1 = v2) | (v1 = v5)) <=> ((v1 = v2) | (v1 = v5) | r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(613,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v1, v2) | r(v1, v5) | (v5 = v2) | (v1 = v2) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v5) | r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[612])).
% 0.30/0.54 tff(614,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v1, v2) | r(v1, v5) | (v5 = v2) | (v1 = v2) | (v1 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2))),
% 0.30/0.54 inference(transitivity,[status(thm)],[613, 611])).
% 0.30/0.54 tff(615,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v1, v2) | r(v1, v5) | (v5 = v2) | (v1 = v2) | (v1 = v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(616,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.30/0.54 tff(617,plain,
% 0.30/0.54 (r(v1, v5) | r(v1, v2) | (v5 = v2) | r(v5, v2)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[616, 60, 126, 99])).
% 0.30/0.54 tff(618,plain,
% 0.30/0.54 (r(v5, v2)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[617, 610, 7, 82])).
% 0.30/0.54 tff(619,plain,
% 0.30/0.54 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v2)) | r(v2, v5))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v2)) | r(v2, v5))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(620,plain,
% 0.30/0.54 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v2)) | r(v2, v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(621,plain,
% 0.30/0.54 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v2)) | r(v2, v5)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.30/0.54 tff(622,plain,
% 0.30/0.54 (r(v2, v5)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[621, 25, 618])).
% 0.30/0.54 tff(623,assumption,(~r(v0, v1)), introduced(assumption)).
% 0.30/0.54 tff(624,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v2 = v1) | r(v2, v1) | r(v0, v1) | r(v0, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | r(v2, v1) | r(v0, v1) | r(v0, v2))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(625,plain,
% 0.30/0.54 ((r(v2, v1) | r(v0, v1) | r(v0, v2) | (v2 = v1) | (v0 = v1) | (v0 = v2)) <=> ((v0 = v1) | (v0 = v2) | (v2 = v1) | r(v2, v1) | r(v0, v1) | r(v0, v2))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(626,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v0, v1) | r(v0, v2) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v2 = v1) | r(v2, v1) | r(v0, v1) | r(v0, v2)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[625])).
% 0.30/0.54 tff(627,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v0, v1) | r(v0, v2) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | r(v2, v1) | r(v0, v1) | r(v0, v2))),
% 0.30/0.54 inference(transitivity,[status(thm)],[626, 624])).
% 0.30/0.54 tff(628,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v0, v1) | r(v0, v2) | (v2 = v1) | (v0 = v1) | (v0 = v2))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(629,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | r(v2, v1) | r(v0, v1) | r(v0, v2)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.30/0.54 tff(630,plain,
% 0.30/0.54 (r(v0, v2)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[629, 60, 95, 187, 127, 9, 623])).
% 0.30/0.54 tff(631,assumption,(r(v2, v5)), introduced(assumption)).
% 0.30/0.54 tff(632,assumption,(~r(v5, v1)), introduced(assumption)).
% 0.30/0.54 tff(633,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | r(v5, v1) | (v5 = v1) | r(v0, v5) | r(v0, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | r(v5, v1) | (v5 = v1) | r(v0, v5) | r(v0, v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(634,plain,
% 0.30/0.54 ((r(v5, v1) | r(v0, v1) | r(v0, v5) | (v5 = v1) | (v0 = v1) | (v0 = v5)) <=> ((v0 = v1) | (v0 = v5) | r(v5, v1) | (v5 = v1) | r(v0, v5) | r(v0, v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(635,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v0, v1) | r(v0, v5) | (v5 = v1) | (v0 = v1) | (v0 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | r(v5, v1) | (v5 = v1) | r(v0, v5) | r(v0, v1)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[634])).
% 0.30/0.54 tff(636,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v0, v1) | r(v0, v5) | (v5 = v1) | (v0 = v1) | (v0 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | r(v5, v1) | (v5 = v1) | r(v0, v5) | r(v0, v1))),
% 0.30/0.54 inference(transitivity,[status(thm)],[635, 633])).
% 0.30/0.54 tff(637,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v0, v1) | r(v0, v5) | (v5 = v1) | (v0 = v1) | (v0 = v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(638,plain,
% 0.30/0.54 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | r(v5, v1) | (v5 = v1) | r(v0, v5) | r(v0, v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.30/0.54 tff(639,plain,
% 0.30/0.54 (r(v0, v5)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[638, 60, 95, 88, 632, 147, 623])).
% 0.30/0.54 tff(640,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v5)) | (~r(v0, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v5)) | (~r(v0, v2)))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(641,plain,
% 0.30/0.54 (((~r(v2, v5)) | (~r(v0, v5)) | (~r(v0, v2)) | (v2 = v5) | (v0 = v5) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v5)) | (~r(v0, v2)))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(642,plain,
% 0.30/0.54 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v5)) | (~r(v0, v5)) | (~r(v0, v2)) | (v2 = v5) | (v0 = v5) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v5)) | (~r(v0, v2))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[641])).
% 0.30/0.55 tff(643,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v5)) | (~r(v0, v5)) | (~r(v0, v2)) | (v2 = v5) | (v0 = v5) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v5)) | (~r(v0, v2)))),
% 0.30/0.55 inference(transitivity,[status(thm)],[642, 640])).
% 0.30/0.55 tff(644,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v5)) | (~r(v0, v5)) | (~r(v0, v2)) | (v2 = v5) | (v0 = v5) | (v0 = v2))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(645,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v5)) | (~r(v0, v2))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.30/0.55 tff(646,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[645, 168, 187, 88, 6, 639, 631, 630])).
% 0.30/0.55 tff(647,plain,(r(v0, v1) | (~r(v2, v5)) | r(v2, v1) | r(v5, v1)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(648,plain,
% 0.30/0.55 (r(v0, v1)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[647, 622, 9, 151])).
% 0.30/0.55 tff(649,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (v4 = v1) | (~r(v4, v1)) | (~r(v0, v4)) | (~r(v0, v1)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v4 = v1) | (~r(v4, v1)) | (~r(v0, v4)) | (~r(v0, v1)))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(650,plain,
% 0.30/0.55 (((~r(v4, v1)) | (~r(v0, v1)) | (~r(v0, v4)) | (v4 = v1) | (v0 = v1) | (v0 = v4)) <=> ((v0 = v1) | (v0 = v4) | (v4 = v1) | (~r(v4, v1)) | (~r(v0, v4)) | (~r(v0, v1)))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(651,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v0, v1)) | (~r(v0, v4)) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (v4 = v1) | (~r(v4, v1)) | (~r(v0, v4)) | (~r(v0, v1))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[650])).
% 0.30/0.55 tff(652,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v0, v1)) | (~r(v0, v4)) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v4 = v1) | (~r(v4, v1)) | (~r(v0, v4)) | (~r(v0, v1)))),
% 0.30/0.55 inference(transitivity,[status(thm)],[651, 649])).
% 0.30/0.55 tff(653,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v0, v1)) | (~r(v0, v4)) | (v4 = v1) | (v0 = v1) | (v0 = v4))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(654,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (v4 = v1) | (~r(v4, v1)) | (~r(v0, v4)) | (~r(v0, v1))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.30/0.55 tff(655,plain,
% 0.30/0.55 (~r(v0, v4)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[654, 168, 95, 250, 131, 603, 648])).
