%------------------------------------------------------------------------------
% 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 : n008.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 0.21s 0.44s
% 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
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 21:11:30 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(r_type, type, (
% 0.21/0.44 r: ( $i * $i ) > $o)).
% 0.21/0.44 tff(v3_type, type, (
% 0.21/0.44 v3: $i)).
% 0.21/0.44 tff(v1_type, type, (
% 0.21/0.44 v1: $i)).
% 0.21/0.44 tff(v2_type, type, (
% 0.21/0.44 v2: $i)).
% 0.21/0.44 tff(v5_type, type, (
% 0.21/0.44 v5: $i)).
% 0.21/0.44 tff(v4_type, type, (
% 0.21/0.44 v4: $i)).
% 0.21/0.44 tff(v0_type, type, (
% 0.21/0.44 v0: $i)).
% 0.21/0.44 tff(1,assumption,(~r(v1, v2)), introduced(assumption)).
% 0.21/0.44 tff(2,assumption,(r(v2, v5)), introduced(assumption)).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 ((v4 = v0) <=> (v0 = v4)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((v0 = v4) <=> (v4 = v0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[3])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 ((~(v0 = v4)) <=> (~(v4 = v0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 ((~(v0 = v4)) <=> (~(v0 = v4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(7,axiom,(~(v0 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv4')).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (~(v0 = v4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (~(v4 = v0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.21/0.44 tff(10,assumption,(~r(v2, v4)), introduced(assumption)).
% 0.21/0.44 tff(11,assumption,(~r(v0, v4)), introduced(assumption)).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 ((v2 = v0) <=> (v0 = v2)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 ((v0 = v2) <=> (v2 = v0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[12])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 ((~(v0 = v2)) <=> (~(v2 = v0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[13])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 ((~(v0 = v2)) <=> (~(v0 = v2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(16,axiom,(~(v0 = v2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv2')).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (~(v0 = v2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (~(v2 = v0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 ((v1 = v0) <=> (v0 = v1)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(20,plain,
% 0.21/0.44 ((v0 = v1) <=> (v1 = v0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[19])).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 ((~(v0 = v1)) <=> (~(v1 = v0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[20])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~(v0 = v1)) <=> (~(v0 = v1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(23,axiom,(~(v0 = v1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv1')).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (~(v0 = v1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (~(v1 = v0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.44 tff(26,assumption,(~r(v3, v0)), introduced(assumption)).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 ((v5 = v1) <=> (v1 = v5)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 ((v1 = v5) <=> (v5 = v1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[27])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 ((~(v1 = v5)) <=> (~(v5 = v1))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 ((~(v1 = v5)) <=> (~(v1 = v5))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(31,axiom,(~(v1 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv5')).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (~(v1 = v5)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (~(v5 = v1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 ((v5 = v2) <=> (v2 = v5)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 ((v2 = v5) <=> (v5 = v2)),
% 0.21/0.44 inference(symmetry,[status(thm)],[34])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 ((~(v2 = v5)) <=> (~(v5 = v2))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 ((~(v2 = v5)) <=> (~(v2 = v5))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(38,axiom,(~(v2 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v2nv5')).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (~(v2 = v5)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (~(v5 = v2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((v5 = v4) <=> (v4 = v5)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 ((v4 = v5) <=> (v5 = v4)),
% 0.21/0.44 inference(symmetry,[status(thm)],[41])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~(v4 = v5)) <=> (~(v5 = v4))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[42])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 ((~(v4 = v5)) <=> (~(v4 = v5))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(45,axiom,(~(v4 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v4nv5')).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (~(v4 = v5)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (~(v5 = v4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.21/0.44 tff(48,assumption,(~r(v3, v2)), introduced(assumption)).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 ((v3 = v2) <=> (v2 = v3)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 ((v2 = v3) <=> (v3 = v2)),
% 0.21/0.44 inference(symmetry,[status(thm)],[49])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 ((~(v2 = v3)) <=> (~(v3 = v2))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[50])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 ((~(v2 = v3)) <=> (~(v2 = v3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(53,axiom,(~(v2 = v3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v2nv3')).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (~(v2 = v3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (~(v3 = v2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.21/0.44 tff(56,assumption,(~r(v0, v2)), introduced(assumption)).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 ((v3 = v0) <=> (v0 = v3)),
% 0.21/0.44 inference(commutativity,[status(thm)],[])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 ((v0 = v3) <=> (v3 = v0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[57])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 ((~(v0 = v3)) <=> (~(v3 = v0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((~(v0 = v3)) <=> (~(v0 = v3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(61,axiom,(~(v0 = v3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv3')).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (~(v0 = v3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (~(v3 = v0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (^[Z: $i, Y: $i, X: $i] : refl((r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) <=> (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((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, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> (r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ((r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)))), rewrite(((r(X, Y) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)) <=> (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.44 tff(69,axiom,(![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rno3acl')).
% 0.21/0.44 tff(70,plain,
% 0.21/0.45 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.45 tff(72,plain,(
% 0.21/0.45 ![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.45 inference(skolemize,[status(sab)],[71])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | r(v3, v0) | (v3 = v0) | r(v0, v2) | (v3 = v2) | r(v3, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | r(v3, v0) | (v3 = v0) | r(v0, v2) | (v3 = v2) | r(v3, v2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 ((r(v3, v0) | r(v0, v2) | r(v3, v2) | (v0 = v2) | (v3 = v2) | (v3 = v0)) <=> ((v0 = v2) | r(v3, v0) | (v3 = v0) | r(v0, v2) | (v3 = v2) | r(v3, v2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v2) | r(v3, v2) | (v0 = v2) | (v3 = v2) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | r(v3, v0) | (v3 = v0) | r(v0, v2) | (v3 = v2) | r(v3, v2)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v2) | r(v3, v2) | (v0 = v2) | (v3 = v2) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | r(v3, v0) | (v3 = v0) | r(v0, v2) | (v3 = v2) | r(v3, v2))),
% 0.21/0.45 inference(transitivity,[status(thm)],[76, 74])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v2) | r(v3, v2) | (v0 = v2) | (v3 = v2) | (v3 = v0))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | r(v3, v0) | (v3 = v0) | r(v0, v2) | (v3 = v2) | r(v3, v2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[79, 73, 17, 26, 63, 56, 55, 48])).
% 0.21/0.45 tff(81,plain,(r(v0, v2) | r(v3, v0) | r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (r(v0, v2)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[81, 48, 26])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (^[Y: $i, X: $i] : refl(((~r(X, Y)) | r(Y, X)) <=> ((~r(X, Y)) | r(Y, X)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(86,axiom,(![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rsym')).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.45 tff(88,plain,(
% 0.21/0.45 ![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.45 inference(skolemize,[status(sab)],[87])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v2)) | r(v2, v0))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v2)) | r(v2, v0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v2)) | r(v2, v0))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v2)) | r(v2, v0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (r(v2, v0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[92, 89, 82])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 ((v2 = v1) <=> (v1 = v2)),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 ((v1 = v2) <=> (v2 = v1)),
% 0.21/0.45 inference(symmetry,[status(thm)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 ((~(v1 = v2)) <=> (~(v2 = v1))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 ((~(v1 = v2)) <=> (~(v1 = v2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(98,axiom,(~(v1 = v2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv2')).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (~(v1 = v2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (~(v2 = v1)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.21/0.45 tff(101,assumption,(r(v2, v3)), introduced(assumption)).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v3)) | r(v3, v2))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v3)) | r(v3, v2))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v3)) | r(v3, v2))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v3)) | r(v3, v2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[104, 89, 48, 101])).
% 0.21/0.45 tff(106,plain,((~r(v2, v3)) | r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (~r(v2, v3)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[106, 48])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 ((v4 = v2) <=> (v2 = v4)),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 ((v2 = v4) <=> (v4 = v2)),
% 0.21/0.45 inference(symmetry,[status(thm)],[108])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 ((~(v2 = v4)) <=> (~(v4 = v2))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 ((~(v2 = v4)) <=> (~(v2 = v4))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(112,axiom,(~(v2 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v2nv4')).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (~(v2 = v4)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (~(v4 = v2)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.21/0.45 tff(115,assumption,(~r(v5, v3)), introduced(assumption)).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v5)) | r(v5, v3))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v5)) | r(v5, v3))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v5)) | r(v5, v3))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v5)) | r(v5, v3)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (~r(v3, v5)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[118, 89, 115])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 ((~(v3 = v5)) <=> (~(v3 = v5))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(121,axiom,(~(v3 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v3nv5')).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (~(v3 = v5)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 ((~(v0 = v5)) <=> (~(v0 = v5))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(124,axiom,(~(v0 = v5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v0nv5')).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (~(v0 = v5)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v3 = v5) | r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v3 = v5) | r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((r(v3, v0) | r(v0, v5) | r(v3, v5) | (v0 = v5) | (v3 = v5) | (v3 = v0)) <=> ((v0 = v5) | (v3 = v5) | r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v5) | r(v3, v5) | (v0 = v5) | (v3 = v5) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v3 = v5) | r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v5) | r(v3, v5) | (v0 = v5) | (v3 = v5) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v3 = v5) | r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0))),
% 0.21/0.46 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v5) | r(v3, v5) | (v0 = v5) | (v3 = v5) | (v3 = v0))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v3 = v5) | r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (r(v3, v0) | r(v0, v5) | r(v3, v5) | (v3 = v0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[131, 73, 125, 122])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (r(v3, v0) | r(v0, v5) | r(v3, v5)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[132, 63])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (r(v0, v5)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[133, 26, 119])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v5)) | r(v5, v0))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v5)) | r(v5, v0))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v5)) | r(v5, v0))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v5)) | r(v5, v0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (r(v5, v0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[137, 89, 134])).
% 0.21/0.46 tff(139,assumption,(r(v0, v3)), introduced(assumption)).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v3)) | r(v3, v0))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v3)) | r(v3, v0))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v3)) | r(v3, v0))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v3)) | r(v3, v0)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[142, 89, 26, 139])).
% 0.21/0.46 tff(144,plain,((~r(v0, v3)) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (~r(v0, v3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[144, 26])).
% 0.21/0.46 tff(146,assumption,(~r(v3, v4)), introduced(assumption)).
% 0.21/0.46 tff(147,assumption,(~r(v0, v3)), introduced(assumption)).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ((~(v3 = v4)) <=> (~(v3 = v4))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(149,axiom,(~(v3 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v3nv4')).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (~(v3 = v4)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | r(v0, v3) | r(v0, v4) | r(v3, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | r(v0, v3) | r(v0, v4) | r(v3, v4))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 ((r(v0, v3) | r(v3, v4) | r(v0, v4) | (v3 = v4) | (v0 = v4) | (v0 = v3)) <=> ((v0 = v3) | (v0 = v4) | (v3 = v4) | r(v0, v3) | r(v0, v4) | r(v3, v4))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v3, v4) | r(v0, v4) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | r(v0, v3) | r(v0, v4) | r(v3, v4)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[152])).
% 0.30/0.46 tff(154,plain,
% 0.30/0.46 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v3, v4) | r(v0, v4) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | r(v0, v3) | r(v0, v4) | r(v3, v4))),
% 0.30/0.46 inference(transitivity,[status(thm)],[153, 151])).
% 0.30/0.46 tff(155,plain,
% 0.30/0.46 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v3, v4) | r(v0, v4) | (v3 = v4) | (v0 = v4) | (v0 = v3))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(156,plain,
% 0.30/0.46 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | r(v0, v3) | r(v0, v4) | r(v3, v4)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.30/0.46 tff(157,plain,
% 0.30/0.46 (r(v0, v4)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[156, 73, 62, 8, 150, 147, 146])).
% 0.30/0.46 tff(158,plain,
% 0.30/0.46 ((v5 = v0) <=> (v0 = v5)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(159,plain,
% 0.30/0.46 ((v0 = v5) <=> (v5 = v0)),
% 0.30/0.46 inference(symmetry,[status(thm)],[158])).
% 0.30/0.46 tff(160,plain,
% 0.30/0.46 ((~(v0 = v5)) <=> (~(v5 = v0))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[159])).
% 0.30/0.46 tff(161,plain,
% 0.30/0.46 (~(v5 = v0)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[125, 160])).
% 0.30/0.46 tff(162,assumption,(r(v5, v0)), introduced(assumption)).
% 0.30/0.46 tff(163,plain,
% 0.30/0.46 (^[Z: $i, Y: $i, X: $i] : refl(((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) <=> ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.30/0.46 inference(bind,[status(th)],[])).
% 0.30/0.46 tff(164,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(quant_intro,[status(thm)],[163])).
% 0.30/0.46 tff(165,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(166,plain,
% 0.30/0.46 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((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, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) <=> ((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> (((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(Y, Z))))), rewrite((((~r(X, Y)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y)) | (~r(Y, Z))) <=> ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.30/0.46 inference(bind,[status(th)],[])).
% 0.30/0.46 tff(167,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(quant_intro,[status(thm)],[166])).
% 0.30/0.46 tff(168,axiom,(![Z: $i, Y: $i, X: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rno3cl')).
% 0.30/0.46 tff(169,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.30/0.46 tff(170,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.30/0.46 tff(171,plain,(
% 0.30/0.46 ![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(skolemize,[status(sab)],[170])).
% 0.30/0.46 tff(172,plain,
% 0.30/0.46 (![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.30/0.46 tff(173,plain,
% 0.30/0.46 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (~r(v5, v0)) | (v5 = v0) | (~r(v5, v4)) | (~r(v0, v4)) | (v5 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (~r(v5, v0)) | (v5 = v0) | (~r(v5, v4)) | (~r(v0, v4)) | (v5 = v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(174,plain,
% 0.30/0.46 (((~r(v5, v0)) | (~r(v0, v4)) | (~r(v5, v4)) | (v0 = v4) | (v5 = v4) | (v5 = v0)) <=> ((v0 = v4) | (~r(v5, v0)) | (v5 = v0) | (~r(v5, v4)) | (~r(v0, v4)) | (v5 = v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(175,plain,
% 0.30/0.46 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v0)) | (~r(v0, v4)) | (~r(v5, v4)) | (v0 = v4) | (v5 = v4) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (~r(v5, v0)) | (v5 = v0) | (~r(v5, v4)) | (~r(v0, v4)) | (v5 = v4)))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[174])).
% 0.30/0.46 tff(176,plain,
% 0.30/0.46 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v0)) | (~r(v0, v4)) | (~r(v5, v4)) | (v0 = v4) | (v5 = v4) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (~r(v5, v0)) | (v5 = v0) | (~r(v5, v4)) | (~r(v0, v4)) | (v5 = v4))),
% 0.30/0.46 inference(transitivity,[status(thm)],[175, 173])).
% 0.30/0.46 tff(177,plain,
% 0.30/0.46 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v0)) | (~r(v0, v4)) | (~r(v5, v4)) | (v0 = v4) | (v5 = v4) | (v5 = v0))),
% 0.30/0.46 inference(quant_inst,[status(thm)],[])).
% 0.30/0.46 tff(178,plain,
% 0.30/0.46 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (~r(v5, v0)) | (v5 = v0) | (~r(v5, v4)) | (~r(v0, v4)) | (v5 = v4)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.30/0.46 tff(179,plain,
% 0.30/0.46 (~r(v5, v4)),
% 0.30/0.46 inference(unit_resolution,[status(thm)],[178, 172, 8, 162, 161, 157, 47])).
% 0.30/0.46 tff(180,plain,
% 0.30/0.46 ((v5 = v3) <=> (v3 = v5)),
% 0.30/0.46 inference(commutativity,[status(thm)],[])).
% 0.30/0.46 tff(181,plain,
% 0.30/0.46 ((v3 = v5) <=> (v5 = v3)),
% 0.30/0.46 inference(symmetry,[status(thm)],[180])).
% 0.30/0.46 tff(182,plain,
% 0.30/0.46 ((~(v3 = v5)) <=> (~(v5 = v3))),
% 0.30/0.46 inference(monotonicity,[status(thm)],[181])).
% 0.30/0.46 tff(183,plain,
% 0.30/0.46 (~(v5 = v3)),
% 0.30/0.46 inference(modus_ponens,[status(thm)],[122, 182])).
% 0.30/0.46 tff(184,plain,
% 0.30/0.46 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | r(v5, v3) | (v5 = v3) | r(v5, v4) | (v5 = v4) | r(v3, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | r(v5, v3) | (v5 = v3) | r(v5, v4) | (v5 = v4) | r(v3, v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(185,plain,
% 0.30/0.46 ((r(v5, v3) | r(v3, v4) | r(v5, v4) | (v3 = v4) | (v5 = v4) | (v5 = v3)) <=> ((v3 = v4) | r(v5, v3) | (v5 = v3) | r(v5, v4) | (v5 = v4) | r(v3, v4))),
% 0.30/0.46 inference(rewrite,[status(thm)],[])).
% 0.30/0.46 tff(186,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v3, v4) | r(v5, v4) | (v3 = v4) | (v5 = v4) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | r(v5, v3) | (v5 = v3) | r(v5, v4) | (v5 = v4) | r(v3, v4)))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[185])).