% 0.30/0.55 tff(656,plain,
% 0.30/0.55 (r(v5, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[342, 380, 82])).
% 0.30/0.55 tff(657,plain,
% 0.30/0.55 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v3)) | r(v3, v5))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v3)) | r(v3, v5))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(658,plain,
% 0.30/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v3)) | r(v3, v5))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(659,plain,
% 0.30/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v3)) | r(v3, v5)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.30/0.55 tff(660,plain,
% 0.30/0.55 (r(v3, v5)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[659, 25, 656])).
% 0.30/0.55 tff(661,assumption,(~r(v1, v2)), introduced(assumption)).
% 0.30/0.55 tff(662,plain,
% 0.30/0.55 (r(v5, v2)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[617, 661, 7, 82])).
% 0.30/0.55 tff(663,plain,
% 0.30/0.55 (r(v2, v5)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[621, 25, 662])).
% 0.30/0.55 tff(664,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(665,plain,
% 0.30/0.55 (((~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)) | (v3 = v5) | (v2 = v5) | (v2 = v3)) <=> ((v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(666,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)) | (v3 = v5) | (v2 = v5) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[665])).
% 0.30/0.55 tff(667,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)) | (v3 = v5) | (v2 = v5) | (v2 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)))),
% 0.30/0.55 inference(transitivity,[status(thm)],[666, 664])).
% 0.30/0.55 tff(668,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3)) | (v3 = v5) | (v2 = v5) | (v2 = v3))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(669,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v5)) | (~r(v2, v3))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.30/0.55 tff(670,plain,
% 0.30/0.55 (~r(v2, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[669, 168, 198, 6, 230, 663, 660])).
% 0.30/0.55 tff(671,plain,
% 0.30/0.55 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v2)) | r(v2, v3))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v2)) | r(v2, v3))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(672,plain,
% 0.30/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v2)) | r(v2, v3))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(673,plain,
% 0.30/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v2)) | r(v2, v3)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.30/0.55 tff(674,plain,
% 0.30/0.55 (~r(v3, v2)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[673, 25, 670])).
% 0.30/0.55 tff(675,plain,
% 0.30/0.55 ((v3 = v2) <=> (v2 = v3)),
% 0.30/0.55 inference(commutativity,[status(thm)],[])).
% 0.30/0.55 tff(676,plain,
% 0.30/0.55 ((v2 = v3) <=> (v3 = v2)),
% 0.30/0.55 inference(symmetry,[status(thm)],[675])).
% 0.30/0.55 tff(677,plain,
% 0.30/0.55 ((~(v2 = v3)) <=> (~(v3 = v2))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[676])).
% 0.30/0.55 tff(678,plain,
% 0.30/0.55 (~(v3 = v2)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[198, 677])).
% 0.30/0.55 tff(679,plain,
% 0.30/0.55 (~r(v3, v1)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[566, 380])).
% 0.30/0.55 tff(680,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v3 = v1) | r(v3, v1) | r(v1, v2) | (v3 = v2) | r(v3, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v3 = v1) | r(v3, v1) | r(v1, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(681,plain,
% 0.30/0.55 ((r(v1, v2) | r(v3, v2) | r(v3, v1) | (v1 = v2) | (v3 = v2) | (v3 = v1)) <=> ((v1 = v2) | (v3 = v1) | r(v3, v1) | r(v1, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(682,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v2) | r(v3, v2) | r(v3, v1) | (v1 = v2) | (v3 = v2) | (v3 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v3 = v1) | r(v3, v1) | r(v1, v2) | (v3 = v2) | r(v3, v2)))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[681])).
% 0.30/0.55 tff(683,plain,
% 0.30/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v2) | r(v3, v2) | r(v3, v1) | (v1 = v2) | (v3 = v2) | (v3 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v3 = v1) | r(v3, v1) | r(v1, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.55 inference(transitivity,[status(thm)],[682, 680])).
% 0.30/0.55 tff(684,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v2) | r(v3, v2) | r(v3, v1) | (v1 = v2) | (v3 = v2) | (v3 = v1))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(685,plain,
% 0.30/0.55 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v3 = v1) | r(v3, v1) | r(v1, v2) | (v3 = v2) | r(v3, v2)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.30/0.55 tff(686,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[685, 60, 126, 72, 679, 661, 678, 674])).
% 0.30/0.55 tff(687,plain,(r(v1, v3) | r(v1, v2) | r(v1, v5)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(688,plain,
% 0.30/0.55 (r(v1, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[687, 610, 82])).
% 0.30/0.55 tff(689,plain,
% 0.30/0.55 (r(v3, v1)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[346, 25, 688])).
% 0.30/0.55 tff(690,plain,
% 0.30/0.55 (~r(v0, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[214, 168, 95, 208, 72, 689, 648])).
% 0.30/0.55 tff(691,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[263, 60, 208, 250, 38, 40, 8, 322])).
% 0.40/0.55 tff(692,plain,(r(v0, v3) | r(v3, v4) | r(v0, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(693,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[692, 690, 655, 40])).
% 0.40/0.55 tff(694,plain,(r(v2, v1) | r(v3, v4) | r(v1, v5)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(695,plain,
% 0.40/0.55 (r(v2, v1)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[694, 82, 40])).
% 0.40/0.55 tff(696,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v4 = v1) | (~r(v4, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v4 = v1) | (~r(v4, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v4)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(697,plain,
% 0.40/0.55 (((~r(v4, v1)) | (~r(v2, v1)) | (~r(v2, v4)) | (v4 = v1) | (v2 = v1) | (v2 = v4)) <=> ((v2 = v4) | (v4 = v1) | (~r(v4, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v4)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(698,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v2, v1)) | (~r(v2, v4)) | (v4 = v1) | (v2 = v1) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v4 = v1) | (~r(v4, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v4))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[697])).
% 0.40/0.55 tff(699,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v2, v1)) | (~r(v2, v4)) | (v4 = v1) | (v2 = v1) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v4 = v1) | (~r(v4, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v4)))),
% 0.40/0.55 inference(transitivity,[status(thm)],[698, 696])).
% 0.40/0.55 tff(700,plain,
% 0.40/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v2, v1)) | (~r(v2, v4)) | (v4 = v1) | (v2 = v1) | (v2 = v4))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(701,plain,
% 0.40/0.55 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v4 = v1) | (~r(v4, v1)) | (v2 = v1) | (~r(v2, v1)) | (~r(v2, v4))),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.40/0.55 tff(702,plain,
% 0.40/0.55 (~r(v2, v4)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[701, 168, 119, 131, 603, 127, 695])).
% 0.40/0.55 tff(703,assumption,(~r(v2, v4)), introduced(assumption)).
% 0.40/0.55 tff(704,assumption,(~r(v0, v2)), introduced(assumption)).