% 0.30/0.47 tff(187,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v3, v4) | r(v5, v4) | (v3 = v4) | (v5 = v4) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | r(v5, v3) | (v5 = v3) | r(v5, v4) | (v5 = v4) | r(v3, v4))),
% 0.30/0.47 inference(transitivity,[status(thm)],[186, 184])).
% 0.30/0.47 tff(188,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v3, v4) | r(v5, v4) | (v3 = v4) | (v5 = v4) | (v5 = v3))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(189,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | r(v5, v3) | (v5 = v3) | r(v5, v4) | (v5 = v4) | r(v3, v4)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.30/0.47 tff(190,plain,
% 0.30/0.47 (r(v5, v4) | (v5 = v4)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[189, 73, 150, 115, 183, 146])).
% 0.30/0.47 tff(191,plain,
% 0.30/0.47 ($false),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[190, 179, 47])).
% 0.30/0.47 tff(192,plain,(r(v3, v4) | r(v5, v3) | (~r(v5, v0)) | r(v0, v3)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47 tff(193,plain,
% 0.30/0.47 (r(v3, v4)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[192, 145, 138, 115])).
% 0.30/0.47 tff(194,assumption,(r(v0, v5)), introduced(assumption)).
% 0.30/0.47 tff(195,plain,
% 0.30/0.47 (r(v5, v0)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[137, 89, 194])).
% 0.30/0.47 tff(196,plain,
% 0.30/0.47 (r(v3, v4)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[192, 147, 195, 115])).
% 0.30/0.47 tff(197,assumption,(r(v4, v2)), introduced(assumption)).
% 0.30/0.47 tff(198,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v3 = v2) | (~r(v4, v2)) | (v4 = v2) | (~r(v3, v2)) | (~r(v3, v4)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v3 = v2) | (~r(v4, v2)) | (v4 = v2) | (~r(v3, v2)) | (~r(v3, v4)))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(199,plain,
% 0.30/0.47 (((~r(v3, v4)) | (~r(v4, v2)) | (~r(v3, v2)) | (v4 = v2) | (v3 = v2) | (v3 = v4)) <=> ((v3 = v4) | (v3 = v2) | (~r(v4, v2)) | (v4 = v2) | (~r(v3, v2)) | (~r(v3, v4)))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(200,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v4, v2)) | (~r(v3, v2)) | (v4 = v2) | (v3 = v2) | (v3 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (v3 = v2) | (~r(v4, v2)) | (v4 = v2) | (~r(v3, v2)) | (~r(v3, v4))))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[199])).
% 0.30/0.47 tff(201,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v4, v2)) | (~r(v3, v2)) | (v4 = v2) | (v3 = v2) | (v3 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v3 = v2) | (~r(v4, v2)) | (v4 = v2) | (~r(v3, v2)) | (~r(v3, v4)))),
% 0.30/0.47 inference(transitivity,[status(thm)],[200, 198])).
% 0.30/0.47 tff(202,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v4, v2)) | (~r(v3, v2)) | (v4 = v2) | (v3 = v2) | (v3 = v4))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(203,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (v3 = v2) | (~r(v4, v2)) | (v4 = v2) | (~r(v3, v2)) | (~r(v3, v4))),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.30/0.47 tff(204,plain,
% 0.30/0.47 ((v4 = v2) | (~r(v3, v2))),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[203, 172, 150, 55, 197, 196])).
% 0.30/0.47 tff(205,plain,
% 0.30/0.47 (~r(v3, v2)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[204, 114])).
% 0.30/0.47 tff(206,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | r(v0, v3) | r(v0, v2) | (v3 = v2) | r(v3, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | r(v0, v3) | r(v0, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(207,plain,
% 0.30/0.47 ((r(v0, v3) | r(v3, v2) | r(v0, v2) | (v3 = v2) | (v0 = v2) | (v0 = v3)) <=> ((v0 = v2) | (v0 = v3) | r(v0, v3) | r(v0, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(208,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v3, v2) | r(v0, v2) | (v3 = v2) | (v0 = v2) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | r(v0, v3) | r(v0, v2) | (v3 = v2) | r(v3, v2)))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[207])).
% 0.30/0.47 tff(209,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v3, v2) | r(v0, v2) | (v3 = v2) | (v0 = v2) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | r(v0, v3) | r(v0, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.47 inference(transitivity,[status(thm)],[208, 206])).
% 0.30/0.47 tff(210,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v3) | r(v3, v2) | r(v0, v2) | (v3 = v2) | (v0 = v2) | (v0 = v3))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(211,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | r(v0, v3) | r(v0, v2) | (v3 = v2) | r(v3, v2)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.30/0.47 tff(212,plain,
% 0.30/0.47 (r(v0, v2)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[211, 73, 17, 62, 147, 55, 205])).
% 0.30/0.47 tff(213,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | (v5 = v3) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v5, v3) | (v5 = v3) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(214,plain,
% 0.30/0.47 ((r(v5, v3) | r(v3, v2) | r(v5, v2) | (v3 = v2) | (v5 = v2) | (v5 = v3)) <=> (r(v5, v3) | (v5 = v3) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.47 inference(rewrite,[status(thm)],[])).
% 0.30/0.47 tff(215,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v3, v2) | r(v5, v2) | (v3 = v2) | (v5 = v2) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | (v5 = v3) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2)))),
% 0.30/0.47 inference(monotonicity,[status(thm)],[214])).
% 0.30/0.47 tff(216,plain,
% 0.30/0.47 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v3, v2) | r(v5, v2) | (v3 = v2) | (v5 = v2) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v5, v3) | (v5 = v3) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.47 inference(transitivity,[status(thm)],[215, 213])).
% 0.30/0.47 tff(217,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v3) | r(v3, v2) | r(v5, v2) | (v3 = v2) | (v5 = v2) | (v5 = v3))),
% 0.30/0.47 inference(quant_inst,[status(thm)],[])).
% 0.30/0.47 tff(218,plain,
% 0.30/0.47 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v5, v3) | (v5 = v3) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2)),
% 0.30/0.47 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.30/0.47 tff(219,plain,
% 0.30/0.47 (r(v5, v2)),
% 0.30/0.47 inference(unit_resolution,[status(thm)],[218, 73, 115, 183, 40, 55, 205])).
% 0.30/0.48 tff(220,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(221,plain,
% 0.30/0.48 (((~r(v0, v5)) | (~r(v5, v2)) | (~r(v0, v2)) | (v5 = v2) | (v0 = v2) | (v0 = v5)) <=> ((v0 = v2) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(222,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v2)) | (~r(v0, v2)) | (v5 = v2) | (v0 = v2) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2)))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[221])).
% 0.30/0.48 tff(223,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v2)) | (~r(v0, v2)) | (v5 = v2) | (v0 = v2) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2))),
% 0.30/0.48 inference(transitivity,[status(thm)],[222, 220])).
% 0.30/0.48 tff(224,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v2)) | (~r(v0, v2)) | (v5 = v2) | (v0 = v2) | (v0 = v5))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(225,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.30/0.48 tff(226,plain,
% 0.30/0.48 ((~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2)) | (v5 = v2)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[225, 172, 17, 125])).
% 0.30/0.48 tff(227,plain,
% 0.30/0.48 ((~r(v0, v5)) | (~r(v0, v2)) | (~r(v5, v2))),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[226, 40])).
% 0.30/0.48 tff(228,plain,
% 0.30/0.48 ($false),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[227, 219, 212, 194])).
% 0.30/0.48 tff(229,plain,(r(v0, v3) | (~r(v0, v5)) | r(v5, v3) | (~r(v4, v2))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48 tff(230,plain,
% 0.30/0.48 (~r(v4, v2)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[229, 145, 115, 134])).
% 0.30/0.48 tff(231,assumption,(r(v3, v4)), introduced(assumption)).
% 0.30/0.48 tff(232,plain,
% 0.30/0.48 (r(v3, v2)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[79, 73, 17, 26, 63, 56, 55])).
% 0.30/0.48 tff(233,assumption,(r(v3, v2)), introduced(assumption)).
% 0.30/0.48 tff(234,assumption,(r(v2, v4)), introduced(assumption)).
% 0.30/0.48 tff(235,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v3 = v4) | (~r(v2, v4)) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v4)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v3 = v4) | (~r(v2, v4)) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v4)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(236,plain,
% 0.30/0.48 (((~r(v3, v2)) | (~r(v2, v4)) | (~r(v3, v4)) | (v2 = v4) | (v3 = v4) | (v3 = v2)) <=> ((v2 = v4) | (v3 = v4) | (~r(v2, v4)) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v4)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(237,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v4)) | (~r(v3, v4)) | (v2 = v4) | (v3 = v4) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v3 = v4) | (~r(v2, v4)) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v4))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[236])).
% 0.30/0.48 tff(238,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v4)) | (~r(v3, v4)) | (v2 = v4) | (v3 = v4) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v3 = v4) | (~r(v2, v4)) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v4)))),
% 0.30/0.48 inference(transitivity,[status(thm)],[237, 235])).
% 0.30/0.48 tff(239,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v4)) | (~r(v3, v4)) | (v2 = v4) | (v3 = v4) | (v3 = v2))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(240,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v3 = v4) | (~r(v2, v4)) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v4))),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.30/0.48 tff(241,plain,
% 0.30/0.48 ($false),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[240, 172, 113, 150, 234, 55, 233, 231])).
% 0.30/0.48 tff(242,plain,((~r(v2, v4)) | (~r(v3, v2)) | (~r(v3, v4))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48 tff(243,plain,
% 0.30/0.48 (~r(v2, v4)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[242, 232, 231])).
% 0.30/0.48 tff(244,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | (v2 = v4) | r(v2, v4) | r(v0, v2) | r(v0, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | r(v2, v4) | r(v0, v2) | r(v0, v4))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(245,plain,
% 0.30/0.48 ((r(v0, v2) | r(v2, v4) | r(v0, v4) | (v2 = v4) | (v0 = v4) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v4) | (v2 = v4) | r(v2, v4) | r(v0, v2) | r(v0, v4))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(246,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v4) | r(v0, v4) | (v2 = v4) | (v0 = v4) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | (v2 = v4) | r(v2, v4) | r(v0, v2) | r(v0, v4)))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[245])).
% 0.30/0.48 tff(247,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v4) | r(v0, v4) | (v2 = v4) | (v0 = v4) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | r(v2, v4) | r(v0, v2) | r(v0, v4))),
% 0.30/0.48 inference(transitivity,[status(thm)],[246, 244])).
% 0.30/0.48 tff(248,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v4) | r(v0, v4) | (v2 = v4) | (v0 = v4) | (v0 = v2))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(249,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | (v2 = v4) | r(v2, v4) | r(v0, v2) | r(v0, v4)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.30/0.48 tff(250,plain,
% 0.30/0.48 (r(v0, v4)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[249, 73, 17, 8, 113, 243, 56])).
% 0.30/0.48 tff(251,plain,
% 0.30/0.48 ((~r(v5, v4)) | (v5 = v4)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[178, 172, 8, 162, 161, 250])).
% 0.30/0.48 tff(252,plain,
% 0.30/0.48 (~r(v5, v4)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[251, 47])).
% 0.30/0.48 tff(253,plain,
% 0.30/0.48 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v5)) | r(v5, v4))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v5)) | r(v5, v4))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(254,plain,
% 0.30/0.48 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v5)) | r(v5, v4))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(255,plain,
% 0.30/0.48 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v5)) | r(v5, v4)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.30/0.48 tff(256,plain,
% 0.30/0.48 (~r(v4, v5)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[255, 89, 252])).
% 0.30/0.48 tff(257,plain,
% 0.30/0.48 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v4)) | r(v4, v0))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v4)) | r(v4, v0))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(258,plain,
% 0.30/0.48 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v0, v4)) | r(v4, v0))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(259,plain,
% 0.30/0.48 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v0, v4)) | r(v4, v0)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.30/0.48 tff(260,plain,
% 0.30/0.48 (r(v4, v0)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[259, 89, 250])).
% 0.30/0.48 tff(261,plain,
% 0.30/0.48 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v4)) | r(v4, v3))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v4)) | r(v4, v3))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(262,plain,
% 0.30/0.48 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v4)) | r(v4, v3))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(263,plain,
% 0.30/0.48 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v4)) | r(v4, v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.30/0.48 tff(264,plain,
% 0.30/0.48 (r(v4, v3)),
% 0.30/0.48 inference(unit_resolution,[status(thm)],[263, 89, 231])).
% 0.30/0.48 tff(265,plain,
% 0.30/0.48 ((v4 = v3) <=> (v3 = v4)),
% 0.30/0.48 inference(commutativity,[status(thm)],[])).
% 0.30/0.48 tff(266,plain,
% 0.30/0.48 ((v3 = v4) <=> (v4 = v3)),
% 0.30/0.48 inference(symmetry,[status(thm)],[265])).
% 0.30/0.48 tff(267,plain,
% 0.30/0.48 ((~(v3 = v4)) <=> (~(v4 = v3))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[266])).
% 0.30/0.48 tff(268,plain,
% 0.30/0.48 (~(v4 = v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[150, 267])).
% 0.30/0.48 tff(269,assumption,(r(v4, v3)), introduced(assumption)).
% 0.30/0.48 tff(270,assumption,(r(v1, v4)), introduced(assumption)).
% 0.30/0.48 tff(271,plain,
% 0.30/0.48 ((~(v1 = v4)) <=> (~(v1 = v4))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(272,axiom,(~(v1 = v4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv4')).
% 0.30/0.48 tff(273,plain,
% 0.30/0.48 (~(v1 = v4)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.30/0.48 tff(274,plain,
% 0.30/0.48 ((~(v1 = v3)) <=> (~(v1 = v3))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(275,axiom,(~(v1 = v3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','v1nv3')).
% 0.30/0.48 tff(276,plain,
% 0.30/0.48 (~(v1 = v3)),
% 0.30/0.48 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.30/0.48 tff(277,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v1, v4)) | (~r(v1, v3)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v1, v4)) | (~r(v1, v3)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(278,plain,
% 0.30/0.48 (((~r(v1, v4)) | (~r(v4, v3)) | (~r(v1, v3)) | (v4 = v3) | (v1 = v3) | (v1 = v4)) <=> ((v1 = v3) | (v1 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v1, v4)) | (~r(v1, v3)))),
% 0.30/0.48 inference(rewrite,[status(thm)],[])).
% 0.30/0.48 tff(279,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v3)) | (~r(v1, v3)) | (v4 = v3) | (v1 = v3) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v1, v4)) | (~r(v1, v3))))),
% 0.30/0.48 inference(monotonicity,[status(thm)],[278])).
% 0.30/0.48 tff(280,plain,
% 0.30/0.48 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v3)) | (~r(v1, v3)) | (v4 = v3) | (v1 = v3) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v1, v4)) | (~r(v1, v3)))),
% 0.30/0.48 inference(transitivity,[status(thm)],[279, 277])).
% 0.30/0.48 tff(281,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v3)) | (~r(v1, v3)) | (v4 = v3) | (v1 = v3) | (v1 = v4))),
% 0.30/0.48 inference(quant_inst,[status(thm)],[])).
% 0.30/0.48 tff(282,plain,
% 0.30/0.48 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (~r(v4, v3)) | (v4 = v3) | (~r(v1, v4)) | (~r(v1, v3))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.30/0.49 tff(283,plain,
% 0.30/0.49 ((v4 = v3) | (~r(v1, v3))),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[282, 172, 276, 273, 270, 269])).
% 0.30/0.49 tff(284,plain,
% 0.30/0.49 (~r(v1, v3)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[283, 268])).
% 0.30/0.49 tff(285,assumption,(r(v4, v0)), introduced(assumption)).
% 0.30/0.49 tff(286,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v4)) | (~r(v1, v0)) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v4)) | (~r(v1, v0)) | (v1 = v0))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(287,plain,
% 0.30/0.49 (((~r(v1, v4)) | (~r(v4, v0)) | (~r(v1, v0)) | (v4 = v0) | (v1 = v0) | (v1 = v4)) <=> ((v1 = v4) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v4)) | (~r(v1, v0)) | (v1 = v0))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(288,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v0)) | (~r(v1, v0)) | (v4 = v0) | (v1 = v0) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v4)) | (~r(v1, v0)) | (v1 = v0)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[287])).
% 0.30/0.49 tff(289,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v0)) | (~r(v1, v0)) | (v4 = v0) | (v1 = v0) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v4)) | (~r(v1, v0)) | (v1 = v0))),
% 0.30/0.49 inference(transitivity,[status(thm)],[288, 286])).
% 0.30/0.49 tff(290,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v0)) | (~r(v1, v0)) | (v4 = v0) | (v1 = v0) | (v1 = v4))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(291,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v4)) | (~r(v1, v0)) | (v1 = v0)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.30/0.49 tff(292,plain,
% 0.30/0.49 ((~r(v1, v0)) | (v1 = v0)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[291, 172, 273, 270, 285, 9])).
% 0.30/0.49 tff(293,plain,
% 0.30/0.49 (~r(v1, v0)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[292, 25])).