% 0.40/0.55 tff(705,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | (v2 = v4) | r(v0, v4) | r(v2, v4) | r(v0, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | r(v0, v4) | r(v2, v4) | r(v0, v2))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(706,plain,
% 0.40/0.55 ((r(v2, v4) | r(v0, v4) | r(v0, v2) | (v2 = v4) | (v0 = v4) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v4) | (v2 = v4) | r(v0, v4) | r(v2, v4) | r(v0, v2))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(707,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v0, v4) | r(v0, v2) | (v2 = v4) | (v0 = v4) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | (v2 = v4) | r(v0, v4) | r(v2, v4) | r(v0, v2)))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[706])).
% 0.40/0.55 tff(708,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v0, v4) | r(v0, v2) | (v2 = v4) | (v0 = v4) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | r(v0, v4) | r(v2, v4) | r(v0, v2))),
% 0.40/0.55 inference(transitivity,[status(thm)],[707, 705])).
% 0.40/0.55 tff(709,plain,
% 0.40/0.55 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v0, v4) | r(v0, v2) | (v2 = v4) | (v0 = v4) | (v0 = v2))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(710,plain,
% 0.40/0.55 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | r(v0, v4) | r(v2, v4) | r(v0, v2)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.40/0.55 tff(711,plain,
% 0.40/0.55 ($false),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[710, 60, 187, 250, 119, 8, 703, 704])).
% 0.40/0.55 tff(712,plain,(r(v0, v2) | r(v0, v4) | r(v2, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55 tff(713,plain,
% 0.40/0.55 (r(v0, v2)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[712, 8, 703])).
% 0.40/0.55 tff(714,plain,
% 0.40/0.55 (r(v2, v3)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[304, 60, 198, 119, 38, 40, 703])).
% 0.40/0.55 tff(715,plain,
% 0.40/0.55 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v3)) | r(v3, v2))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v3)) | r(v3, v2))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(716,plain,
% 0.40/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v3)) | r(v3, v2))),
% 0.40/0.55 inference(quant_inst,[status(thm)],[])).
% 0.40/0.55 tff(717,plain,
% 0.40/0.55 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v3)) | r(v3, v2)),
% 0.40/0.55 inference(modus_ponens,[status(thm)],[716, 715])).
% 0.40/0.55 tff(718,plain,
% 0.40/0.55 (r(v3, v2)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[717, 25, 714])).
% 0.40/0.55 tff(719,plain,
% 0.40/0.55 (r(v0, v3)),
% 0.40/0.55 inference(unit_resolution,[status(thm)],[692, 8, 40])).
% 0.40/0.55 tff(720,plain,
% 0.40/0.55 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (v3 = v2) | (~r(v3, v2)) | (~r(v0, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (v3 = v2) | (~r(v3, v2)) | (~r(v0, v2)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(721,plain,
% 0.40/0.56 (((~r(v3, v2)) | (~r(v0, v2)) | (~r(v0, v3)) | (v3 = v2) | (v0 = v2) | (v0 = v3)) <=> ((v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (v3 = v2) | (~r(v3, v2)) | (~r(v0, v2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(722,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v0, v2)) | (~r(v0, v3)) | (v3 = v2) | (v0 = v2) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (v3 = v2) | (~r(v3, v2)) | (~r(v0, v2))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[721])).
% 0.40/0.56 tff(723,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v0, v2)) | (~r(v0, v3)) | (v3 = v2) | (v0 = v2) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (v3 = v2) | (~r(v3, v2)) | (~r(v0, v2)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[722, 720])).
% 0.40/0.56 tff(724,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v0, v2)) | (~r(v0, v3)) | (v3 = v2) | (v0 = v2) | (v0 = v3))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(725,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (v3 = v2) | (~r(v3, v2)) | (~r(v0, v2))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.40/0.56 tff(726,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[725, 168, 187, 208, 719, 678, 718, 713])).
% 0.40/0.56 tff(727,plain,(r(v0, v4) | r(v2, v4) | r(v3, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(728,plain,
% 0.40/0.56 (r(v0, v4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[727, 702, 40])).
% 0.40/0.56 tff(729,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v1 = v4) | (~r(v1, v4)) | (v1 = v0) | (~r(v0, v4)) | (~r(v1, v0)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | (~r(v1, v4)) | (v1 = v0) | (~r(v0, v4)) | (~r(v1, v0)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(730,plain,
% 0.40/0.56 (((~r(v0, v4)) | (~r(v1, v4)) | (~r(v1, v0)) | (v0 = v4) | (v1 = v4) | (v1 = v0)) <=> ((v0 = v4) | (v1 = v4) | (~r(v1, v4)) | (v1 = v0) | (~r(v0, v4)) | (~r(v1, v0)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(731,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v1, v4)) | (~r(v1, v0)) | (v0 = v4) | (v1 = v4) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v1 = v4) | (~r(v1, v4)) | (v1 = v0) | (~r(v0, v4)) | (~r(v1, v0))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[730])).
% 0.40/0.56 tff(732,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v1, v4)) | (~r(v1, v0)) | (v0 = v4) | (v1 = v4) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | (~r(v1, v4)) | (v1 = v0) | (~r(v0, v4)) | (~r(v1, v0)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[731, 729])).
% 0.40/0.56 tff(733,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v1, v4)) | (~r(v1, v0)) | (v0 = v4) | (v1 = v4) | (v1 = v0))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(734,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | (~r(v1, v4)) | (v1 = v0) | (~r(v0, v4)) | (~r(v1, v0))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[733, 732])).
% 0.40/0.56 tff(735,plain,
% 0.40/0.56 (~r(v1, v0)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[734, 168, 250, 47, 599, 96, 728])).
% 0.40/0.56 tff(736,plain,
% 0.40/0.56 (r(v2, v3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[304, 60, 198, 119, 38, 40, 702])).
% 0.40/0.56 tff(737,plain,
% 0.40/0.56 (r(v3, v2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[717, 25, 736])).
% 0.40/0.56 tff(738,plain,
% 0.40/0.56 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v1)) | r(v1, v2))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v1)) | r(v1, v2))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(739,plain,
% 0.40/0.56 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v1)) | r(v1, v2))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(740,plain,
% 0.40/0.56 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v1)) | r(v1, v2)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[739, 738])).
% 0.40/0.56 tff(741,plain,
% 0.40/0.56 (r(v1, v2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[740, 25, 695])).
% 0.40/0.56 tff(742,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v3) | (~r(v1, v3)) | (~r(v1, v2)) | (v3 = v2) | (~r(v3, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v3) | (~r(v1, v3)) | (~r(v1, v2)) | (v3 = v2) | (~r(v3, v2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(743,plain,
% 0.40/0.56 (((~r(v3, v2)) | (~r(v1, v2)) | (~r(v1, v3)) | (v3 = v2) | (v1 = v2) | (v1 = v3)) <=> ((v1 = v2) | (v1 = v3) | (~r(v1, v3)) | (~r(v1, v2)) | (v3 = v2) | (~r(v3, v2)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(744,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v1, v2)) | (~r(v1, v3)) | (v3 = v2) | (v1 = v2) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v3) | (~r(v1, v3)) | (~r(v1, v2)) | (v3 = v2) | (~r(v3, v2))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[743])).