% 0.30/0.49 tff(294,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v0) | (v1 = v0) | r(v1, v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v0) | (v1 = v0) | r(v1, v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(295,plain,
% 0.30/0.49 ((r(v1, v0) | r(v0, v3) | r(v1, v3) | (v0 = v3) | (v1 = v3) | (v1 = v0)) <=> ((v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v0) | (v1 = v0) | r(v1, v3))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(296,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v3) | r(v1, v3) | (v0 = v3) | (v1 = v3) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v0) | (v1 = v0) | r(v1, v3)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[295])).
% 0.30/0.49 tff(297,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v3) | r(v1, v3) | (v0 = v3) | (v1 = v3) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v0) | (v1 = v0) | r(v1, v3))),
% 0.30/0.49 inference(transitivity,[status(thm)],[296, 294])).
% 0.30/0.49 tff(298,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v3) | r(v1, v3) | (v0 = v3) | (v1 = v3) | (v1 = v0))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(299,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v0) | (v1 = v0) | r(v1, v3)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.30/0.49 tff(300,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[299, 73, 62, 276, 147, 293, 25, 284])).
% 0.30/0.49 tff(301,plain,((~r(v1, v4)) | r(v0, v3) | (~r(v4, v3)) | (~r(v4, v0))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(302,plain,
% 0.30/0.49 (~r(v1, v4)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[301, 264, 145, 260])).
% 0.30/0.49 tff(303,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v1 = v5) | (v4 = v5) | r(v1, v4) | r(v4, v5) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v1 = v5) | (v4 = v5) | r(v1, v4) | r(v4, v5) | r(v1, v5))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(304,plain,
% 0.30/0.49 ((r(v1, v4) | r(v4, v5) | r(v1, v5) | (v4 = v5) | (v1 = v5) | (v1 = v4)) <=> ((v1 = v4) | (v1 = v5) | (v4 = v5) | r(v1, v4) | r(v4, v5) | r(v1, v5))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(305,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v5) | r(v1, v5) | (v4 = v5) | (v1 = v5) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v1 = v5) | (v4 = v5) | r(v1, v4) | r(v4, v5) | r(v1, v5)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[304])).
% 0.30/0.49 tff(306,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v5) | r(v1, v5) | (v4 = v5) | (v1 = v5) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v1 = v5) | (v4 = v5) | r(v1, v4) | r(v4, v5) | r(v1, v5))),
% 0.30/0.49 inference(transitivity,[status(thm)],[305, 303])).
% 0.30/0.49 tff(307,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v5) | r(v1, v5) | (v4 = v5) | (v1 = v5) | (v1 = v4))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(308,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v1 = v5) | (v4 = v5) | r(v1, v4) | r(v4, v5) | r(v1, v5)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.30/0.49 tff(309,plain,
% 0.30/0.49 (r(v1, v5)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[308, 73, 273, 32, 46, 302, 256])).
% 0.30/0.49 tff(310,assumption,(~r(v4, v2)), introduced(assumption)).
% 0.30/0.49 tff(311,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v4) | r(v1, v4) | r(v4, v2) | (v4 = v2) | r(v1, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v4) | r(v1, v4) | r(v4, v2) | (v4 = v2) | r(v1, v2))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(312,plain,
% 0.30/0.49 ((r(v1, v4) | r(v4, v2) | r(v1, v2) | (v4 = v2) | (v1 = v2) | (v1 = v4)) <=> ((v1 = v2) | (v1 = v4) | r(v1, v4) | r(v4, v2) | (v4 = v2) | r(v1, v2))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(313,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v2) | r(v1, v2) | (v4 = v2) | (v1 = v2) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v4) | r(v1, v4) | r(v4, v2) | (v4 = v2) | r(v1, v2)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[312])).
% 0.30/0.49 tff(314,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v2) | r(v1, v2) | (v4 = v2) | (v1 = v2) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v4) | r(v1, v4) | r(v4, v2) | (v4 = v2) | r(v1, v2))),
% 0.30/0.49 inference(transitivity,[status(thm)],[313, 311])).
% 0.30/0.49 tff(315,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v2) | r(v1, v2) | (v4 = v2) | (v1 = v2) | (v1 = v4))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(316,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v4) | r(v1, v4) | r(v4, v2) | (v4 = v2) | r(v1, v2)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.30/0.49 tff(317,plain,
% 0.30/0.49 (r(v1, v2)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[316, 73, 99, 273, 302, 310, 114])).
% 0.30/0.49 tff(318,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (v4 = v5) | r(v2, v4) | r(v4, v5) | r(v2, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | r(v2, v4) | r(v4, v5) | r(v2, v5))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(319,plain,
% 0.30/0.49 ((r(v2, v4) | r(v4, v5) | r(v2, v5) | (v4 = v5) | (v2 = v5) | (v2 = v4)) <=> ((v2 = v4) | (v2 = v5) | (v4 = v5) | r(v2, v4) | r(v4, v5) | r(v2, v5))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(320,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v4, v5) | r(v2, v5) | (v4 = v5) | (v2 = v5) | (v2 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (v4 = v5) | r(v2, v4) | r(v4, v5) | r(v2, v5)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[319])).
% 0.30/0.49 tff(321,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v4, v5) | r(v2, v5) | (v4 = v5) | (v2 = v5) | (v2 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | r(v2, v4) | r(v4, v5) | r(v2, v5))),
% 0.30/0.49 inference(transitivity,[status(thm)],[320, 318])).
% 0.30/0.49 tff(322,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v4, v5) | r(v2, v5) | (v4 = v5) | (v2 = v5) | (v2 = v4))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(323,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | r(v2, v4) | r(v4, v5) | r(v2, v5)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.30/0.49 tff(324,plain,
% 0.30/0.49 (r(v2, v5)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[323, 73, 113, 39, 46, 243, 256])).
% 0.30/0.49 tff(325,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v5) | (v2 = v5) | (~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | (v2 = v5) | (~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(326,plain,
% 0.30/0.49 (((~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)) | (v2 = v5) | (v1 = v5) | (v1 = v2)) <=> ((v1 = v2) | (v1 = v5) | (v2 = v5) | (~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(327,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)) | (v2 = v5) | (v1 = v5) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v5) | (v2 = v5) | (~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5))))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[326])).
% 0.30/0.49 tff(328,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)) | (v2 = v5) | (v1 = v5) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | (v2 = v5) | (~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)))),
% 0.30/0.49 inference(transitivity,[status(thm)],[327, 325])).
% 0.30/0.49 tff(329,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5)) | (v2 = v5) | (v1 = v5) | (v1 = v2))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(330,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | (v2 = v5) | (~r(v1, v2)) | (~r(v2, v5)) | (~r(v1, v5))),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.30/0.49 tff(331,plain,
% 0.30/0.49 ($false),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[330, 172, 99, 32, 39, 324, 317, 309])).
% 0.30/0.49 tff(332,plain,(r(v0, v2) | r(v4, v2) | (~r(v3, v4)) | (~r(v5, v0)) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49 tff(333,plain,
% 0.30/0.49 (r(v0, v2)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[332, 230, 193, 138, 26])).
% 0.30/0.49 tff(334,plain,
% 0.30/0.49 (~r(v5, v2)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[227, 333, 134])).
% 0.30/0.49 tff(335,plain,
% 0.30/0.49 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v5)) | r(v5, v2))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v5)) | r(v5, v2))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(336,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v5)) | r(v5, v2))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(337,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v5)) | r(v5, v2)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.30/0.49 tff(338,plain,
% 0.30/0.49 (~r(v2, v5)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[337, 89, 334])).
% 0.30/0.49 tff(339,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v4 = v5) | r(v4, v2) | r(v4, v5) | (v4 = v2) | r(v2, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v4 = v5) | r(v4, v2) | r(v4, v5) | (v4 = v2) | r(v2, v5))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(340,plain,
% 0.30/0.49 ((r(v4, v2) | r(v2, v5) | r(v4, v5) | (v2 = v5) | (v4 = v5) | (v4 = v2)) <=> ((v2 = v5) | (v4 = v5) | r(v4, v2) | r(v4, v5) | (v4 = v2) | r(v2, v5))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(341,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | r(v2, v5) | r(v4, v5) | (v2 = v5) | (v4 = v5) | (v4 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v4 = v5) | r(v4, v2) | r(v4, v5) | (v4 = v2) | r(v2, v5)))),
% 0.30/0.49 inference(monotonicity,[status(thm)],[340])).
% 0.30/0.49 tff(342,plain,
% 0.30/0.49 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | r(v2, v5) | r(v4, v5) | (v2 = v5) | (v4 = v5) | (v4 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v4 = v5) | r(v4, v2) | r(v4, v5) | (v4 = v2) | r(v2, v5))),
% 0.30/0.49 inference(transitivity,[status(thm)],[341, 339])).
% 0.30/0.49 tff(343,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v2) | r(v2, v5) | r(v4, v5) | (v2 = v5) | (v4 = v5) | (v4 = v2))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.49 tff(344,plain,
% 0.30/0.49 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v4 = v5) | r(v4, v2) | r(v4, v5) | (v4 = v2) | r(v2, v5)),
% 0.30/0.49 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.30/0.49 tff(345,plain,
% 0.30/0.49 (r(v4, v5) | (v4 = v2)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[344, 73, 39, 46, 230, 338])).
% 0.30/0.49 tff(346,plain,
% 0.30/0.49 (r(v4, v5)),
% 0.30/0.49 inference(unit_resolution,[status(thm)],[345, 114])).
% 0.30/0.49 tff(347,plain,
% 0.30/0.49 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v4)) | r(v4, v2))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v4)) | r(v4, v2))),
% 0.30/0.49 inference(rewrite,[status(thm)],[])).
% 0.30/0.49 tff(348,plain,
% 0.30/0.49 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v4)) | r(v4, v2))),
% 0.30/0.49 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(349,plain,
% 0.30/0.50 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v4)) | r(v4, v2)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.30/0.50 tff(350,plain,
% 0.30/0.50 (~r(v2, v4)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[349, 89, 230])).
% 0.30/0.50 tff(351,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v5) | r(v3, v5) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | r(v3, v5) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(352,plain,
% 0.30/0.50 ((r(v3, v5) | r(v5, v2) | r(v3, v2) | (v5 = v2) | (v3 = v2) | (v3 = v5)) <=> ((v3 = v5) | r(v3, v5) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(353,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v5) | r(v5, v2) | r(v3, v2) | (v5 = v2) | (v3 = v2) | (v3 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v5) | r(v3, v5) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2)))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[352])).
% 0.30/0.50 tff(354,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v5) | r(v5, v2) | r(v3, v2) | (v5 = v2) | (v3 = v2) | (v3 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | r(v3, v5) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2))),
% 0.30/0.50 inference(transitivity,[status(thm)],[353, 351])).
% 0.30/0.50 tff(355,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v5) | r(v5, v2) | r(v3, v2) | (v5 = v2) | (v3 = v2) | (v3 = v5))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(356,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | r(v3, v5) | (v5 = v2) | r(v5, v2) | (v3 = v2) | r(v3, v2)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.30/0.50 tff(357,plain,
% 0.30/0.50 (r(v3, v2)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[356, 73, 122, 119, 334, 40, 55])).
% 0.30/0.50 tff(358,plain,
% 0.30/0.50 ((v3 = v1) <=> (v1 = v3)),
% 0.30/0.50 inference(commutativity,[status(thm)],[])).
% 0.30/0.50 tff(359,plain,
% 0.30/0.50 ((v1 = v3) <=> (v3 = v1)),
% 0.30/0.50 inference(symmetry,[status(thm)],[358])).
% 0.30/0.50 tff(360,plain,
% 0.30/0.50 ((~(v1 = v3)) <=> (~(v3 = v1))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[359])).
% 0.30/0.50 tff(361,plain,
% 0.30/0.50 (~(v3 = v1)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[276, 360])).
% 0.30/0.50 tff(362,assumption,(r(v0, v2)), introduced(assumption)).
% 0.30/0.50 tff(363,assumption,(r(v2, v1)), introduced(assumption)).
% 0.30/0.50 tff(364,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v2)) | (~r(v0, v1)) | (~r(v2, v1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v2)) | (~r(v0, v1)) | (~r(v2, v1)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(365,plain,
% 0.30/0.50 (((~r(v0, v2)) | (~r(v2, v1)) | (~r(v0, v1)) | (v2 = v1) | (v0 = v1) | (v0 = v2)) <=> ((v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v2)) | (~r(v0, v1)) | (~r(v2, v1)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(366,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v2)) | (~r(v2, v1)) | (~r(v0, v1)) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v2)) | (~r(v0, v1)) | (~r(v2, v1))))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[365])).
% 0.30/0.50 tff(367,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v2)) | (~r(v2, v1)) | (~r(v0, v1)) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v2)) | (~r(v0, v1)) | (~r(v2, v1)))),
% 0.30/0.50 inference(transitivity,[status(thm)],[366, 364])).
% 0.30/0.50 tff(368,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v2)) | (~r(v2, v1)) | (~r(v0, v1)) | (v2 = v1) | (v0 = v1) | (v0 = v2))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(369,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | (v2 = v1) | (~r(v0, v2)) | (~r(v0, v1)) | (~r(v2, v1))),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.30/0.50 tff(370,plain,
% 0.30/0.50 (~r(v0, v1)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[369, 172, 24, 17, 363, 100, 362])).
% 0.30/0.50 tff(371,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | r(v3, v0) | (v3 = v0) | r(v0, v1) | r(v3, v1) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | r(v3, v0) | (v3 = v0) | r(v0, v1) | r(v3, v1) | (v3 = v1))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(372,plain,
% 0.30/0.50 ((r(v3, v0) | r(v0, v1) | r(v3, v1) | (v0 = v1) | (v3 = v1) | (v3 = v0)) <=> ((v0 = v1) | r(v3, v0) | (v3 = v0) | r(v0, v1) | r(v3, v1) | (v3 = v1))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(373,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v1) | r(v3, v1) | (v0 = v1) | (v3 = v1) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | r(v3, v0) | (v3 = v0) | r(v0, v1) | r(v3, v1) | (v3 = v1)))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[372])).
% 0.30/0.50 tff(374,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v1) | r(v3, v1) | (v0 = v1) | (v3 = v1) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | r(v3, v0) | (v3 = v0) | r(v0, v1) | r(v3, v1) | (v3 = v1))),
% 0.30/0.50 inference(transitivity,[status(thm)],[373, 371])).
% 0.30/0.50 tff(375,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v1) | r(v3, v1) | (v0 = v1) | (v3 = v1) | (v3 = v0))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(376,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | r(v3, v0) | (v3 = v0) | r(v0, v1) | r(v3, v1) | (v3 = v1)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.30/0.50 tff(377,plain,
% 0.30/0.50 (r(v3, v1)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[376, 73, 24, 26, 63, 370, 361])).
% 0.30/0.50 tff(378,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v1) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v1)) | (v3 = v1) | (~r(v2, v1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v1)) | (v3 = v1) | (~r(v2, v1)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(379,plain,
% 0.30/0.50 (((~r(v3, v2)) | (~r(v2, v1)) | (~r(v3, v1)) | (v2 = v1) | (v3 = v1) | (v3 = v2)) <=> ((v2 = v1) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v1)) | (v3 = v1) | (~r(v2, v1)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(380,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v1)) | (~r(v3, v1)) | (v2 = v1) | (v3 = v1) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v1) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v1)) | (v3 = v1) | (~r(v2, v1))))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[379])).
% 0.30/0.50 tff(381,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v1)) | (~r(v3, v1)) | (v2 = v1) | (v3 = v1) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v1)) | (v3 = v1) | (~r(v2, v1)))),
% 0.30/0.50 inference(transitivity,[status(thm)],[380, 378])).
% 0.30/0.50 tff(382,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v1)) | (~r(v3, v1)) | (v2 = v1) | (v3 = v1) | (v3 = v2))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(383,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | (v3 = v2) | (~r(v3, v2)) | (~r(v3, v1)) | (v3 = v1) | (~r(v2, v1))),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.30/0.50 tff(384,plain,
% 0.30/0.50 ((~r(v3, v1)) | (v3 = v1)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[383, 172, 363, 100, 55, 233])).
% 0.30/0.50 tff(385,plain,
% 0.30/0.50 ($false),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[384, 377, 361])).
% 0.30/0.50 tff(386,plain,((~r(v2, v1)) | (~r(v3, v2)) | r(v3, v0) | (~r(v0, v2))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50 tff(387,plain,
% 0.30/0.50 (~r(v2, v1)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[386, 357, 26, 333])).
% 0.30/0.50 tff(388,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v2 = v4) | r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(389,plain,
% 0.30/0.50 ((r(v2, v1) | r(v1, v4) | r(v2, v4) | (v1 = v4) | (v2 = v4) | (v2 = v1)) <=> ((v1 = v4) | (v2 = v4) | r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(390,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v1, v4) | r(v2, v4) | (v1 = v4) | (v2 = v4) | (v2 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v2 = v4) | r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4)))),
% 0.30/0.50 inference(monotonicity,[status(thm)],[389])).
% 0.30/0.50 tff(391,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v1, v4) | r(v2, v4) | (v1 = v4) | (v2 = v4) | (v2 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4))),
% 0.30/0.50 inference(transitivity,[status(thm)],[390, 388])).
% 0.30/0.50 tff(392,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | r(v1, v4) | r(v2, v4) | (v1 = v4) | (v2 = v4) | (v2 = v1))),
% 0.30/0.50 inference(quant_inst,[status(thm)],[])).