% 0.40/0.56 tff(745,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v1, v2)) | (~r(v1, v3)) | (v3 = v2) | (v1 = v2) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v3) | (~r(v1, v3)) | (~r(v1, v2)) | (v3 = v2) | (~r(v3, v2)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[744, 742])).
% 0.40/0.56 tff(746,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v1, v2)) | (~r(v1, v3)) | (v3 = v2) | (v1 = v2) | (v1 = v3))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(747,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v3) | (~r(v1, v3)) | (~r(v1, v2)) | (v3 = v2) | (~r(v3, v2))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.40/0.56 tff(748,plain,
% 0.40/0.56 (~r(v1, v3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[747, 168, 126, 50, 741, 678, 737])).
% 0.40/0.56 tff(749,plain,
% 0.40/0.56 (r(v5, v3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[342, 748, 82])).
% 0.40/0.56 tff(750,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v5 = v3) | (~r(v5, v3)) | (v5 = v2) | (~r(v5, v2)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v5 = v3) | (~r(v5, v3)) | (v5 = v2) | (~r(v5, v2)) | (~r(v2, v3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(751,plain,
% 0.40/0.56 (((~r(v2, v3)) | (~r(v5, v3)) | (~r(v5, v2)) | (v2 = v3) | (v5 = v3) | (v5 = v2)) <=> ((v2 = v3) | (v5 = v3) | (~r(v5, v3)) | (v5 = v2) | (~r(v5, v2)) | (~r(v2, v3)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(752,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v5, v3)) | (~r(v5, v2)) | (v2 = v3) | (v5 = v3) | (v5 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v5 = v3) | (~r(v5, v3)) | (v5 = v2) | (~r(v5, v2)) | (~r(v2, v3))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[751])).
% 0.40/0.56 tff(753,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v5, v3)) | (~r(v5, v2)) | (v2 = v3) | (v5 = v3) | (v5 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v5 = v3) | (~r(v5, v3)) | (v5 = v2) | (~r(v5, v2)) | (~r(v2, v3)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[752, 750])).
% 0.40/0.56 tff(754,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v5, v3)) | (~r(v5, v2)) | (v2 = v3) | (v5 = v3) | (v5 = v2))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(755,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v5 = v3) | (~r(v5, v3)) | (v5 = v2) | (~r(v5, v2)) | (~r(v2, v3))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.40/0.56 tff(756,plain,
% 0.40/0.56 (~r(v5, v2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[755, 168, 198, 231, 749, 7, 736])).
% 0.40/0.56 tff(757,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v4, v1)) | (~r(v4, v2)) | (v2 = v1) | (v4 = v1) | (v4 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v2, v1)) | (~r(v4, v1)) | (~r(v4, v2)) | (v2 = v1) | (v4 = v1) | (v4 = v2))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(758,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v4, v1)) | (~r(v4, v2)) | (v2 = v1) | (v4 = v1) | (v4 = v2))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(759,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v2, v1)) | (~r(v4, v1)) | (~r(v4, v2)) | (v2 = v1) | (v4 = v1) | (v4 = v2)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.40/0.56 tff(760,plain,
% 0.40/0.56 (~r(v4, v2)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[759, 168, 131, 603, 127, 695, 120])).
% 0.40/0.56 tff(761,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | (v4 = v2) | r(v5, v4) | (v5 = v4) | (v5 = v2) | r(v5, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(v4, v2) | (v4 = v2) | r(v5, v4) | (v5 = v4) | (v5 = v2) | r(v5, v2))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(762,plain,
% 0.40/0.56 ((r(v4, v2) | r(v5, v2) | r(v5, v4) | (v4 = v2) | (v5 = v2) | (v5 = v4)) <=> (r(v4, v2) | (v4 = v2) | r(v5, v4) | (v5 = v4) | (v5 = v2) | r(v5, v2))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(763,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | r(v5, v2) | r(v5, v4) | (v4 = v2) | (v5 = v2) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | (v4 = v2) | r(v5, v4) | (v5 = v4) | (v5 = v2) | r(v5, v2)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[762])).
% 0.40/0.56 tff(764,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | r(v5, v2) | r(v5, v4) | (v4 = v2) | (v5 = v2) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(v4, v2) | (v4 = v2) | r(v5, v4) | (v5 = v4) | (v5 = v2) | r(v5, v2))),
% 0.40/0.56 inference(transitivity,[status(thm)],[763, 761])).
% 0.40/0.56 tff(765,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | r(v5, v2) | r(v5, v4) | (v4 = v2) | (v5 = v2) | (v5 = v4))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(766,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(v4, v2) | (v4 = v2) | r(v5, v4) | (v5 = v4) | (v5 = v2) | r(v5, v2)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.40/0.56 tff(767,plain,
% 0.40/0.56 (r(v5, v4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[766, 60, 16, 760, 120, 7, 756])).
% 0.40/0.56 tff(768,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (~r(v5, v4)) | (~r(v5, v0)) | (v5 = v0) | (v5 = v4) | (~r(v0, v4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (~r(v5, v4)) | (~r(v5, v0)) | (v5 = v0) | (v5 = v4) | (~r(v0, v4)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(769,plain,
% 0.40/0.56 (((~r(v0, v4)) | (~r(v5, v4)) | (~r(v5, v0)) | (v0 = v4) | (v5 = v4) | (v5 = v0)) <=> ((v0 = v4) | (~r(v5, v4)) | (~r(v5, v0)) | (v5 = v0) | (v5 = v4) | (~r(v0, v4)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(770,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v5, v4)) | (~r(v5, v0)) | (v0 = v4) | (v5 = v4) | (v5 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (~r(v5, v4)) | (~r(v5, v0)) | (v5 = v0) | (v5 = v4) | (~r(v0, v4))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[769])).
% 0.40/0.56 tff(771,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v5, v4)) | (~r(v5, v0)) | (v0 = v4) | (v5 = v4) | (v5 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (~r(v5, v4)) | (~r(v5, v0)) | (v5 = v0) | (v5 = v4) | (~r(v0, v4)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[770, 768])).
% 0.40/0.56 tff(772,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v5, v4)) | (~r(v5, v0)) | (v0 = v4) | (v5 = v4) | (v5 = v0))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(773,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (~r(v5, v4)) | (~r(v5, v0)) | (v5 = v0) | (v5 = v4) | (~r(v0, v4))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.40/0.56 tff(774,plain,
% 0.40/0.56 (~r(v5, v0)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[773, 168, 250, 767, 16, 89, 728])).
% 0.40/0.56 tff(775,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[107, 774, 735, 82])).
% 0.40/0.56 tff(776,plain,(r(v1, v5) | r(v3, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(777,plain,
% 0.40/0.56 (r(v1, v5)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[776, 40])).
% 0.40/0.56 tff(778,plain,
% 0.40/0.56 (r(v5, v1)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[393, 25, 777])).
% 0.40/0.56 tff(779,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v5, v1)) | (~r(v5, v4)) | (v4 = v1) | (v5 = v1) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v1)) | (~r(v5, v1)) | (~r(v5, v4)) | (v4 = v1) | (v5 = v1) | (v5 = v4))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(780,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v5, v1)) | (~r(v5, v4)) | (v4 = v1) | (v5 = v1) | (v5 = v4))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(781,plain,
% 0.40/0.56 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v1)) | (~r(v5, v1)) | (~r(v5, v4)) | (v4 = v1) | (v5 = v1) | (v5 = v4)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.40/0.56 tff(782,plain,
% 0.40/0.56 (~r(v5, v4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[781, 168, 778, 147, 131, 603, 16])).
% 0.40/0.56 tff(783,plain,
% 0.40/0.56 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v5 = v3) | r(v5, v3) | r(v3, v4) | r(v5, v4) | (v5 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v5 = v3) | r(v5, v3) | r(v3, v4) | r(v5, v4) | (v5 = v4))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(784,plain,
% 0.40/0.56 ((r(v3, v4) | r(v5, v4) | r(v5, v3) | (v3 = v4) | (v5 = v4) | (v5 = v3)) <=> ((v3 = v4) | (v5 = v3) | r(v5, v3) | r(v3, v4) | r(v5, v4) | (v5 = v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(785,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v5, v4) | r(v5, v3) | (v3 = v4) | (v5 = v4) | (v5 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v5 = v3) | r(v5, v3) | r(v3, v4) | r(v5, v4) | (v5 = v4)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[784])).
% 0.40/0.57 tff(786,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v5, v4) | r(v5, v3) | (v3 = v4) | (v5 = v4) | (v5 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v5 = v3) | r(v5, v3) | r(v3, v4) | r(v5, v4) | (v5 = v4))),
% 0.40/0.57 inference(transitivity,[status(thm)],[785, 783])).
% 0.40/0.57 tff(787,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v4) | r(v5, v4) | r(v5, v3) | (v3 = v4) | (v5 = v4) | (v5 = v3))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(788,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v5 = v3) | r(v5, v3) | r(v3, v4) | r(v5, v4) | (v5 = v4)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.40/0.57 tff(789,plain,
% 0.40/0.57 (r(v5, v3)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[788, 60, 38, 231, 40, 782, 16])).
% 0.40/0.57 tff(790,plain,
% 0.40/0.57 (~r(v1, v3)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[239, 789, 777])).
% 0.40/0.57 tff(791,plain,
% 0.40/0.57 (~r(v3, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[566, 790])).
% 0.40/0.57 tff(792,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v0, v5)) | (~r(v0, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v0, v5)) | (~r(v0, v3)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(793,plain,
% 0.40/0.57 (((~r(v5, v3)) | (~r(v0, v3)) | (~r(v0, v5)) | (v5 = v3) | (v0 = v3) | (v0 = v5)) <=> ((v0 = v3) | (v0 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v0, v5)) | (~r(v0, v3)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(794,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v0, v3)) | (~r(v0, v5)) | (v5 = v3) | (v0 = v3) | (v0 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v0, v5)) | (~r(v0, v3))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[793])).
% 0.40/0.57 tff(795,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v0, v3)) | (~r(v0, v5)) | (v5 = v3) | (v0 = v3) | (v0 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v0, v5)) | (~r(v0, v3)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[794, 792])).
% 0.40/0.57 tff(796,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v0, v3)) | (~r(v0, v5)) | (v5 = v3) | (v0 = v3) | (v0 = v5))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(797,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v0, v5)) | (~r(v0, v3))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[796, 795])).
% 0.40/0.57 tff(798,plain,
% 0.40/0.57 (~r(v0, v5)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[797, 168, 208, 88, 231, 789, 719])).
% 0.40/0.57 tff(799,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v5) | (v5 = v1) | (v4 = v1) | (~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | (v5 = v1) | (v4 = v1) | (~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(800,plain,
% 0.40/0.57 (((~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)) | (v5 = v1) | (v4 = v1) | (v4 = v5)) <=> ((v4 = v5) | (v5 = v1) | (v4 = v1) | (~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(801,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)) | (v5 = v1) | (v4 = v1) | (v4 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v4 = v5) | (v5 = v1) | (v4 = v1) | (~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[800])).
% 0.40/0.57 tff(802,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)) | (v5 = v1) | (v4 = v1) | (v4 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | (v5 = v1) | (v4 = v1) | (~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[801, 799])).
% 0.40/0.57 tff(803,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5)) | (v5 = v1) | (v4 = v1) | (v4 = v5))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(804,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v4 = v5) | (v5 = v1) | (v4 = v1) | (~r(v5, v1)) | (~r(v4, v1)) | (~r(v4, v5))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.40/0.57 tff(805,plain,
% 0.40/0.57 (~r(v4, v5)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[804, 168, 15, 778, 147, 131, 603])).
% 0.40/0.57 tff(806,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v0 = v5) | (v4 = v5) | r(v4, v5) | r(v0, v5) | r(v0, v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v0 = v5) | (v4 = v5) | r(v4, v5) | r(v0, v5) | r(v0, v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(807,plain,
% 0.40/0.57 ((r(v4, v5) | r(v0, v5) | r(v0, v4) | (v4 = v5) | (v0 = v5) | (v0 = v4)) <=> ((v0 = v4) | (v0 = v5) | (v4 = v5) | r(v4, v5) | r(v0, v5) | r(v0, v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(808,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v0, v5) | r(v0, v4) | (v4 = v5) | (v0 = v5) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v0 = v5) | (v4 = v5) | r(v4, v5) | r(v0, v5) | r(v0, v4)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[807])).
% 0.40/0.57 tff(809,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v0, v5) | r(v0, v4) | (v4 = v5) | (v0 = v5) | (v0 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v0 = v5) | (v4 = v5) | r(v4, v5) | r(v0, v5) | r(v0, v4))),
% 0.40/0.57 inference(transitivity,[status(thm)],[808, 806])).
% 0.40/0.57 tff(810,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v5) | r(v0, v5) | r(v0, v4) | (v4 = v5) | (v0 = v5) | (v0 = v4))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(811,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v0 = v5) | (v4 = v5) | r(v4, v5) | r(v0, v5) | r(v0, v4)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.40/0.57 tff(812,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[811, 60, 250, 88, 15, 805, 8, 798])).
% 0.40/0.57 tff(813,plain,(r(v0, v4) | r(v3, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(814,plain,
% 0.40/0.57 (r(v0, v4)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[813, 40])).
% 0.40/0.57 tff(815,assumption,(r(v0, v1)), introduced(assumption)).
% 0.40/0.57 tff(816,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[654, 168, 95, 250, 131, 603, 279, 815])).
% 0.40/0.57 tff(817,plain,((~r(v0, v1)) | (~r(v0, v4))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(818,plain,
% 0.40/0.57 (~r(v0, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[817, 814])).
% 0.40/0.57 tff(819,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v3 = v1) | r(v3, v1) | r(v0, v3) | r(v0, v1))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v3 = v1) | r(v3, v1) | r(v0, v3) | r(v0, v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(820,plain,
% 0.40/0.57 ((r(v3, v1) | r(v0, v1) | r(v0, v3) | (v3 = v1) | (v0 = v1) | (v0 = v3)) <=> ((v0 = v1) | (v0 = v3) | (v3 = v1) | r(v3, v1) | r(v0, v3) | r(v0, v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(821,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v1) | r(v0, v1) | r(v0, v3) | (v3 = v1) | (v0 = v1) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v3) | (v3 = v1) | r(v3, v1) | r(v0, v3) | r(v0, v1)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[820])).