% 0.30/0.50 tff(393,plain,
% 0.30/0.50 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4)),
% 0.30/0.50 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.30/0.50 tff(394,plain,
% 0.30/0.50 (r(v2, v1) | (v2 = v1) | r(v1, v4) | r(v2, v4)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[393, 73, 273, 113])).
% 0.30/0.50 tff(395,plain,
% 0.30/0.50 (r(v2, v1) | r(v1, v4) | r(v2, v4)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[394, 100])).
% 0.30/0.50 tff(396,plain,
% 0.30/0.50 (r(v1, v4)),
% 0.30/0.50 inference(unit_resolution,[status(thm)],[395, 387, 350])).
% 0.30/0.50 tff(397,plain,
% 0.30/0.50 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v1 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v1, v4)) | (~r(v1, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v1 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v1, v4)) | (~r(v1, v5)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(398,plain,
% 0.30/0.50 (((~r(v1, v4)) | (~r(v4, v5)) | (~r(v1, v5)) | (v4 = v5) | (v1 = v5) | (v1 = v4)) <=> ((v1 = v4) | (v1 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v1, v4)) | (~r(v1, v5)))),
% 0.30/0.50 inference(rewrite,[status(thm)],[])).
% 0.30/0.50 tff(399,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v5)) | (~r(v1, v5)) | (v4 = v5) | (v1 = v5) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v1 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v1, v4)) | (~r(v1, v5))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[398])).
% 0.30/0.51 tff(400,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v5)) | (~r(v1, v5)) | (v4 = v5) | (v1 = v5) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v1 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v1, v4)) | (~r(v1, v5)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[399, 397])).
% 0.30/0.51 tff(401,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v4)) | (~r(v4, v5)) | (~r(v1, v5)) | (v4 = v5) | (v1 = v5) | (v1 = v4))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(402,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v1 = v5) | (v4 = v5) | (~r(v4, v5)) | (~r(v1, v4)) | (~r(v1, v5))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.30/0.51 tff(403,plain,
% 0.30/0.51 (~r(v1, v5)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[402, 172, 273, 32, 46, 396, 346])).
% 0.30/0.51 tff(404,plain,
% 0.30/0.51 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v2)) | r(v2, v1))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v2)) | r(v2, v1))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(405,plain,
% 0.30/0.51 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v2)) | r(v2, v1))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(406,plain,
% 0.30/0.51 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v2)) | r(v2, v1)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.30/0.51 tff(407,plain,
% 0.30/0.51 (~r(v1, v2)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[406, 89, 387])).
% 0.30/0.51 tff(408,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v5) | (v2 = v5) | r(v2, v5) | r(v1, v2) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | (v2 = v5) | r(v2, v5) | r(v1, v2) | r(v1, v5))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(409,plain,
% 0.30/0.51 ((r(v1, v2) | r(v2, v5) | r(v1, v5) | (v2 = v5) | (v1 = v5) | (v1 = v2)) <=> ((v1 = v2) | (v1 = v5) | (v2 = v5) | r(v2, v5) | r(v1, v2) | r(v1, v5))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(410,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v2) | r(v2, v5) | r(v1, v5) | (v2 = v5) | (v1 = v5) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v5) | (v2 = v5) | r(v2, v5) | r(v1, v2) | r(v1, v5)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[409])).
% 0.30/0.51 tff(411,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v2) | r(v2, v5) | r(v1, v5) | (v2 = v5) | (v1 = v5) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | (v2 = v5) | r(v2, v5) | r(v1, v2) | r(v1, v5))),
% 0.30/0.51 inference(transitivity,[status(thm)],[410, 408])).
% 0.30/0.51 tff(412,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v2) | r(v2, v5) | r(v1, v5) | (v2 = v5) | (v1 = v5) | (v1 = v2))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(413,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v5) | (v2 = v5) | r(v2, v5) | r(v1, v2) | r(v1, v5)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.30/0.51 tff(414,plain,
% 0.30/0.51 ($false),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[413, 73, 99, 32, 39, 338, 407, 403])).
% 0.30/0.51 tff(415,plain,(r(v3, v0) | r(v5, v3)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51 tff(416,plain,
% 0.30/0.51 (r(v5, v3)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[415, 26])).
% 0.30/0.51 tff(417,plain,
% 0.30/0.51 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v3)) | r(v3, v5))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v3)) | r(v3, v5))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(418,plain,
% 0.30/0.51 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v3)) | r(v3, v5))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(419,plain,
% 0.30/0.51 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v3)) | r(v3, v5)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.30/0.51 tff(420,plain,
% 0.30/0.51 (r(v3, v5)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[419, 89, 416])).
% 0.30/0.51 tff(421,assumption,(~r(v5, v0)), introduced(assumption)).
% 0.30/0.51 tff(422,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v3 = v4) | r(v3, v0) | (v3 = v0) | r(v0, v4) | r(v3, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v3 = v4) | r(v3, v0) | (v3 = v0) | r(v0, v4) | r(v3, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(423,plain,
% 0.30/0.51 ((r(v3, v0) | r(v0, v4) | r(v3, v4) | (v0 = v4) | (v3 = v4) | (v3 = v0)) <=> ((v0 = v4) | (v3 = v4) | r(v3, v0) | (v3 = v0) | r(v0, v4) | r(v3, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(424,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v4) | r(v3, v4) | (v0 = v4) | (v3 = v4) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v3 = v4) | r(v3, v0) | (v3 = v0) | r(v0, v4) | r(v3, v4)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[423])).
% 0.30/0.51 tff(425,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v4) | r(v3, v4) | (v0 = v4) | (v3 = v4) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v3 = v4) | r(v3, v0) | (v3 = v0) | r(v0, v4) | r(v3, v4))),
% 0.30/0.51 inference(transitivity,[status(thm)],[424, 422])).
% 0.30/0.51 tff(426,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v0) | r(v0, v4) | r(v3, v4) | (v0 = v4) | (v3 = v4) | (v3 = v0))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(427,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v3 = v4) | r(v3, v0) | (v3 = v0) | r(v0, v4) | r(v3, v4)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.30/0.51 tff(428,plain,
% 0.30/0.51 (r(v3, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[427, 73, 8, 150, 26, 63, 11])).
% 0.30/0.51 tff(429,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v4)) | (v5 = v4) | (~r(v3, v4)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v4)) | (v5 = v4) | (~r(v3, v4)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(430,plain,
% 0.30/0.51 (((~r(v5, v3)) | (~r(v3, v4)) | (~r(v5, v4)) | (v3 = v4) | (v5 = v4) | (v5 = v3)) <=> ((v3 = v4) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v4)) | (v5 = v4) | (~r(v3, v4)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(431,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v3, v4)) | (~r(v5, v4)) | (v3 = v4) | (v5 = v4) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v4)) | (v5 = v4) | (~r(v3, v4))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[430])).
% 0.30/0.51 tff(432,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v3, v4)) | (~r(v5, v4)) | (v3 = v4) | (v5 = v4) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v4)) | (v5 = v4) | (~r(v3, v4)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[431, 429])).
% 0.30/0.51 tff(433,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v3, v4)) | (~r(v5, v4)) | (v3 = v4) | (v5 = v4) | (v5 = v3))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(434,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v4)) | (v5 = v4) | (~r(v3, v4))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.30/0.51 tff(435,plain,
% 0.30/0.51 (~r(v5, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[434, 172, 150, 416, 183, 428, 47])).
% 0.30/0.51 tff(436,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v5 = v0) | r(v5, v0) | r(v5, v4) | (v5 = v4) | r(v0, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v5 = v0) | r(v5, v0) | r(v5, v4) | (v5 = v4) | r(v0, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(437,plain,
% 0.30/0.51 ((r(v5, v0) | r(v0, v4) | r(v5, v4) | (v0 = v4) | (v5 = v4) | (v5 = v0)) <=> ((v0 = v4) | (v5 = v0) | r(v5, v0) | r(v5, v4) | (v5 = v4) | r(v0, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(438,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v0, v4) | r(v5, v4) | (v0 = v4) | (v5 = v4) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v5 = v0) | r(v5, v0) | r(v5, v4) | (v5 = v4) | r(v0, v4)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[437])).
% 0.30/0.51 tff(439,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v0, v4) | r(v5, v4) | (v0 = v4) | (v5 = v4) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v5 = v0) | r(v5, v0) | r(v5, v4) | (v5 = v4) | r(v0, v4))),
% 0.30/0.51 inference(transitivity,[status(thm)],[438, 436])).
% 0.30/0.51 tff(440,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v0, v4) | r(v5, v4) | (v0 = v4) | (v5 = v4) | (v5 = v0))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(441,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v5 = v0) | r(v5, v0) | r(v5, v4) | (v5 = v4) | r(v0, v4)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.30/0.51 tff(442,plain,
% 0.30/0.51 (r(v5, v4) | (v5 = v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[441, 73, 8, 421, 161, 11])).
% 0.30/0.51 tff(443,plain,
% 0.30/0.51 ($false),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[442, 435, 47])).
% 0.30/0.51 tff(444,plain,(r(v0, v4) | r(v5, v0) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51 tff(445,plain,
% 0.30/0.51 (r(v0, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[444, 421, 26])).
% 0.30/0.51 tff(446,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v2 = v4) | (~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v2 = v4) | (~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(447,plain,
% 0.30/0.51 (((~r(v2, v0)) | (~r(v0, v4)) | (~r(v2, v4)) | (v0 = v4) | (v2 = v4) | (v2 = v0)) <=> ((v0 = v4) | (v2 = v4) | (~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4)))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(448,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v0)) | (~r(v0, v4)) | (~r(v2, v4)) | (v0 = v4) | (v2 = v4) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v2 = v4) | (~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4))))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[447])).
% 0.30/0.51 tff(449,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v0)) | (~r(v0, v4)) | (~r(v2, v4)) | (v0 = v4) | (v2 = v4) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v2 = v4) | (~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4)))),
% 0.30/0.51 inference(transitivity,[status(thm)],[448, 446])).
% 0.30/0.51 tff(450,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v0)) | (~r(v0, v4)) | (~r(v2, v4)) | (v0 = v4) | (v2 = v4) | (v2 = v0))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(451,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v2 = v4) | (~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4))),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.30/0.51 tff(452,plain,
% 0.30/0.51 ((~r(v2, v0)) | (~r(v2, v4)) | (v2 = v0) | (~r(v0, v4))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[451, 172, 8, 113])).
% 0.30/0.51 tff(453,plain,
% 0.30/0.51 ((~r(v2, v0)) | (~r(v2, v4)) | (~r(v0, v4))),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[452, 18])).
% 0.30/0.51 tff(454,plain,
% 0.30/0.51 (~r(v2, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[453, 445, 93])).
% 0.30/0.51 tff(455,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v3 = v4) | r(v2, v4) | (v3 = v2) | r(v3, v2) | r(v3, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v3 = v4) | r(v2, v4) | (v3 = v2) | r(v3, v2) | r(v3, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(456,plain,
% 0.30/0.51 ((r(v3, v2) | r(v2, v4) | r(v3, v4) | (v2 = v4) | (v3 = v4) | (v3 = v2)) <=> ((v2 = v4) | (v3 = v4) | r(v2, v4) | (v3 = v2) | r(v3, v2) | r(v3, v4))),
% 0.30/0.51 inference(rewrite,[status(thm)],[])).
% 0.30/0.51 tff(457,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v4) | r(v3, v4) | (v2 = v4) | (v3 = v4) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v3 = v4) | r(v2, v4) | (v3 = v2) | r(v3, v2) | r(v3, v4)))),
% 0.30/0.51 inference(monotonicity,[status(thm)],[456])).
% 0.30/0.51 tff(458,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v4) | r(v3, v4) | (v2 = v4) | (v3 = v4) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v3 = v4) | r(v2, v4) | (v3 = v2) | r(v3, v2) | r(v3, v4))),
% 0.30/0.51 inference(transitivity,[status(thm)],[457, 455])).
% 0.30/0.51 tff(459,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v4) | r(v3, v4) | (v2 = v4) | (v3 = v4) | (v3 = v2))),
% 0.30/0.51 inference(quant_inst,[status(thm)],[])).
% 0.30/0.51 tff(460,plain,
% 0.30/0.51 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v3 = v4) | r(v2, v4) | (v3 = v2) | r(v3, v2) | r(v3, v4)),
% 0.30/0.51 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.30/0.51 tff(461,plain,
% 0.30/0.51 (r(v3, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[460, 73, 113, 150, 454, 55, 48])).
% 0.30/0.51 tff(462,plain,
% 0.30/0.51 (r(v4, v3)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[263, 89, 461])).
% 0.30/0.51 tff(463,plain,
% 0.30/0.51 (r(v4, v0)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[259, 89, 445])).
% 0.30/0.51 tff(464,plain,
% 0.30/0.51 (~r(v1, v4)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[301, 463, 462, 145])).
% 0.30/0.51 tff(465,plain,
% 0.30/0.51 (r(v2, v1)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[395, 464, 454])).
% 0.30/0.51 tff(466,plain,
% 0.30/0.51 (~r(v0, v1)),
% 0.30/0.51 inference(unit_resolution,[status(thm)],[369, 172, 24, 17, 465, 100, 82])).
% 0.30/0.51 tff(467,plain,
% 0.30/0.51 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v5 = v0) | r(v5, v0) | r(v0, v1) | r(v5, v1) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v5 = v0) | r(v5, v0) | r(v0, v1) | r(v5, v1) | (v5 = v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(468,plain,
% 0.30/0.52 ((r(v5, v0) | r(v0, v1) | r(v5, v1) | (v0 = v1) | (v5 = v1) | (v5 = v0)) <=> ((v0 = v1) | (v5 = v0) | r(v5, v0) | r(v0, v1) | r(v5, v1) | (v5 = v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(469,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v0, v1) | r(v5, v1) | (v0 = v1) | (v5 = v1) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v5 = v0) | r(v5, v0) | r(v0, v1) | r(v5, v1) | (v5 = v1)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[468])).
% 0.30/0.52 tff(470,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v0, v1) | r(v5, v1) | (v0 = v1) | (v5 = v1) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v5 = v0) | r(v5, v0) | r(v0, v1) | r(v5, v1) | (v5 = v1))),
% 0.30/0.52 inference(transitivity,[status(thm)],[469, 467])).
% 0.30/0.52 tff(471,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v0) | r(v0, v1) | r(v5, v1) | (v0 = v1) | (v5 = v1) | (v5 = v0))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(472,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v5 = v0) | r(v5, v0) | r(v0, v1) | r(v5, v1) | (v5 = v1)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.30/0.52 tff(473,plain,
% 0.30/0.52 (r(v5, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[472, 73, 24, 421, 161, 33, 466])).
% 0.30/0.52 tff(474,plain,
% 0.30/0.52 (~r(v0, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[137, 89, 421])).
% 0.30/0.52 tff(475,plain,
% 0.30/0.52 (r(v3, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[133, 474, 26])).
% 0.30/0.52 tff(476,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v5) | (v4 = v5) | (~r(v3, v5)) | (~r(v4, v3)) | (v4 = v3) | (~r(v4, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | (v4 = v5) | (~r(v3, v5)) | (~r(v4, v3)) | (v4 = v3) | (~r(v4, v5)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(477,plain,
% 0.30/0.52 (((~r(v4, v3)) | (~r(v3, v5)) | (~r(v4, v5)) | (v3 = v5) | (v4 = v5) | (v4 = v3)) <=> ((v3 = v5) | (v4 = v5) | (~r(v3, v5)) | (~r(v4, v3)) | (v4 = v3) | (~r(v4, v5)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(478,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v3, v5)) | (~r(v4, v5)) | (v3 = v5) | (v4 = v5) | (v4 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v5) | (v4 = v5) | (~r(v3, v5)) | (~r(v4, v3)) | (v4 = v3) | (~r(v4, v5))))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[477])).
% 0.30/0.52 tff(479,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v3, v5)) | (~r(v4, v5)) | (v3 = v5) | (v4 = v5) | (v4 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | (v4 = v5) | (~r(v3, v5)) | (~r(v4, v3)) | (v4 = v3) | (~r(v4, v5)))),
% 0.30/0.52 inference(transitivity,[status(thm)],[478, 476])).
% 0.30/0.52 tff(480,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v3)) | (~r(v3, v5)) | (~r(v4, v5)) | (v3 = v5) | (v4 = v5) | (v4 = v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(481,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | (v4 = v5) | (~r(v3, v5)) | (~r(v4, v3)) | (v4 = v3) | (~r(v4, v5))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.30/0.52 tff(482,plain,
% 0.30/0.52 (~r(v4, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[481, 172, 122, 46, 475, 462, 268])).
% 0.30/0.52 tff(483,plain,
% 0.30/0.52 (r(v2, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[323, 73, 113, 39, 46, 454, 482])).
% 0.30/0.52 tff(484,plain,
% 0.30/0.52 (r(v5, v2)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[337, 89, 483])).