% 0.40/0.57 tff(822,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v1) | r(v0, v1) | r(v0, v3) | (v3 = v1) | (v0 = v1) | (v0 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v3 = v1) | r(v3, v1) | r(v0, v3) | r(v0, v1))),
% 0.40/0.57 inference(transitivity,[status(thm)],[821, 819])).
% 0.40/0.57 tff(823,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v1) | r(v0, v1) | r(v0, v3) | (v3 = v1) | (v0 = v1) | (v0 = v3))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(824,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v3) | (v3 = v1) | r(v3, v1) | r(v0, v3) | r(v0, v1)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[823, 822])).
% 0.40/0.57 tff(825,plain,
% 0.40/0.57 (r(v3, v1) | r(v0, v3) | r(v0, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[824, 60, 95, 208, 72])).
% 0.40/0.57 tff(826,plain,
% 0.40/0.57 (r(v0, v3)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[825, 818, 791])).
% 0.40/0.57 tff(827,assumption,(r(v2, v3)), introduced(assumption)).
% 0.40/0.57 tff(828,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (v2 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (v2 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (~r(v2, v3)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(829,plain,
% 0.40/0.57 (((~r(v2, v3)) | (~r(v0, v3)) | (~r(v0, v2)) | (v2 = v3) | (v0 = v3) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v3) | (v2 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (~r(v2, v3)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(830,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v0, v3)) | (~r(v0, v2)) | (v2 = v3) | (v0 = v3) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (v2 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (~r(v2, v3))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[829])).
% 0.40/0.57 tff(831,plain,
% 0.40/0.57 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v0, v3)) | (~r(v0, v2)) | (v2 = v3) | (v0 = v3) | (v0 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (v2 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (~r(v2, v3)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[830, 828])).
% 0.40/0.57 tff(832,plain,
% 0.40/0.57 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v0, v3)) | (~r(v0, v2)) | (v2 = v3) | (v0 = v3) | (v0 = v2))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(833,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (v2 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (~r(v2, v3))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.40/0.58 tff(834,plain,
% 0.40/0.58 (~r(v0, v2)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[833, 168, 187, 208, 198, 582, 827])).
% 0.40/0.58 tff(835,assumption,(r(v5, v3)), introduced(assumption)).
% 0.40/0.58 tff(836,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v2, v5)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v2, v5)) | (~r(v2, v3)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(837,plain,
% 0.40/0.58 (((~r(v5, v3)) | (~r(v2, v3)) | (~r(v2, v5)) | (v5 = v3) | (v2 = v3) | (v2 = v5)) <=> ((v2 = v3) | (v2 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v2, v5)) | (~r(v2, v3)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(838,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v2, v3)) | (~r(v2, v5)) | (v5 = v3) | (v2 = v3) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v2, v5)) | (~r(v2, v3))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[837])).
% 0.40/0.58 tff(839,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v2, v3)) | (~r(v2, v5)) | (v5 = v3) | (v2 = v3) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v2, v5)) | (~r(v2, v3)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[838, 836])).
% 0.40/0.58 tff(840,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v2, v3)) | (~r(v2, v5)) | (v5 = v3) | (v2 = v3) | (v2 = v5))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(841,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v5 = v3) | (~r(v5, v3)) | (~r(v2, v5)) | (~r(v2, v3))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.40/0.58 tff(842,plain,
% 0.40/0.58 (~r(v2, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[841, 168, 198, 6, 231, 835, 827])).
% 0.40/0.58 tff(843,plain,
% 0.40/0.58 (~r(v0, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[797, 168, 208, 88, 231, 835, 582])).
% 0.40/0.58 tff(844,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[295, 60, 187, 88, 6, 843, 842, 834])).
% 0.40/0.58 tff(845,plain,((~r(v2, v3)) | (~r(v0, v3)) | (~r(v5, v3))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(846,plain,
% 0.40/0.58 (~r(v2, v3)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[845, 826, 789])).
% 0.40/0.58 tff(847,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | r(v4, v3) | (v4 = v3) | r(v2, v4) | r(v2, v3))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | r(v4, v3) | (v4 = v3) | r(v2, v4) | r(v2, v3))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(848,plain,
% 0.40/0.58 ((r(v4, v3) | r(v2, v3) | r(v2, v4) | (v4 = v3) | (v2 = v3) | (v2 = v4)) <=> ((v2 = v3) | (v2 = v4) | r(v4, v3) | (v4 = v3) | r(v2, v4) | r(v2, v3))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(849,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v2, v3) | r(v2, v4) | (v4 = v3) | (v2 = v3) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | r(v4, v3) | (v4 = v3) | r(v2, v4) | r(v2, v3)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[848])).
% 0.40/0.58 tff(850,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v2, v3) | r(v2, v4) | (v4 = v3) | (v2 = v3) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | r(v4, v3) | (v4 = v3) | r(v2, v4) | r(v2, v3))),
% 0.40/0.58 inference(transitivity,[status(thm)],[849, 847])).
% 0.40/0.58 tff(851,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v2, v3) | r(v2, v4) | (v4 = v3) | (v2 = v3) | (v2 = v4))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(852,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | r(v4, v3) | (v4 = v3) | r(v2, v4) | r(v2, v3)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[851, 850])).
% 0.40/0.58 tff(853,plain,
% 0.40/0.58 (r(v2, v4)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[852, 60, 198, 119, 44, 39, 846])).
% 0.40/0.58 tff(854,plain,
% 0.40/0.58 (r(v1, v3) | r(v2, v1) | r(v2, v3)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[386, 60, 50, 198, 127])).
% 0.40/0.58 tff(855,plain,
% 0.40/0.58 (r(v2, v1)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[854, 846, 790])).
% 0.40/0.58 tff(856,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[701, 168, 119, 131, 603, 127, 855, 853])).
% 0.40/0.58 tff(857,plain,(r(v3, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(858,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(859,plain,
% 0.40/0.58 (((~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)) | (v3 = v4) | (v1 = v4) | (v1 = v3)) <=> ((v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(860,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)) | (v3 = v4) | (v1 = v4) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[859])).
% 0.40/0.58 tff(861,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)) | (v3 = v4) | (v1 = v4) | (v1 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[860, 858])).
% 0.40/0.58 tff(862,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)) | (v3 = v4) | (v1 = v4) | (v1 = v3))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(863,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.40/0.58 tff(864,plain,
% 0.40/0.58 ((~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[863, 168, 50, 47, 38])).
% 0.40/0.58 tff(865,plain,
% 0.40/0.58 ((~r(v1, v3)) | (~r(v3, v4))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[864, 599])).
% 0.40/0.58 tff(866,plain,
% 0.40/0.58 (~r(v1, v3)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[865, 857])).
% 0.40/0.58 tff(867,plain,
% 0.40/0.58 (r(v2, v1) | r(v2, v3)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[854, 866])).