% 0.30/0.52 tff(485,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v1) | (~r(v5, v2)) | (v5 = v2) | (~r(v2, v1)) | (~r(v5, v1)) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | (~r(v5, v2)) | (v5 = v2) | (~r(v2, v1)) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(486,plain,
% 0.30/0.52 (((~r(v5, v2)) | (~r(v2, v1)) | (~r(v5, v1)) | (v2 = v1) | (v5 = v1) | (v5 = v2)) <=> ((v2 = v1) | (~r(v5, v2)) | (v5 = v2) | (~r(v2, v1)) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(487,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v1)) | (~r(v5, v1)) | (v2 = v1) | (v5 = v1) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v1) | (~r(v5, v2)) | (v5 = v2) | (~r(v2, v1)) | (~r(v5, v1)) | (v5 = v1)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[486])).
% 0.30/0.52 tff(488,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v1)) | (~r(v5, v1)) | (v2 = v1) | (v5 = v1) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | (~r(v5, v2)) | (v5 = v2) | (~r(v2, v1)) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.52 inference(transitivity,[status(thm)],[487, 485])).
% 0.30/0.52 tff(489,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v1)) | (~r(v5, v1)) | (v2 = v1) | (v5 = v1) | (v5 = v2))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(490,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v1) | (~r(v5, v2)) | (v5 = v2) | (~r(v2, v1)) | (~r(v5, v1)) | (v5 = v1)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.30/0.52 tff(491,plain,
% 0.30/0.52 ((~r(v5, v1)) | (v5 = v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[490, 172, 465, 100, 484, 40])).
% 0.30/0.52 tff(492,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[491, 473, 33])).
% 0.30/0.52 tff(493,plain,(r(v5, v0) | r(v3, v0) | r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(494,plain,
% 0.30/0.52 (r(v5, v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[493, 48, 26])).
% 0.30/0.52 tff(495,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(496,plain,
% 0.30/0.52 (((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v2 = v0) | (v5 = v0) | (v5 = v2)) <=> ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(497,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v2 = v0) | (v5 = v0) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[496])).
% 0.30/0.52 tff(498,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v2 = v0) | (v5 = v0) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0))),
% 0.30/0.52 inference(transitivity,[status(thm)],[497, 495])).
% 0.30/0.52 tff(499,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v2 = v0) | (v5 = v0) | (v5 = v2))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(500,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.30/0.52 tff(501,plain,
% 0.30/0.52 ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0)) | (v5 = v2) | (v2 = v0) | (v5 = v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[500, 172])).
% 0.30/0.52 tff(502,plain,
% 0.30/0.52 ((~r(v5, v2)) | (~r(v2, v0)) | (~r(v5, v0))),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[501, 40, 18, 161])).
% 0.30/0.52 tff(503,plain,
% 0.30/0.52 (~r(v5, v2)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[502, 494, 93])).
% 0.30/0.52 tff(504,plain,
% 0.30/0.52 (~r(v2, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[337, 89, 503])).
% 0.30/0.52 tff(505,assumption,(~r(v2, v3)), introduced(assumption)).
% 0.30/0.52 tff(506,assumption,(~r(v2, v1)), introduced(assumption)).
% 0.30/0.52 tff(507,assumption,(~r(v3, v1)), introduced(assumption)).
% 0.30/0.52 tff(508,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | r(v2, v1) | (v2 = v1) | r(v2, v3) | r(v3, v1) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | r(v2, v1) | (v2 = v1) | r(v2, v3) | r(v3, v1) | (v3 = v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(509,plain,
% 0.30/0.52 ((r(v2, v3) | r(v3, v1) | r(v2, v1) | (v3 = v1) | (v2 = v1) | (v2 = v3)) <=> ((v2 = v3) | r(v2, v1) | (v2 = v1) | r(v2, v3) | r(v3, v1) | (v3 = v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(510,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v3) | r(v3, v1) | r(v2, v1) | (v3 = v1) | (v2 = v1) | (v2 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | r(v2, v1) | (v2 = v1) | r(v2, v3) | r(v3, v1) | (v3 = v1)))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[509])).
% 0.30/0.52 tff(511,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v3) | r(v3, v1) | r(v2, v1) | (v3 = v1) | (v2 = v1) | (v2 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | r(v2, v1) | (v2 = v1) | r(v2, v3) | r(v3, v1) | (v3 = v1))),
% 0.30/0.52 inference(transitivity,[status(thm)],[510, 508])).
% 0.30/0.52 tff(512,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v3) | r(v3, v1) | r(v2, v1) | (v3 = v1) | (v2 = v1) | (v2 = v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(513,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | r(v2, v1) | (v2 = v1) | r(v2, v3) | r(v3, v1) | (v3 = v1)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.30/0.52 tff(514,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[513, 73, 54, 506, 100, 507, 361, 505])).
% 0.30/0.52 tff(515,plain,(r(v3, v1) | r(v2, v1) | r(v2, v3)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(516,plain,
% 0.30/0.52 (r(v3, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[515, 506, 505])).
% 0.30/0.52 tff(517,plain,
% 0.30/0.52 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v1)) | r(v1, v3))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v1)) | r(v1, v3))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(518,plain,
% 0.30/0.52 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v1)) | r(v1, v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(519,plain,
% 0.30/0.52 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v1)) | r(v1, v3)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.30/0.52 tff(520,plain,
% 0.30/0.52 (r(v1, v3)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[519, 89, 516])).
% 0.30/0.52 tff(521,assumption,(r(v3, v5)), introduced(assumption)).
% 0.30/0.52 tff(522,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v1, v3)) | (~r(v1, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v1, v3)) | (~r(v1, v5)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(523,plain,
% 0.30/0.52 (((~r(v1, v3)) | (~r(v3, v5)) | (~r(v1, v5)) | (v3 = v5) | (v1 = v5) | (v1 = v3)) <=> ((v1 = v3) | (v1 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v1, v3)) | (~r(v1, v5)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(524,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v5)) | (~r(v1, v5)) | (v3 = v5) | (v1 = v5) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v1, v3)) | (~r(v1, v5))))),
% 0.30/0.52 inference(monotonicity,[status(thm)],[523])).
% 0.30/0.52 tff(525,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v5)) | (~r(v1, v5)) | (v3 = v5) | (v1 = v5) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v1, v3)) | (~r(v1, v5)))),
% 0.30/0.52 inference(transitivity,[status(thm)],[524, 522])).
% 0.30/0.52 tff(526,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v5)) | (~r(v1, v5)) | (v3 = v5) | (v1 = v5) | (v1 = v3))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(527,plain,
% 0.30/0.52 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v1, v3)) | (~r(v1, v5))),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.30/0.52 tff(528,plain,
% 0.30/0.52 (~r(v1, v5)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[527, 172, 276, 32, 122, 521, 520])).
% 0.30/0.52 tff(529,plain,
% 0.30/0.52 (~r(v1, v2)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[406, 89, 506])).
% 0.30/0.52 tff(530,assumption,(~r(v2, v5)), introduced(assumption)).
% 0.30/0.52 tff(531,plain,
% 0.30/0.52 ($false),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[413, 73, 99, 32, 39, 530, 529, 528])).
% 0.30/0.52 tff(532,plain,(r(v2, v1) | r(v2, v5) | (~r(v3, v5)) | r(v2, v3)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52 tff(533,plain,
% 0.30/0.52 (r(v2, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[532, 504, 420, 107])).
% 0.30/0.52 tff(534,plain,
% 0.30/0.52 (~r(v0, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[369, 172, 24, 17, 533, 100, 82])).
% 0.30/0.52 tff(535,plain,
% 0.30/0.52 (r(v3, v1)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[376, 73, 24, 26, 63, 361, 534])).
% 0.30/0.52 tff(536,plain,
% 0.30/0.52 (r(v1, v3)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[519, 89, 535])).
% 0.30/0.52 tff(537,plain,
% 0.30/0.52 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v0)) | r(v0, v1))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v0)) | r(v0, v1))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.52 tff(538,plain,
% 0.30/0.52 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v0)) | r(v0, v1))),
% 0.30/0.52 inference(quant_inst,[status(thm)],[])).
% 0.30/0.52 tff(539,plain,
% 0.30/0.52 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v0)) | r(v0, v1)),
% 0.30/0.52 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.30/0.52 tff(540,plain,
% 0.30/0.52 (~r(v1, v0)),
% 0.30/0.52 inference(unit_resolution,[status(thm)],[539, 89, 534])).
% 0.30/0.52 tff(541,assumption,(r(v1, v3)), introduced(assumption)).
% 0.30/0.52 tff(542,plain,
% 0.30/0.52 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)))),
% 0.30/0.52 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(543,plain,
% 0.30/0.53 (((~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)) | (v3 = v4) | (v1 = v4) | (v1 = v3)) <=> ((v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(544,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)) | (v3 = v4) | (v1 = v4) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[543])).
% 0.30/0.53 tff(545,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)) | (v3 = v4) | (v1 = v4) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3)))),
% 0.30/0.53 inference(transitivity,[status(thm)],[544, 542])).
% 0.30/0.53 tff(546,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v4)) | (~r(v1, v4)) | (v3 = v4) | (v1 = v4) | (v1 = v3))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(547,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | (v3 = v4) | (~r(v3, v4)) | (~r(v1, v4)) | (~r(v1, v3))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.30/0.53 tff(548,plain,
% 0.30/0.53 (~r(v1, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[547, 172, 276, 273, 150, 428, 541])).
% 0.30/0.53 tff(549,assumption,(~r(v1, v0)), introduced(assumption)).
% 0.30/0.53 tff(550,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v1, v0) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v1, v0) | (v1 = v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(551,plain,
% 0.30/0.53 ((r(v1, v0) | r(v0, v4) | r(v1, v4) | (v0 = v4) | (v1 = v4) | (v1 = v0)) <=> ((v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v1, v0) | (v1 = v0))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(552,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v4) | r(v1, v4) | (v0 = v4) | (v1 = v4) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v1, v0) | (v1 = v0)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[551])).
% 0.30/0.53 tff(553,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v4) | r(v1, v4) | (v0 = v4) | (v1 = v4) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v1, v0) | (v1 = v0))),
% 0.30/0.53 inference(transitivity,[status(thm)],[552, 550])).
% 0.30/0.53 tff(554,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v4) | r(v1, v4) | (v0 = v4) | (v1 = v4) | (v1 = v0))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(555,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v1 = v4) | r(v1, v4) | r(v0, v4) | r(v1, v0) | (v1 = v0)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.30/0.53 tff(556,plain,
% 0.30/0.53 (r(v1, v4) | (v1 = v0)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[555, 73, 8, 273, 11, 549])).
% 0.30/0.53 tff(557,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[556, 548, 25])).
% 0.30/0.53 tff(558,plain,(r(v0, v4) | r(v1, v0) | (~r(v1, v3)) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(559,plain,
% 0.30/0.53 (r(v0, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[558, 540, 536, 26])).
% 0.30/0.53 tff(560,plain,
% 0.30/0.53 (~r(v2, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[453, 559, 93])).
% 0.30/0.53 tff(561,plain,
% 0.30/0.53 (r(v3, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[460, 73, 113, 150, 560, 55, 48])).
% 0.30/0.53 tff(562,plain,
% 0.30/0.53 (~r(v5, v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[434, 172, 150, 416, 183, 561, 47])).
% 0.30/0.53 tff(563,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2) | r(v5, v4) | (v5 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2) | r(v5, v4) | (v5 = v4))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(564,plain,
% 0.30/0.53 ((r(v5, v2) | r(v2, v4) | r(v5, v4) | (v2 = v4) | (v5 = v4) | (v5 = v2)) <=> ((v2 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2) | r(v5, v4) | (v5 = v4))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(565,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v2, v4) | r(v5, v4) | (v2 = v4) | (v5 = v4) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2) | r(v5, v4) | (v5 = v4)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[564])).
% 0.30/0.53 tff(566,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v2, v4) | r(v5, v4) | (v2 = v4) | (v5 = v4) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2) | r(v5, v4) | (v5 = v4))),
% 0.30/0.53 inference(transitivity,[status(thm)],[565, 563])).
% 0.30/0.53 tff(567,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v2, v4) | r(v5, v4) | (v2 = v4) | (v5 = v4) | (v5 = v2))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(568,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v2, v4) | (v5 = v2) | r(v5, v2) | r(v5, v4) | (v5 = v4)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.30/0.53 tff(569,plain,
% 0.30/0.53 (r(v5, v4) | (v5 = v4)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[568, 73, 113, 560, 503, 40])).
% 0.30/0.53 tff(570,plain,
% 0.30/0.53 ($false),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[569, 562, 47])).
% 0.30/0.53 tff(571,plain,(r(v3, v2) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53 tff(572,plain,
% 0.30/0.53 (r(v3, v2)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[571, 26])).
% 0.30/0.53 tff(573,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (v5 = v3) | (~r(v5, v2)) | (v5 = v2) | (v3 = v2) | (~r(v3, v2)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v2)) | (v5 = v2) | (v3 = v2) | (~r(v3, v2)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(574,plain,
% 0.30/0.53 (((~r(v5, v3)) | (~r(v3, v2)) | (~r(v5, v2)) | (v3 = v2) | (v5 = v2) | (v5 = v3)) <=> ((~r(v5, v3)) | (v5 = v3) | (~r(v5, v2)) | (v5 = v2) | (v3 = v2) | (~r(v3, v2)))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(575,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v3, v2)) | (~r(v5, v2)) | (v3 = v2) | (v5 = v2) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (v5 = v3) | (~r(v5, v2)) | (v5 = v2) | (v3 = v2) | (~r(v3, v2))))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[574])).
% 0.30/0.53 tff(576,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v3, v2)) | (~r(v5, v2)) | (v3 = v2) | (v5 = v2) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v2)) | (v5 = v2) | (v3 = v2) | (~r(v3, v2)))),
% 0.30/0.53 inference(transitivity,[status(thm)],[575, 573])).
% 0.30/0.53 tff(577,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v3)) | (~r(v3, v2)) | (~r(v5, v2)) | (v3 = v2) | (v5 = v2) | (v5 = v3))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(578,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v3)) | (v5 = v3) | (~r(v5, v2)) | (v5 = v2) | (v3 = v2) | (~r(v3, v2))),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.30/0.53 tff(579,plain,
% 0.30/0.53 (~r(v5, v2)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[578, 172, 416, 183, 40, 55, 572])).
% 0.30/0.53 tff(580,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | (v2 = v1) | (v5 = v2) | r(v5, v2) | r(v5, v1) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v2, v1) | (v2 = v1) | (v5 = v2) | r(v5, v2) | r(v5, v1) | (v5 = v1))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(581,plain,
% 0.30/0.53 ((r(v5, v2) | r(v2, v1) | r(v5, v1) | (v2 = v1) | (v5 = v1) | (v5 = v2)) <=> (r(v2, v1) | (v2 = v1) | (v5 = v2) | r(v5, v2) | r(v5, v1) | (v5 = v1))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(582,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v2, v1) | r(v5, v1) | (v2 = v1) | (v5 = v1) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | (v2 = v1) | (v5 = v2) | r(v5, v2) | r(v5, v1) | (v5 = v1)))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[581])).
% 0.30/0.53 tff(583,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v2, v1) | r(v5, v1) | (v2 = v1) | (v5 = v1) | (v5 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v2, v1) | (v2 = v1) | (v5 = v2) | r(v5, v2) | r(v5, v1) | (v5 = v1))),
% 0.30/0.53 inference(transitivity,[status(thm)],[582, 580])).
% 0.30/0.53 tff(584,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v2) | r(v2, v1) | r(v5, v1) | (v2 = v1) | (v5 = v1) | (v5 = v2))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(585,plain,
% 0.30/0.53 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v2, v1) | (v2 = v1) | (v5 = v2) | r(v5, v2) | r(v5, v1) | (v5 = v1)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.30/0.53 tff(586,plain,
% 0.30/0.53 (r(v5, v1) | (v5 = v1)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[585, 73, 506, 100, 579, 40])).
% 0.30/0.53 tff(587,plain,
% 0.30/0.53 (r(v5, v1)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[586, 33])).
% 0.30/0.53 tff(588,plain,
% 0.30/0.53 ((v4 = v1) <=> (v1 = v4)),
% 0.30/0.53 inference(commutativity,[status(thm)],[])).
% 0.30/0.53 tff(589,plain,
% 0.30/0.53 ((v1 = v4) <=> (v4 = v1)),
% 0.30/0.53 inference(symmetry,[status(thm)],[588])).
% 0.30/0.53 tff(590,plain,
% 0.30/0.53 ((~(v1 = v4)) <=> (~(v4 = v1))),
% 0.30/0.53 inference(monotonicity,[status(thm)],[589])).
% 0.30/0.53 tff(591,plain,
% 0.30/0.53 (~(v4 = v1)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[273, 590])).
% 0.30/0.53 tff(592,plain,
% 0.30/0.53 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v2)) | r(v2, v3))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v2)) | r(v2, v3))),
% 0.30/0.53 inference(rewrite,[status(thm)],[])).
% 0.30/0.53 tff(593,plain,
% 0.30/0.53 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v2)) | r(v2, v3))),
% 0.30/0.53 inference(quant_inst,[status(thm)],[])).
% 0.30/0.53 tff(594,plain,
% 0.30/0.53 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v2)) | r(v2, v3)),
% 0.30/0.53 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.30/0.53 tff(595,plain,
% 0.30/0.53 (r(v2, v3)),
% 0.30/0.53 inference(unit_resolution,[status(thm)],[594, 89, 572])).
% 0.30/0.53 tff(596,plain,
% 0.30/0.53 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v3)) | (~r(v2, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v3)) | (~r(v2, v5)))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(597,plain,
% 0.30/0.54 (((~r(v2, v3)) | (~r(v3, v5)) | (~r(v2, v5)) | (v3 = v5) | (v2 = v5) | (v2 = v3)) <=> ((v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v3)) | (~r(v2, v5)))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(598,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v3, v5)) | (~r(v2, v5)) | (v3 = v5) | (v2 = v5) | (v2 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v3)) | (~r(v2, v5))))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[597])).
% 0.30/0.54 tff(599,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v3, v5)) | (~r(v2, v5)) | (v3 = v5) | (v2 = v5) | (v2 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v3)) | (~r(v2, v5)))),
% 0.30/0.54 inference(transitivity,[status(thm)],[598, 596])).
% 0.30/0.54 tff(600,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v3)) | (~r(v3, v5)) | (~r(v2, v5)) | (v3 = v5) | (v2 = v5) | (v2 = v3))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(601,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v3) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v2, v3)) | (~r(v2, v5))),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.30/0.54 tff(602,plain,
% 0.30/0.54 (~r(v2, v5)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[601, 172, 54, 39, 122, 475, 595])).
% 0.30/0.54 tff(603,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v2 = v0) | (v5 = v0) | r(v2, v0) | r(v5, v0) | r(v2, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v2 = v0) | (v5 = v0) | r(v2, v0) | r(v5, v0) | r(v2, v5))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(604,plain,
% 0.30/0.54 ((r(v2, v5) | r(v5, v0) | r(v2, v0) | (v5 = v0) | (v2 = v0) | (v2 = v5)) <=> ((v2 = v5) | (v2 = v0) | (v5 = v0) | r(v2, v0) | r(v5, v0) | r(v2, v5))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(605,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v5) | r(v5, v0) | r(v2, v0) | (v5 = v0) | (v2 = v0) | (v2 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v2 = v0) | (v5 = v0) | r(v2, v0) | r(v5, v0) | r(v2, v5)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[604])).
% 0.30/0.54 tff(606,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v5) | r(v5, v0) | r(v2, v0) | (v5 = v0) | (v2 = v0) | (v2 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v2 = v0) | (v5 = v0) | r(v2, v0) | r(v5, v0) | r(v2, v5))),
% 0.30/0.54 inference(transitivity,[status(thm)],[605, 603])).
% 0.30/0.54 tff(607,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v5) | r(v5, v0) | r(v2, v0) | (v5 = v0) | (v2 = v0) | (v2 = v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(608,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v2 = v0) | (v5 = v0) | r(v2, v0) | r(v5, v0) | r(v2, v5)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.30/0.54 tff(609,plain,
% 0.30/0.54 (r(v2, v0)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[608, 73, 39, 421, 18, 161, 602])).
% 0.30/0.54 tff(610,plain,
% 0.30/0.54 (~r(v2, v4)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[453, 609, 445])).
% 0.30/0.54 tff(611,plain,
% 0.30/0.54 (r(v1, v4)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[395, 610, 506])).
% 0.30/0.54 tff(612,plain,
% 0.30/0.54 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v1, v4)) | r(v4, v1))) <=> ((~![Y: $i, X: $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(613,plain,
% 0.30/0.54 ((~![Y: $i, X: $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(614,plain,
% 0.30/0.54 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v1, v4)) | r(v4, v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.30/0.54 tff(615,plain,
% 0.30/0.54 (r(v4, v1)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[614, 89, 611])).
% 0.30/0.54 tff(616,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(617,plain,
% 0.30/0.54 (((~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1) | (v0 = v1) | (v0 = v4)) <=> ((v0 = v1) | (v0 = v4) | (~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(618,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | (~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[617])).
% 0.30/0.54 tff(619,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1))),
% 0.30/0.54 inference(transitivity,[status(thm)],[618, 616])).
% 0.30/0.54 tff(620,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1) | (v0 = v1) | (v0 = v4))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(621,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | (~r(v0, v4)) | (~r(v4, v1)) | (~r(v0, v1)) | (v4 = v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.30/0.54 tff(622,plain,
% 0.30/0.54 (~r(v0, v1)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[621, 172, 24, 8, 445, 615, 591])).
% 0.30/0.54 tff(623,plain,
% 0.30/0.54 (r(v5, v4) | (v5 = v4)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[568, 73, 113, 610, 579, 40])).
% 0.30/0.54 tff(624,plain,
% 0.30/0.54 (r(v5, v4)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[623, 47])).
% 0.30/0.54 tff(625,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (v5 = v4) | (~r(v4, v1)) | (v4 = v1) | (~r(v5, v1)) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v4)) | (v5 = v4) | (~r(v4, v1)) | (v4 = v1) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(626,plain,
% 0.30/0.54 (((~r(v5, v4)) | (~r(v4, v1)) | (~r(v5, v1)) | (v4 = v1) | (v5 = v1) | (v5 = v4)) <=> ((~r(v5, v4)) | (v5 = v4) | (~r(v4, v1)) | (v4 = v1) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(627,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (~r(v4, v1)) | (~r(v5, v1)) | (v4 = v1) | (v5 = v1) | (v5 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (v5 = v4) | (~r(v4, v1)) | (v4 = v1) | (~r(v5, v1)) | (v5 = v1)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[626])).
% 0.30/0.54 tff(628,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (~r(v4, v1)) | (~r(v5, v1)) | (v4 = v1) | (v5 = v1) | (v5 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v4)) | (v5 = v4) | (~r(v4, v1)) | (v4 = v1) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.54 inference(transitivity,[status(thm)],[627, 625])).
% 0.30/0.54 tff(629,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v5, v4)) | (~r(v4, v1)) | (~r(v5, v1)) | (v4 = v1) | (v5 = v1) | (v5 = v4))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(630,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v5, v4)) | (v5 = v4) | (~r(v4, v1)) | (v4 = v1) | (~r(v5, v1)) | (v5 = v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.30/0.54 tff(631,plain,
% 0.30/0.54 ((~r(v5, v1)) | (v5 = v1)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[630, 172, 615, 591, 624, 47])).
% 0.30/0.54 tff(632,plain,
% 0.30/0.54 (~r(v5, v1)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[631, 33])).
% 0.30/0.54 tff(633,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | r(v0, v5) | r(v0, v1) | r(v5, v1) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | r(v0, v5) | r(v0, v1) | r(v5, v1) | (v5 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(634,plain,
% 0.30/0.54 ((r(v0, v5) | r(v5, v1) | r(v0, v1) | (v5 = v1) | (v0 = v1) | (v0 = v5)) <=> ((v0 = v1) | (v0 = v5) | r(v0, v5) | r(v0, v1) | r(v5, v1) | (v5 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(635,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v5) | r(v5, v1) | r(v0, v1) | (v5 = v1) | (v0 = v1) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | r(v0, v5) | r(v0, v1) | r(v5, v1) | (v5 = v1)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[634])).
% 0.30/0.54 tff(636,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v5) | r(v5, v1) | r(v0, v1) | (v5 = v1) | (v0 = v1) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | r(v0, v5) | r(v0, v1) | r(v5, v1) | (v5 = v1))),
% 0.30/0.54 inference(transitivity,[status(thm)],[635, 633])).
% 0.30/0.54 tff(637,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v5) | r(v5, v1) | r(v0, v1) | (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 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | r(v0, v5) | r(v0, v1) | r(v5, v1) | (v5 = v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.30/0.54 tff(639,plain,
% 0.30/0.54 ($false),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[638, 73, 24, 125, 474, 632, 33, 622])).
% 0.30/0.54 tff(640,plain,(r(v5, v0) | r(v2, v1) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54 tff(641,plain,
% 0.30/0.54 (r(v5, v0)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[640, 506, 26])).
% 0.30/0.54 tff(642,plain,
% 0.30/0.54 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v0)) | r(v0, v5))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v0)) | r(v0, v5))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(643,plain,
% 0.30/0.54 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v0)) | r(v0, v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(644,plain,
% 0.30/0.54 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v0)) | r(v0, v5)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.30/0.54 tff(645,plain,
% 0.30/0.54 (r(v0, v5)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[644, 89, 641])).
% 0.30/0.54 tff(646,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v1)) | (~r(v5, v1)) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v1)) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(647,plain,
% 0.30/0.54 (((~r(v0, v5)) | (~r(v5, v1)) | (~r(v0, v1)) | (v5 = v1) | (v0 = v1) | (v0 = v5)) <=> ((v0 = v1) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v1)) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(648,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v1)) | (~r(v0, v1)) | (v5 = v1) | (v0 = v1) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v1)) | (~r(v5, v1)) | (v5 = v1)))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[647])).
% 0.30/0.54 tff(649,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v1)) | (~r(v0, v1)) | (v5 = v1) | (v0 = v1) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v1)) | (~r(v5, v1)) | (v5 = v1))),
% 0.30/0.54 inference(transitivity,[status(thm)],[648, 646])).
% 0.30/0.54 tff(650,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v1)) | (~r(v0, v1)) | (v5 = v1) | (v0 = v1) | (v0 = v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(651,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v1)) | (~r(v5, v1)) | (v5 = v1)),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.30/0.54 tff(652,plain,
% 0.30/0.54 (~r(v0, v1)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[651, 172, 24, 125, 645, 587, 33])).
% 0.30/0.54 tff(653,plain,
% 0.30/0.54 (~r(v2, v5)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[337, 89, 579])).
% 0.30/0.54 tff(654,plain,
% 0.30/0.54 (r(v1, v5)),
% 0.30/0.54 inference(unit_resolution,[status(thm)],[413, 73, 99, 32, 39, 653, 529])).
% 0.30/0.54 tff(655,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (~r(v5, v3)) | (v5 = v3) | (~r(v1, v3)) | (~r(v1, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (~r(v5, v3)) | (v5 = v3) | (~r(v1, v3)) | (~r(v1, v5)))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(656,plain,
% 0.30/0.54 (((~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)) | (v5 = v3) | (v1 = v3) | (v1 = v5)) <=> ((v1 = v3) | (v1 = v5) | (~r(v5, v3)) | (v5 = v3) | (~r(v1, v3)) | (~r(v1, v5)))),
% 0.30/0.54 inference(rewrite,[status(thm)],[])).
% 0.30/0.54 tff(657,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | (~r(v5, v3)) | (v5 = v3) | (~r(v1, v3)) | (~r(v1, v5))))),
% 0.30/0.54 inference(monotonicity,[status(thm)],[656])).
% 0.30/0.54 tff(658,plain,
% 0.30/0.54 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (~r(v5, v3)) | (v5 = v3) | (~r(v1, v3)) | (~r(v1, v5)))),
% 0.30/0.54 inference(transitivity,[status(thm)],[657, 655])).
% 0.30/0.54 tff(659,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v5)) | (~r(v5, v3)) | (~r(v1, v3)) | (v5 = v3) | (v1 = v3) | (v1 = v5))),
% 0.30/0.54 inference(quant_inst,[status(thm)],[])).
% 0.30/0.54 tff(660,plain,
% 0.30/0.54 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | (~r(v5, v3)) | (v5 = v3) | (~r(v1, v3)) | (~r(v1, v5))),
% 0.30/0.54 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.30/0.55 tff(661,plain,
% 0.30/0.55 (~r(v1, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[660, 172, 276, 32, 416, 183, 654])).
% 0.30/0.55 tff(662,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v3) | r(v0, v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v3) | r(v0, v1))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(663,plain,
% 0.30/0.55 ((r(v0, v1) | r(v1, v3) | r(v0, v3) | (v1 = v3) | (v0 = v3) | (v0 = v1)) <=> ((v0 = v1) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v3) | r(v0, v1))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(664,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v1) | r(v1, v3) | r(v0, v3) | (v1 = v3) | (v0 = v3) | (v0 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v3) | r(v0, v1)))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[663])).
% 0.30/0.55 tff(665,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v1) | r(v1, v3) | r(v0, v3) | (v1 = v3) | (v0 = v3) | (v0 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v3) | r(v0, v1))),
% 0.30/0.55 inference(transitivity,[status(thm)],[664, 662])).
% 0.30/0.55 tff(666,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v1) | r(v1, v3) | r(v0, v3) | (v1 = v3) | (v0 = v3) | (v0 = v1))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(667,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v1 = v3) | (v0 = v3) | r(v0, v3) | r(v1, v3) | r(v0, v1)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.30/0.55 tff(668,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[667, 73, 24, 62, 276, 145, 661, 652])).
% 0.30/0.55 tff(669,plain,(r(v2, v1) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(670,plain,
% 0.30/0.55 (r(v2, v1)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[669, 26])).
% 0.30/0.55 tff(671,plain,
% 0.30/0.55 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v1)) | r(v1, v2))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v1)) | r(v1, v2))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(672,plain,
% 0.30/0.55 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v1)) | r(v1, v2))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(673,plain,
% 0.30/0.55 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v1)) | r(v1, v2)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.30/0.55 tff(674,plain,
% 0.30/0.55 (r(v1, v2)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[673, 89, 670])).
% 0.30/0.55 tff(675,plain,
% 0.30/0.55 (~r(v0, v2)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[386, 670, 26, 572])).
% 0.30/0.55 tff(676,plain,
% 0.30/0.55 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v0)) | r(v0, v2))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v0)) | r(v0, v2))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(677,plain,
% 0.30/0.55 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v2, v0)) | r(v0, v2))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(678,plain,
% 0.30/0.55 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v2, v0)) | r(v0, v2)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.30/0.55 tff(679,plain,
% 0.30/0.55 (~r(v2, v0)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[678, 89, 675])).
% 0.30/0.55 tff(680,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v2 = v3) | r(v0, v3) | (v2 = v0) | r(v2, v0) | r(v2, v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v2 = v3) | r(v0, v3) | (v2 = v0) | r(v2, v0) | r(v2, v3))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(681,plain,
% 0.30/0.55 ((r(v2, v0) | r(v0, v3) | r(v2, v3) | (v0 = v3) | (v2 = v3) | (v2 = v0)) <=> ((v0 = v3) | (v2 = v3) | r(v0, v3) | (v2 = v0) | r(v2, v0) | r(v2, v3))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(682,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v3) | r(v2, v3) | (v0 = v3) | (v2 = v3) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v2 = v3) | r(v0, v3) | (v2 = v0) | r(v2, v0) | r(v2, v3)))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[681])).
% 0.30/0.55 tff(683,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v3) | r(v2, v3) | (v0 = v3) | (v2 = v3) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v2 = v3) | r(v0, v3) | (v2 = v0) | r(v2, v0) | r(v2, v3))),
% 0.30/0.55 inference(transitivity,[status(thm)],[682, 680])).
% 0.30/0.55 tff(684,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v3) | r(v2, v3) | (v0 = v3) | (v2 = v3) | (v2 = v0))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(685,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v2 = v3) | r(v0, v3) | (v2 = v0) | r(v2, v0) | r(v2, v3)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.30/0.55 tff(686,plain,
% 0.30/0.55 (r(v2, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[685, 73, 62, 54, 145, 679, 18])).
% 0.30/0.55 tff(687,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v2) | (v2 = v3) | (~r(v2, v3)) | (~r(v1, v3)) | (~r(v1, v2)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v2) | (v2 = v3) | (~r(v2, v3)) | (~r(v1, v3)) | (~r(v1, v2)))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(688,plain,
% 0.30/0.55 (((~r(v1, v2)) | (~r(v2, v3)) | (~r(v1, v3)) | (v2 = v3) | (v1 = v3) | (v1 = v2)) <=> ((v1 = v3) | (v1 = v2) | (v2 = v3) | (~r(v2, v3)) | (~r(v1, v3)) | (~r(v1, v2)))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(689,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v3)) | (~r(v1, v3)) | (v2 = v3) | (v1 = v3) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v2) | (v2 = v3) | (~r(v2, v3)) | (~r(v1, v3)) | (~r(v1, v2))))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[688])).
% 0.30/0.55 tff(690,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v3)) | (~r(v1, v3)) | (v2 = v3) | (v1 = v3) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v2) | (v2 = v3) | (~r(v2, v3)) | (~r(v1, v3)) | (~r(v1, v2)))),
% 0.30/0.55 inference(transitivity,[status(thm)],[689, 687])).
% 0.30/0.55 tff(691,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v3)) | (~r(v1, v3)) | (v2 = v3) | (v1 = v3) | (v1 = v2))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(692,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v2) | (v2 = v3) | (~r(v2, v3)) | (~r(v1, v3)) | (~r(v1, v2))),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.30/0.55 tff(693,plain,
% 0.30/0.55 (~r(v1, v3)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[692, 172, 99, 276, 54, 686, 674])).