% 0.40/0.58 tff(868,plain,
% 0.40/0.58 (r(v2, v3)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[867, 9])).
% 0.40/0.58 tff(869,plain,
% 0.40/0.58 (r(v4, v3)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[492, 857])).
% 0.40/0.58 tff(870,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v2, v4)) | (~r(v2, v3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v2, v4)) | (~r(v2, v3)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(871,plain,
% 0.40/0.58 (((~r(v4, v3)) | (~r(v2, v3)) | (~r(v2, v4)) | (v4 = v3) | (v2 = v3) | (v2 = v4)) <=> ((v2 = v3) | (v2 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v2, v4)) | (~r(v2, v3)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(872,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v2, v3)) | (~r(v2, v4)) | (v4 = v3) | (v2 = v3) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v2, v4)) | (~r(v2, v3))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[871])).
% 0.40/0.58 tff(873,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v2, v3)) | (~r(v2, v4)) | (v4 = v3) | (v2 = v3) | (v2 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v2, v4)) | (~r(v2, v3)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[872, 870])).
% 0.40/0.58 tff(874,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v2, v3)) | (~r(v2, v4)) | (v4 = v3) | (v2 = v3) | (v2 = v4))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(875,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v2, v4)) | (~r(v2, v3))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.40/0.58 tff(876,plain,
% 0.40/0.58 (~r(v2, v4)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[875, 168, 198, 119, 869, 39, 868])).
% 0.40/0.58 tff(877,plain,
% 0.40/0.58 (r(v0, v2)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[712, 876, 8])).
% 0.40/0.58 tff(878,plain,
% 0.40/0.58 (r(v1, v2) | r(v1, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[687, 866])).
% 0.40/0.58 tff(879,plain,
% 0.40/0.58 (r(v1, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[878, 610])).
% 0.40/0.58 tff(880,plain,
% 0.40/0.58 (r(v5, v1)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[393, 25, 879])).
% 0.40/0.58 tff(881,plain,
% 0.40/0.58 (~r(v5, v4)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[781, 168, 880, 147, 131, 603, 16])).
% 0.40/0.58 tff(882,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | r(v5, v4) | (v5 = v4) | r(v2, v4) | r(v2, v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | r(v5, v4) | (v5 = v4) | r(v2, v4) | r(v2, v5))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(883,plain,
% 0.40/0.58 ((r(v5, v4) | r(v2, v4) | r(v2, v5) | (v5 = v4) | (v2 = v4) | (v2 = v5)) <=> ((v2 = v4) | (v2 = v5) | r(v5, v4) | (v5 = v4) | r(v2, v4) | r(v2, v5))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(884,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v4) | r(v2, v4) | r(v2, v5) | (v5 = v4) | (v2 = v4) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | r(v5, v4) | (v5 = v4) | r(v2, v4) | r(v2, v5)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[883])).
% 0.40/0.58 tff(885,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v4) | r(v2, v4) | r(v2, v5) | (v5 = v4) | (v2 = v4) | (v2 = v5))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | r(v5, v4) | (v5 = v4) | r(v2, v4) | r(v2, v5))),
% 0.40/0.58 inference(transitivity,[status(thm)],[884, 882])).
% 0.40/0.58 tff(886,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v4) | r(v2, v4) | r(v2, v5) | (v5 = v4) | (v2 = v4) | (v2 = v5))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(887,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | r(v5, v4) | (v5 = v4) | r(v2, v4) | r(v2, v5)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.40/0.58 tff(888,plain,
% 0.40/0.58 (r(v2, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[887, 60, 119, 6, 881, 16, 876])).
% 0.40/0.58 tff(889,plain,
% 0.40/0.58 (~r(v4, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[804, 168, 15, 880, 147, 131, 603])).
% 0.40/0.58 tff(890,assumption,(~r(v4, v5)), introduced(assumption)).
% 0.40/0.58 tff(891,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[811, 60, 250, 88, 15, 890, 8, 289])).
% 0.40/0.58 tff(892,plain,(r(v0, v5) | r(v4, v5) | r(v0, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(893,plain,
% 0.40/0.58 (r(v0, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[892, 889, 8])).
% 0.40/0.58 tff(894,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[645, 168, 187, 88, 6, 893, 888, 877])).
% 0.40/0.58 tff(895,plain,(r(v2, v1) | r(v0, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(896,plain,
% 0.40/0.58 (r(v2, v1)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[895, 8])).
% 0.40/0.58 tff(897,plain,
% 0.40/0.58 (~r(v2, v4)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[701, 168, 119, 131, 603, 127, 896])).
% 0.40/0.58 tff(898,plain,
% 0.40/0.58 (r(v0, v2)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[712, 897, 8])).
% 0.40/0.58 tff(899,plain,
% 0.40/0.58 (r(v1, v2)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[740, 25, 896])).
% 0.40/0.58 tff(900,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v1 = v2) | (v1 = v0) | (~r(v1, v0)) | (~r(v1, v2)) | (~r(v0, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v1 = v2) | (v1 = v0) | (~r(v1, v0)) | (~r(v1, v2)) | (~r(v0, v2)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(901,plain,
% 0.40/0.58 (((~r(v0, v2)) | (~r(v1, v2)) | (~r(v1, v0)) | (v0 = v2) | (v1 = v2) | (v1 = v0)) <=> ((v0 = v2) | (v1 = v2) | (v1 = v0) | (~r(v1, v0)) | (~r(v1, v2)) | (~r(v0, v2)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(902,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v2)) | (~r(v1, v2)) | (~r(v1, v0)) | (v0 = v2) | (v1 = v2) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v1 = v2) | (v1 = v0) | (~r(v1, v0)) | (~r(v1, v2)) | (~r(v0, v2))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[901])).
% 0.40/0.58 tff(903,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v2)) | (~r(v1, v2)) | (~r(v1, v0)) | (v0 = v2) | (v1 = v2) | (v1 = v0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v1 = v2) | (v1 = v0) | (~r(v1, v0)) | (~r(v1, v2)) | (~r(v0, v2)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[902, 900])).
% 0.40/0.58 tff(904,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v2)) | (~r(v1, v2)) | (~r(v1, v0)) | (v0 = v2) | (v1 = v2) | (v1 = v0))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(905,plain,
% 0.40/0.58 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v1 = v2) | (v1 = v0) | (~r(v1, v0)) | (~r(v1, v2)) | (~r(v0, v2))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.40/0.58 tff(906,plain,
% 0.40/0.58 (~r(v1, v0)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[905, 168, 187, 126, 96, 899, 898])).
% 0.40/0.58 tff(907,plain,
% 0.40/0.58 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v1 = v2) | (~r(v0, v1)) | (~r(v1, v2)) | (~r(v0, v2)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v1 = v2) | (~r(v0, v1)) | (~r(v1, v2)) | (~r(v0, v2)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(908,plain,
% 0.40/0.59 (((~r(v1, v2)) | (~r(v0, v2)) | (~r(v0, v1)) | (v1 = v2) | (v0 = v2) | (v0 = v1)) <=> ((v0 = v1) | (v0 = v2) | (v1 = v2) | (~r(v0, v1)) | (~r(v1, v2)) | (~r(v0, v2)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(909,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v0, v2)) | (~r(v0, v1)) | (v1 = v2) | (v0 = v2) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v1 = v2) | (~r(v0, v1)) | (~r(v1, v2)) | (~r(v0, v2))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[908])).