% 0.30/0.55 tff(694,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | r(v3, v0) | (v3 = v0) | r(v1, v0) | (v1 = v0) | r(v1, v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | r(v3, v0) | (v3 = v0) | r(v1, v0) | (v1 = v0) | r(v1, v3))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(695,plain,
% 0.30/0.55 ((r(v1, v3) | r(v3, v0) | r(v1, v0) | (v3 = v0) | (v1 = v0) | (v1 = v3)) <=> ((v1 = v3) | r(v3, v0) | (v3 = v0) | r(v1, v0) | (v1 = v0) | r(v1, v3))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(696,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v3, v0) | r(v1, v0) | (v3 = v0) | (v1 = v0) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | r(v3, v0) | (v3 = v0) | r(v1, v0) | (v1 = v0) | r(v1, v3)))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[695])).
% 0.30/0.55 tff(697,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v3, v0) | r(v1, v0) | (v3 = v0) | (v1 = v0) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | r(v3, v0) | (v3 = v0) | r(v1, v0) | (v1 = v0) | r(v1, v3))),
% 0.30/0.55 inference(transitivity,[status(thm)],[696, 694])).
% 0.30/0.55 tff(698,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v3) | r(v3, v0) | r(v1, v0) | (v3 = v0) | (v1 = v0) | (v1 = v3))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(699,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | r(v3, v0) | (v3 = v0) | r(v1, v0) | (v1 = v0) | r(v1, v3)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.30/0.55 tff(700,plain,
% 0.30/0.55 (r(v1, v0)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[699, 73, 276, 26, 63, 693, 25])).
% 0.30/0.55 tff(701,assumption,(~r(v0, v5)), introduced(assumption)).
% 0.30/0.55 tff(702,plain,
% 0.30/0.55 (r(v3, v5)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[133, 701, 26])).
% 0.30/0.55 tff(703,plain,
% 0.30/0.55 (~r(v2, v5)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[601, 172, 54, 39, 122, 702, 595])).
% 0.30/0.55 tff(704,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v0, v2) | r(v2, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v0, v2) | r(v2, v5))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(705,plain,
% 0.30/0.55 ((r(v0, v2) | r(v2, v5) | r(v0, v5) | (v2 = v5) | (v0 = v5) | (v0 = v2)) <=> ((v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v0, v2) | r(v2, v5))),
% 0.30/0.55 inference(rewrite,[status(thm)],[])).
% 0.30/0.55 tff(706,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v5) | r(v0, v5) | (v2 = v5) | (v0 = v5) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v0, v2) | r(v2, v5)))),
% 0.30/0.55 inference(monotonicity,[status(thm)],[705])).
% 0.30/0.55 tff(707,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v5) | r(v0, v5) | (v2 = v5) | (v0 = v5) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v0, v2) | r(v2, v5))),
% 0.30/0.55 inference(transitivity,[status(thm)],[706, 704])).
% 0.30/0.55 tff(708,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v5) | r(v0, v5) | (v2 = v5) | (v0 = v5) | (v0 = v2))),
% 0.30/0.55 inference(quant_inst,[status(thm)],[])).
% 0.30/0.55 tff(709,plain,
% 0.30/0.55 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | (v2 = v5) | r(v0, v5) | r(v0, v2) | r(v2, v5)),
% 0.30/0.55 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.30/0.55 tff(710,plain,
% 0.30/0.55 ($false),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[709, 73, 17, 125, 39, 701, 675, 703])).
% 0.30/0.55 tff(711,plain,(r(v0, v5) | r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55 tff(712,plain,
% 0.30/0.55 (r(v0, v5)),
% 0.30/0.55 inference(unit_resolution,[status(thm)],[711, 26])).
% 0.30/0.55 tff(713,plain,
% 0.30/0.55 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v1 = v5) | (~r(v0, v5)) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | (~r(v0, v5)) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v5)))),
% 0.30/0.56 inference(rewrite,[status(thm)],[])).
% 0.30/0.56 tff(714,plain,
% 0.30/0.56 (((~r(v1, v0)) | (~r(v0, v5)) | (~r(v1, v5)) | (v0 = v5) | (v1 = v5) | (v1 = v0)) <=> ((v0 = v5) | (v1 = v5) | (~r(v0, v5)) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v5)))),
% 0.30/0.56 inference(rewrite,[status(thm)],[])).
% 0.30/0.56 tff(715,plain,
% 0.30/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v0)) | (~r(v0, v5)) | (~r(v1, v5)) | (v0 = v5) | (v1 = v5) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v1 = v5) | (~r(v0, v5)) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v5))))),
% 0.30/0.56 inference(monotonicity,[status(thm)],[714])).
% 0.30/0.56 tff(716,plain,
% 0.30/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v0)) | (~r(v0, v5)) | (~r(v1, v5)) | (v0 = v5) | (v1 = v5) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | (~r(v0, v5)) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v5)))),
% 0.30/0.56 inference(transitivity,[status(thm)],[715, 713])).
% 0.30/0.56 tff(717,plain,
% 0.30/0.56 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v0)) | (~r(v0, v5)) | (~r(v1, v5)) | (v0 = v5) | (v1 = v5) | (v1 = v0))),
% 0.30/0.56 inference(quant_inst,[status(thm)],[])).
% 0.30/0.56 tff(718,plain,
% 0.30/0.56 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | (~r(v0, v5)) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v5))),
% 0.30/0.56 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.30/0.56 tff(719,plain,
% 0.30/0.56 (~r(v1, v5)),
% 0.30/0.56 inference(unit_resolution,[status(thm)],[718, 172, 125, 32, 712, 700, 25])).
% 0.30/0.56 tff(720,plain,
% 0.30/0.56 (~r(v3, v1)),
% 0.30/0.56 inference(unit_resolution,[status(thm)],[383, 172, 670, 100, 55, 572, 361])).
% 0.30/0.56 tff(721,plain,
% 0.30/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v3 = v5) | r(v3, v5) | r(v3, v1) | (v3 = v1) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v3 = v5) | r(v3, v5) | r(v3, v1) | (v3 = v1) | r(v1, v5))),
% 0.30/0.56 inference(rewrite,[status(thm)],[])).
% 0.30/0.56 tff(722,plain,
% 0.30/0.56 ((r(v3, v1) | r(v1, v5) | r(v3, v5) | (v1 = v5) | (v3 = v5) | (v3 = v1)) <=> ((v1 = v5) | (v3 = v5) | r(v3, v5) | r(v3, v1) | (v3 = v1) | r(v1, v5))),
% 0.30/0.56 inference(rewrite,[status(thm)],[])).
% 0.30/0.56 tff(723,plain,
% 0.30/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v1) | r(v1, v5) | r(v3, v5) | (v1 = v5) | (v3 = v5) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v3 = v5) | r(v3, v5) | r(v3, v1) | (v3 = v1) | r(v1, v5)))),
% 0.30/0.56 inference(monotonicity,[status(thm)],[722])).
% 0.30/0.56 tff(724,plain,
% 0.30/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v1) | r(v1, v5) | r(v3, v5) | (v1 = v5) | (v3 = v5) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v3 = v5) | r(v3, v5) | r(v3, v1) | (v3 = v1) | r(v1, v5))),
% 0.30/0.56 inference(transitivity,[status(thm)],[723, 721])).
% 0.30/0.56 tff(725,plain,
% 0.30/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v1) | r(v1, v5) | r(v3, v5) | (v1 = v5) | (v3 = v5) | (v3 = v1))),
% 0.30/0.56 inference(quant_inst,[status(thm)],[])).
% 0.30/0.56 tff(726,plain,
% 0.30/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v3 = v5) | r(v3, v5) | r(v3, v1) | (v3 = v1) | r(v1, v5)),
% 0.30/0.56 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.30/0.56 tff(727,plain,
% 0.30/0.56 (r(v3, v5)),
% 0.30/0.56 inference(unit_resolution,[status(thm)],[726, 73, 32, 122, 720, 361, 719])).
% 0.40/0.56 tff(728,assumption,(~r(v1, v5)), introduced(assumption)).
% 0.40/0.56 tff(729,assumption,(~r(v4, v1)), introduced(assumption)).
% 0.40/0.56 tff(730,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v4 = v5) | r(v4, v5) | r(v4, v1) | (v4 = v1) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v4 = v5) | r(v4, v5) | r(v4, v1) | (v4 = v1) | r(v1, v5))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(731,plain,
% 0.40/0.56 ((r(v4, v1) | r(v1, v5) | r(v4, v5) | (v1 = v5) | (v4 = v5) | (v4 = v1)) <=> ((v1 = v5) | (v4 = v5) | r(v4, v5) | r(v4, v1) | (v4 = v1) | r(v1, v5))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(732,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v1, v5) | r(v4, v5) | (v1 = v5) | (v4 = v5) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v4 = v5) | r(v4, v5) | r(v4, v1) | (v4 = v1) | r(v1, v5)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[731])).
% 0.40/0.56 tff(733,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v1, v5) | r(v4, v5) | (v1 = v5) | (v4 = v5) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v4 = v5) | r(v4, v5) | r(v4, v1) | (v4 = v1) | r(v1, v5))),
% 0.40/0.56 inference(transitivity,[status(thm)],[732, 730])).
% 0.40/0.56 tff(734,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v1, v5) | r(v4, v5) | (v1 = v5) | (v4 = v5) | (v4 = v1))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(735,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v4 = v5) | r(v4, v5) | r(v4, v1) | (v4 = v1) | r(v1, v5)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.40/0.56 tff(736,plain,
% 0.40/0.56 (r(v4, v5)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[735, 73, 32, 46, 729, 591, 728])).
% 0.40/0.56 tff(737,assumption,(~r(v1, v3)), introduced(assumption)).
% 0.40/0.56 tff(738,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | r(v4, v3) | (v4 = v3) | r(v1, v3) | r(v4, v1) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | r(v4, v3) | (v4 = v3) | r(v1, v3) | r(v4, v1) | (v4 = v1))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(739,plain,
% 0.40/0.56 ((r(v4, v1) | r(v1, v3) | r(v4, v3) | (v1 = v3) | (v4 = v3) | (v4 = v1)) <=> ((v1 = v3) | r(v4, v3) | (v4 = v3) | r(v1, v3) | r(v4, v1) | (v4 = v1))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(740,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v1, v3) | r(v4, v3) | (v1 = v3) | (v4 = v3) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | r(v4, v3) | (v4 = v3) | r(v1, v3) | r(v4, v1) | (v4 = v1)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[739])).
% 0.40/0.56 tff(741,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v1, v3) | r(v4, v3) | (v1 = v3) | (v4 = v3) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | r(v4, v3) | (v4 = v3) | r(v1, v3) | r(v4, v1) | (v4 = v1))),
% 0.40/0.56 inference(transitivity,[status(thm)],[740, 738])).
% 0.40/0.56 tff(742,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v1) | r(v1, v3) | r(v4, v3) | (v1 = v3) | (v4 = v3) | (v4 = v1))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(743,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | r(v4, v3) | (v4 = v3) | r(v1, v3) | r(v4, v1) | (v4 = v1)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.40/0.56 tff(744,plain,
% 0.40/0.56 (r(v4, v3)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[743, 73, 276, 268, 729, 591, 737])).
% 0.40/0.56 tff(745,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[481, 172, 122, 46, 521, 744, 268, 736])).
% 0.40/0.56 tff(746,plain,(r(v4, v1) | (~r(v3, v5)) | r(v1, v5) | r(v1, v3)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(747,plain,
% 0.40/0.56 (r(v4, v1)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[746, 727, 719, 693])).
% 0.40/0.56 tff(748,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1)) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1)) | (v4 = v1))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(749,plain,
% 0.40/0.56 (((~r(v4, v1)) | (~r(v1, v0)) | (~r(v4, v0)) | (v1 = v0) | (v4 = v0) | (v4 = v1)) <=> ((~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1)) | (v4 = v1))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(750,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v1, v0)) | (~r(v4, v0)) | (v1 = v0) | (v4 = v0) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1)) | (v4 = v1)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[749])).
% 0.40/0.56 tff(751,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v1, v0)) | (~r(v4, v0)) | (v1 = v0) | (v4 = v0) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1)) | (v4 = v1))),
% 0.40/0.56 inference(transitivity,[status(thm)],[750, 748])).
% 0.40/0.56 tff(752,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v1)) | (~r(v1, v0)) | (~r(v4, v0)) | (v1 = v0) | (v4 = v0) | (v4 = v1))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(753,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1)) | (v4 = v1)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.40/0.56 tff(754,plain,
% 0.40/0.56 ((~r(v4, v0)) | (v4 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v4, v1))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[753, 172, 591])).
% 0.40/0.56 tff(755,plain,
% 0.40/0.56 ((~r(v4, v0)) | (~r(v1, v0)) | (~r(v4, v1))),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[754, 9, 25])).
% 0.40/0.56 tff(756,plain,
% 0.40/0.56 (~r(v4, v0)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[755, 747, 700])).
% 0.40/0.56 tff(757,plain,
% 0.40/0.56 (~r(v0, v4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[259, 89, 756])).
% 0.40/0.56 tff(758,plain,
% 0.40/0.56 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v1)) | r(v1, v4))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v1)) | r(v1, v4))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(759,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v1)) | r(v1, v4))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(760,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v1)) | r(v1, v4)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.40/0.56 tff(761,plain,
% 0.40/0.56 (r(v1, v4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[760, 89, 747])).
% 0.40/0.56 tff(762,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v2 = v4) | (v2 = v1) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v2, v1)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | (v2 = v1) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v2, v1)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(763,plain,
% 0.40/0.56 (((~r(v2, v1)) | (~r(v1, v4)) | (~r(v2, v4)) | (v1 = v4) | (v2 = v4) | (v2 = v1)) <=> ((v1 = v4) | (v2 = v4) | (v2 = v1) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v2, v1)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(764,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v1, v4)) | (~r(v2, v4)) | (v1 = v4) | (v2 = v4) | (v2 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v4) | (v2 = v4) | (v2 = v1) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v2, v1))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[763])).
% 0.40/0.56 tff(765,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v1, v4)) | (~r(v2, v4)) | (v1 = v4) | (v2 = v4) | (v2 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | (v2 = v1) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v2, v1)))),
% 0.40/0.56 inference(transitivity,[status(thm)],[764, 762])).
% 0.40/0.56 tff(766,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v1)) | (~r(v1, v4)) | (~r(v2, v4)) | (v1 = v4) | (v2 = v4) | (v2 = v1))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(767,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v4) | (v2 = v4) | (v2 = v1) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v2, v1))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.40/0.56 tff(768,plain,
% 0.40/0.56 (~r(v2, v4)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[767, 172, 273, 113, 670, 100, 761])).
% 0.40/0.56 tff(769,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v0, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v0, v4))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(770,plain,
% 0.40/0.56 ((r(v2, v0) | r(v0, v4) | r(v2, v4) | (v0 = v4) | (v2 = v4) | (v2 = v0)) <=> ((v0 = v4) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v0, v4))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(771,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v4) | r(v2, v4) | (v0 = v4) | (v2 = v4) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v0, v4)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[770])).
% 0.40/0.56 tff(772,plain,
% 0.40/0.56 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v4) | r(v2, v4) | (v0 = v4) | (v2 = v4) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v0, v4))),
% 0.40/0.56 inference(transitivity,[status(thm)],[771, 769])).
% 0.40/0.56 tff(773,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v4) | r(v2, v4) | (v0 = v4) | (v2 = v4) | (v2 = v0))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(774,plain,
% 0.40/0.56 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v0, v4)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.40/0.56 tff(775,plain,
% 0.40/0.56 ($false),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[774, 73, 8, 113, 768, 679, 18, 757])).
% 0.40/0.56 tff(776,plain,(r(v3, v0)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56 tff(777,plain,
% 0.40/0.56 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v0)) | r(v0, v3))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v0)) | r(v0, v3))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(778,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v3, v0)) | r(v0, v3))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(779,plain,
% 0.40/0.56 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v3, v0)) | r(v0, v3)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.40/0.57 tff(780,plain,
% 0.40/0.57 (r(v0, v3)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[779, 89, 776])).
% 0.40/0.57 tff(781,plain,
% 0.40/0.57 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v2)) | r(v2, v4))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v2)) | r(v2, v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(782,plain,
% 0.40/0.57 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v2)) | r(v2, v4))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(783,plain,
% 0.40/0.57 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v2)) | r(v2, v4)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.40/0.57 tff(784,plain,
% 0.40/0.57 (~r(v4, v2)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[783, 89, 10])).
% 0.40/0.57 tff(785,plain,
% 0.40/0.57 (r(v3, v4)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[460, 73, 113, 150, 10, 55, 48])).
% 0.40/0.57 tff(786,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v0, v3)) | (~r(v0, v4)) | (~r(v3, v4)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v0, v3)) | (~r(v0, v4)) | (~r(v3, v4)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(787,plain,
% 0.40/0.57 (((~r(v0, v3)) | (~r(v3, v4)) | (~r(v0, v4)) | (v3 = v4) | (v0 = v4) | (v0 = v3)) <=> ((v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v0, v3)) | (~r(v0, v4)) | (~r(v3, v4)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(788,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v4)) | (~r(v0, v4)) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v0, v3)) | (~r(v0, v4)) | (~r(v3, v4))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[787])).
% 0.40/0.57 tff(789,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v4)) | (~r(v0, v4)) | (v3 = v4) | (v0 = v4) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v0, v3)) | (~r(v0, v4)) | (~r(v3, v4)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[788, 786])).