% 0.40/0.59 tff(910,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v0, v2)) | (~r(v0, v1)) | (v1 = v2) | (v0 = v2) | (v0 = v1))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v1 = v2) | (~r(v0, v1)) | (~r(v1, v2)) | (~r(v0, v2)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[909, 907])).
% 0.40/0.59 tff(911,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v0, v2)) | (~r(v0, v1)) | (v1 = v2) | (v0 = v2) | (v0 = v1))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(912,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v1 = v2) | (~r(v0, v1)) | (~r(v1, v2)) | (~r(v0, v2))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.40/0.59 tff(913,plain,
% 0.40/0.59 (~r(v0, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[912, 168, 95, 187, 126, 899, 898])).
% 0.40/0.59 tff(914,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v4 = v1) | (~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v4 = v1) | (~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(915,plain,
% 0.40/0.59 (((~r(v4, v1)) | (~r(v3, v1)) | (~r(v3, v4)) | (v4 = v1) | (v3 = v1) | (v3 = v4)) <=> ((v3 = v4) | (v4 = v1) | (~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(916,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v3, v1)) | (~r(v3, v4)) | (v4 = v1) | (v3 = v1) | (v3 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v4 = v1) | (~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[915])).
% 0.40/0.59 tff(917,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v3, v1)) | (~r(v3, v4)) | (v4 = v1) | (v3 = v1) | (v3 = v4))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v4 = v1) | (~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[916, 914])).
% 0.40/0.59 tff(918,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v3, v1)) | (~r(v3, v4)) | (v4 = v1) | (v3 = v1) | (v3 = v4))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(919,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v4 = v1) | (~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.40/0.59 tff(920,plain,
% 0.40/0.59 ((~r(v4, v1)) | (v3 = v1) | (~r(v3, v4)) | (~r(v3, v1))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[919, 168, 38, 131])).
% 0.40/0.59 tff(921,plain,
% 0.40/0.59 ((~r(v4, v1)) | (~r(v3, v4)) | (~r(v3, v1))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[920, 72])).
% 0.40/0.59 tff(922,plain,
% 0.40/0.59 ((~r(v3, v4)) | (~r(v3, v1))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[921, 603])).
% 0.40/0.59 tff(923,plain,
% 0.40/0.59 (~r(v3, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[922, 857])).
% 0.40/0.59 tff(924,plain,
% 0.40/0.59 (r(v0, v3) | r(v0, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[825, 923])).
% 0.40/0.59 tff(925,plain,
% 0.40/0.59 (r(v0, v3)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[924, 913])).
% 0.40/0.59 tff(926,plain,
% 0.40/0.59 (r(v3, v0)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[416, 25, 925])).
% 0.40/0.59 tff(927,assumption,(r(v3, v0)), introduced(assumption)).
% 0.40/0.59 tff(928,plain,
% 0.40/0.59 (r(v5, v0)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[107, 82, 532])).
% 0.40/0.59 tff(929,plain,
% 0.40/0.59 (r(v5, v3) | r(v1, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[342, 866])).
% 0.40/0.59 tff(930,plain,
% 0.40/0.59 (r(v5, v3)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[929, 82])).
% 0.40/0.59 tff(931,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v5, v0)) | (~r(v5, v3)) | (v3 = v0) | (v5 = v0) | (v5 = v3))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v3, v0)) | (~r(v5, v0)) | (~r(v5, v3)) | (v3 = v0) | (v5 = v0) | (v5 = v3))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(932,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v5, v0)) | (~r(v5, v3)) | (v3 = v0) | (v5 = v0) | (v5 = v3))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(933,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v3, v0)) | (~r(v5, v0)) | (~r(v5, v3)) | (v3 = v0) | (v5 = v0) | (v5 = v3)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[932, 931])).
% 0.40/0.59 tff(934,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[933, 168, 231, 930, 89, 928, 353, 927])).
% 0.40/0.59 tff(935,plain,(r(v1, v5) | (~r(v3, v0)) | r(v1, v0)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(936,plain,
% 0.40/0.59 (r(v1, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[935, 926, 906])).
% 0.40/0.59 tff(937,plain,
% 0.40/0.59 (r(v5, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[393, 25, 936])).
% 0.40/0.59 tff(938,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v5, v1)) | (~r(v5, v2)) | (v2 = v1) | (v5 = v1) | (v5 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v2, v1)) | (~r(v5, v1)) | (~r(v5, v2)) | (v2 = v1) | (v5 = v1) | (v5 = v2))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(939,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v5, v1)) | (~r(v5, v2)) | (v2 = v1) | (v5 = v1) | (v5 = v2))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(940,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v2, v1)) | (~r(v5, v1)) | (~r(v5, v2)) | (v2 = v1) | (v5 = v1) | (v5 = v2)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.40/0.59 tff(941,plain,
% 0.40/0.59 (~r(v5, v2)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[940, 168, 937, 147, 127, 896, 7])).
% 0.40/0.59 tff(942,plain,
% 0.40/0.59 (~r(v5, v4)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[781, 168, 937, 147, 131, 603, 16])).
% 0.40/0.59 tff(943,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v5, v4) | (v5 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v5, v4) | (v5 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(944,plain,
% 0.40/0.59 ((r(v2, v4) | r(v5, v4) | r(v5, v2) | (v2 = v4) | (v5 = v4) | (v5 = v2)) <=> ((v2 = v4) | r(v5, v4) | (v5 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(945,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v5, v4) | r(v5, v2) | (v2 = v4) | (v5 = v4) | (v5 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v5, v4) | (v5 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2)))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[944])).
% 0.40/0.59 tff(946,plain,
% 0.40/0.59 (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v5, v4) | r(v5, v2) | (v2 = v4) | (v5 = v4) | (v5 = v2))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v5, v4) | (v5 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2))),
% 0.40/0.59 inference(transitivity,[status(thm)],[945, 943])).
% 0.40/0.59 tff(947,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v5, v4) | r(v5, v2) | (v2 = v4) | (v5 = v4) | (v5 = v2))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(948,plain,
% 0.40/0.59 ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v5, v4) | (v5 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[947, 946])).
% 0.40/0.59 tff(949,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[948, 60, 119, 942, 16, 897, 7, 941])).
% 0.40/0.59 tff(950,plain,(r(v0, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(951,plain,
% 0.40/0.59 (~r(v0, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[817, 950])).
% 0.40/0.59 tff(952,plain,
% 0.40/0.59 ((~r(v0, v3)) | (~r(v0, v4))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[590, 857])).
% 0.40/0.59 tff(953,plain,
% 0.40/0.59 (~r(v0, v3)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[952, 950])).
% 0.40/0.59 tff(954,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[924, 953, 951])).
% 0.40/0.59 % SZS output end Proof
% 0.40/0.59 % E exiting
%------------------------------------------------------------------------------