% 0.40/0.57 tff(790,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v4)) | (~r(v0, v4)) | (v3 = v4) | (v0 = v4) | (v0 = v3))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(791,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v4) | (v3 = v4) | (~r(v0, v3)) | (~r(v0, v4)) | (~r(v3, v4))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.40/0.57 tff(792,plain,
% 0.40/0.57 (~r(v0, v4)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[791, 172, 62, 8, 150, 780, 785])).
% 0.40/0.57 tff(793,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | r(v0, v2) | r(v4, v2) | (v4 = v2) | r(v0, v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | r(v0, v2) | r(v4, v2) | (v4 = v2) | r(v0, v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(794,plain,
% 0.40/0.57 ((r(v0, v4) | r(v4, v2) | r(v0, v2) | (v4 = v2) | (v0 = v2) | (v0 = v4)) <=> ((v0 = v2) | (v0 = v4) | r(v0, v2) | r(v4, v2) | (v4 = v2) | r(v0, v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(795,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v4, v2) | r(v0, v2) | (v4 = v2) | (v0 = v2) | (v0 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v4) | r(v0, v2) | r(v4, v2) | (v4 = v2) | r(v0, v4)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[794])).
% 0.40/0.57 tff(796,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v4, v2) | r(v0, v2) | (v4 = v2) | (v0 = v2) | (v0 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | r(v0, v2) | r(v4, v2) | (v4 = v2) | r(v0, v4))),
% 0.40/0.57 inference(transitivity,[status(thm)],[795, 793])).
% 0.40/0.57 tff(797,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v4, v2) | r(v0, v2) | (v4 = v2) | (v0 = v2) | (v0 = v4))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(798,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v4) | r(v0, v2) | r(v4, v2) | (v4 = v2) | r(v0, v4)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.40/0.57 tff(799,plain,
% 0.40/0.57 (r(v0, v2) | (v4 = v2)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[798, 73, 17, 8, 792, 784])).
% 0.40/0.57 tff(800,plain,
% 0.40/0.57 (r(v0, v2)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[799, 114])).
% 0.40/0.57 tff(801,plain,
% 0.40/0.57 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v0)) | r(v0, v4))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v0)) | r(v0, v4))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(802,plain,
% 0.40/0.57 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v0)) | r(v0, v4))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(803,plain,
% 0.40/0.57 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v0)) | r(v0, v4)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[802, 801])).
% 0.40/0.57 tff(804,plain,
% 0.40/0.57 (~r(v4, v0)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[803, 89, 792])).
% 0.40/0.57 tff(805,plain,
% 0.40/0.57 (r(v3, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[515, 506, 107])).
% 0.40/0.57 tff(806,plain,
% 0.40/0.57 (r(v1, v4)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[395, 10, 506])).
% 0.40/0.57 tff(807,plain,
% 0.40/0.57 (r(v4, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[614, 89, 806])).
% 0.40/0.57 tff(808,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (~r(v3, v4)) | (~r(v4, v1)) | (v4 = v1) | (~r(v3, v1)) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (~r(v3, v4)) | (~r(v4, v1)) | (v4 = v1) | (~r(v3, v1)) | (v3 = v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(809,plain,
% 0.40/0.57 (((~r(v3, v4)) | (~r(v4, v1)) | (~r(v3, v1)) | (v4 = v1) | (v3 = v1) | (v3 = v4)) <=> ((v3 = v4) | (~r(v3, v4)) | (~r(v4, v1)) | (v4 = v1) | (~r(v3, v1)) | (v3 = v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(810,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v4, v1)) | (~r(v3, v1)) | (v4 = v1) | (v3 = v1) | (v3 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v4) | (~r(v3, v4)) | (~r(v4, v1)) | (v4 = v1) | (~r(v3, v1)) | (v3 = v1)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[809])).
% 0.40/0.57 tff(811,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v4, v1)) | (~r(v3, v1)) | (v4 = v1) | (v3 = v1) | (v3 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (~r(v3, v4)) | (~r(v4, v1)) | (v4 = v1) | (~r(v3, v1)) | (v3 = v1))),
% 0.40/0.57 inference(transitivity,[status(thm)],[810, 808])).
% 0.40/0.57 tff(812,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v4)) | (~r(v4, v1)) | (~r(v3, v1)) | (v4 = v1) | (v3 = v1) | (v3 = v4))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(813,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v4) | (~r(v3, v4)) | (~r(v4, v1)) | (v4 = v1) | (~r(v3, v1)) | (v3 = v1)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[812, 811])).
% 0.40/0.57 tff(814,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[813, 172, 150, 785, 807, 591, 805, 361])).
% 0.40/0.57 tff(815,plain,(r(v2, v4) | r(v3, v2) | r(v2, v1)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(816,plain,
% 0.40/0.57 (r(v2, v4)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[815, 506, 48])).
% 0.40/0.57 tff(817,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | r(v2, v1) | (v2 = v1) | r(v0, v2) | r(v0, v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | r(v2, v1) | (v2 = v1) | r(v0, v2) | r(v0, v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(818,plain,
% 0.40/0.57 ((r(v0, v2) | r(v2, v1) | r(v0, v1) | (v2 = v1) | (v0 = v1) | (v0 = v2)) <=> ((v0 = v1) | (v0 = v2) | r(v2, v1) | (v2 = v1) | r(v0, v2) | r(v0, v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(819,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v1) | r(v0, v1) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v2) | r(v2, v1) | (v2 = v1) | r(v0, v2) | r(v0, v1)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[818])).
% 0.40/0.57 tff(820,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v1) | r(v0, v1) | (v2 = v1) | (v0 = v1) | (v0 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | r(v2, v1) | (v2 = v1) | r(v0, v2) | r(v0, v1))),
% 0.40/0.57 inference(transitivity,[status(thm)],[819, 817])).
% 0.40/0.57 tff(821,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v2) | r(v2, v1) | r(v0, v1) | (v2 = v1) | (v0 = v1) | (v0 = v2))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(822,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v2) | r(v2, v1) | (v2 = v1) | r(v0, v2) | r(v0, v1)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.40/0.57 tff(823,plain,
% 0.40/0.57 (r(v0, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[822, 73, 24, 17, 506, 100, 56])).
% 0.40/0.57 tff(824,assumption,(r(v3, v0)), introduced(assumption)).
% 0.40/0.57 tff(825,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v1)) | (~r(v3, v1)) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v1)) | (~r(v3, v1)) | (v3 = v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(826,plain,
% 0.40/0.57 (((~r(v3, v0)) | (~r(v0, v1)) | (~r(v3, v1)) | (v0 = v1) | (v3 = v1) | (v3 = v0)) <=> ((v0 = v1) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v1)) | (~r(v3, v1)) | (v3 = v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(827,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v1)) | (~r(v3, v1)) | (v0 = v1) | (v3 = v1) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v1)) | (~r(v3, v1)) | (v3 = v1)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[826])).
% 0.40/0.57 tff(828,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v1)) | (~r(v3, v1)) | (v0 = v1) | (v3 = v1) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v1)) | (~r(v3, v1)) | (v3 = v1))),
% 0.40/0.57 inference(transitivity,[status(thm)],[827, 825])).
% 0.40/0.57 tff(829,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v1)) | (~r(v3, v1)) | (v0 = v1) | (v3 = v1) | (v3 = v0))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(830,plain,
% 0.40/0.57 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v1)) | (~r(v3, v1)) | (v3 = v1)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.40/0.57 tff(831,plain,
% 0.40/0.57 (~r(v3, v1)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[830, 172, 24, 824, 63, 823, 361])).
% 0.40/0.57 tff(832,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | (v2 = v1) | (v3 = v2) | r(v3, v2) | r(v3, v1) | (v3 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v2, v1) | (v2 = v1) | (v3 = v2) | r(v3, v2) | r(v3, v1) | (v3 = v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(833,plain,
% 0.40/0.57 ((r(v3, v2) | r(v2, v1) | r(v3, v1) | (v2 = v1) | (v3 = v1) | (v3 = v2)) <=> (r(v2, v1) | (v2 = v1) | (v3 = v2) | r(v3, v2) | r(v3, v1) | (v3 = v1))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(834,plain,
% 0.40/0.57 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v1) | r(v3, v1) | (v2 = v1) | (v3 = v1) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v1) | (v2 = v1) | (v3 = v2) | r(v3, v2) | r(v3, v1) | (v3 = v1)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[833])).
% 0.40/0.58 tff(835,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v1) | r(v3, v1) | (v2 = v1) | (v3 = v1) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v2, v1) | (v2 = v1) | (v3 = v2) | r(v3, v2) | r(v3, v1) | (v3 = v1))),
% 0.40/0.58 inference(transitivity,[status(thm)],[834, 832])).
% 0.40/0.58 tff(836,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v1) | r(v3, v1) | (v2 = v1) | (v3 = v1) | (v3 = v2))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(837,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | r(v2, v1) | (v2 = v1) | (v3 = v2) | r(v3, v2) | r(v3, v1) | (v3 = v1)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.40/0.58 tff(838,plain,
% 0.40/0.58 (r(v3, v1) | (v3 = v1)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[837, 73, 506, 100, 55, 48])).
% 0.40/0.58 tff(839,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[838, 831, 361])).
% 0.40/0.58 tff(840,plain,(r(v2, v1) | r(v3, v2) | (~r(v3, v0)) | r(v0, v2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(841,plain,
% 0.40/0.58 (r(v0, v2)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[840, 506, 776, 48])).
% 0.40/0.58 tff(842,assumption,(~r(v2, v0)), introduced(assumption)).
% 0.40/0.58 tff(843,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[92, 89, 362, 842])).
% 0.40/0.58 tff(844,plain,(r(v2, v0) | (~r(v0, v2))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(845,plain,
% 0.40/0.58 (r(v2, v0)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[844, 841])).
% 0.40/0.58 tff(846,assumption,(r(v2, v0)), introduced(assumption)).
% 0.40/0.58 tff(847,plain,
% 0.40/0.58 (~r(v0, v4)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[453, 846, 234])).
% 0.40/0.58 tff(848,plain,
% 0.40/0.58 (~r(v4, v0)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[803, 89, 847])).
% 0.40/0.58 tff(849,assumption,(r(v4, v5)), introduced(assumption)).
% 0.40/0.58 tff(850,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (v4 = v5) | (~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | (~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(851,plain,
% 0.40/0.58 (((~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)) | (v4 = v5) | (v2 = v5) | (v2 = v4)) <=> ((v2 = v4) | (v2 = v5) | (v4 = v5) | (~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(852,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)) | (v4 = v5) | (v2 = v5) | (v2 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | (v2 = v5) | (v4 = v5) | (~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[851])).
% 0.40/0.58 tff(853,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)) | (v4 = v5) | (v2 = v5) | (v2 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | (~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[852, 850])).
% 0.40/0.58 tff(854,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5)) | (v4 = v5) | (v2 = v5) | (v2 = v4))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(855,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | (v2 = v5) | (v4 = v5) | (~r(v2, v4)) | (~r(v4, v5)) | (~r(v2, v5))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.40/0.58 tff(856,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[855, 172, 113, 39, 46, 234, 2, 849])).
% 0.40/0.58 tff(857,plain,((~r(v4, v5)) | (~r(v2, v4)) | (~r(v2, v5))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(858,plain,
% 0.40/0.58 (~r(v4, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[857, 2, 234])).
% 0.40/0.58 tff(859,assumption,(~r(v4, v5)), introduced(assumption)).
% 0.40/0.58 tff(860,assumption,(~r(v4, v0)), introduced(assumption)).
% 0.40/0.58 tff(861,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v4 = v5) | r(v0, v5) | r(v4, v5) | r(v4, v0) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v4 = v5) | r(v0, v5) | r(v4, v5) | r(v4, v0) | (v4 = v0))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(862,plain,
% 0.40/0.58 ((r(v4, v0) | r(v0, v5) | r(v4, v5) | (v0 = v5) | (v4 = v5) | (v4 = v0)) <=> ((v0 = v5) | (v4 = v5) | r(v0, v5) | r(v4, v5) | r(v4, v0) | (v4 = v0))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(863,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v0) | r(v0, v5) | r(v4, v5) | (v0 = v5) | (v4 = v5) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v4 = v5) | r(v0, v5) | r(v4, v5) | r(v4, v0) | (v4 = v0)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[862])).
% 0.40/0.58 tff(864,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v0) | r(v0, v5) | r(v4, v5) | (v0 = v5) | (v4 = v5) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v4 = v5) | r(v0, v5) | r(v4, v5) | r(v4, v0) | (v4 = v0))),
% 0.40/0.58 inference(transitivity,[status(thm)],[863, 861])).
% 0.40/0.58 tff(865,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v0) | r(v0, v5) | r(v4, v5) | (v0 = v5) | (v4 = v5) | (v4 = v0))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(866,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v4 = v5) | r(v0, v5) | r(v4, v5) | r(v4, v0) | (v4 = v0)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.40/0.58 tff(867,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[866, 73, 125, 46, 701, 860, 9, 859])).
% 0.40/0.58 tff(868,plain,(r(v0, v5) | r(v4, v0) | r(v4, v5)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(869,plain,
% 0.40/0.58 (r(v0, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[868, 858, 848])).
% 0.40/0.58 tff(870,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v0)) | (v2 = v0) | (~r(v2, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v0)) | (v2 = v0) | (~r(v2, v5)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(871,plain,
% 0.40/0.58 (((~r(v2, v0)) | (~r(v0, v5)) | (~r(v2, v5)) | (v0 = v5) | (v2 = v5) | (v2 = v0)) <=> ((v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v0)) | (v2 = v0) | (~r(v2, v5)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(872,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v0)) | (~r(v0, v5)) | (~r(v2, v5)) | (v0 = v5) | (v2 = v5) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v0)) | (v2 = v0) | (~r(v2, v5))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[871])).
% 0.40/0.58 tff(873,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v0)) | (~r(v0, v5)) | (~r(v2, v5)) | (v0 = v5) | (v2 = v5) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v0)) | (v2 = v0) | (~r(v2, v5)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[872, 870])).
% 0.40/0.58 tff(874,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v2, v0)) | (~r(v0, v5)) | (~r(v2, v5)) | (v0 = v5) | (v2 = v5) | (v2 = v0))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(875,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v2 = v5) | (~r(v0, v5)) | (~r(v2, v0)) | (v2 = v0) | (~r(v2, v5))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.40/0.58 tff(876,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[875, 172, 125, 39, 869, 846, 18, 2])).
% 0.40/0.58 tff(877,plain,((~r(v2, v5)) | (~r(v2, v0)) | (~r(v2, v4))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(878,plain,
% 0.40/0.58 (~r(v2, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[877, 845, 816])).
% 0.40/0.58 tff(879,plain,
% 0.40/0.58 (~r(v3, v5)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[532, 878, 107, 506])).
% 0.40/0.58 tff(880,assumption,(~r(v3, v5)), introduced(assumption)).
% 0.40/0.58 tff(881,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v3 = v5) | r(v3, v5) | (v3 = v2) | r(v3, v2) | r(v2, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v3 = v5) | r(v3, v5) | (v3 = v2) | r(v3, v2) | r(v2, v5))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(882,plain,
% 0.40/0.58 ((r(v3, v2) | r(v2, v5) | r(v3, v5) | (v2 = v5) | (v3 = v5) | (v3 = v2)) <=> ((v2 = v5) | (v3 = v5) | r(v3, v5) | (v3 = v2) | r(v3, v2) | r(v2, v5))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(883,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v5) | r(v3, v5) | (v2 = v5) | (v3 = v5) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v3 = v5) | r(v3, v5) | (v3 = v2) | r(v3, v2) | r(v2, v5)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[882])).
% 0.40/0.58 tff(884,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v5) | r(v3, v5) | (v2 = v5) | (v3 = v5) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v3 = v5) | r(v3, v5) | (v3 = v2) | r(v3, v2) | r(v2, v5))),
% 0.40/0.58 inference(transitivity,[status(thm)],[883, 881])).
% 0.40/0.58 tff(885,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v3, v2) | r(v2, v5) | r(v3, v5) | (v2 = v5) | (v3 = v5) | (v3 = v2))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(886,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v3 = v5) | r(v3, v5) | (v3 = v2) | r(v3, v2) | r(v2, v5)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.40/0.58 tff(887,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[886, 73, 39, 122, 880, 55, 48, 530])).
% 0.40/0.58 tff(888,plain,(r(v2, v5) | r(v3, v5) | r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(889,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[888, 879, 878, 48])).
% 0.40/0.58 tff(890,plain,(r(v2, v1) | r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(891,plain,
% 0.40/0.58 (r(v2, v1)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[890, 48])).
% 0.40/0.58 tff(892,plain,
% 0.40/0.58 (r(v1, v2)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[673, 89, 891])).
% 0.40/0.58 tff(893,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v4, v0) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v4, v0) | (v4 = v0))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(894,plain,
% 0.40/0.58 ((r(v2, v4) | r(v4, v0) | r(v2, v0) | (v4 = v0) | (v2 = v0) | (v2 = v4)) <=> ((v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v4, v0) | (v4 = v0))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(895,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v4, v0) | r(v2, v0) | (v4 = v0) | (v2 = v0) | (v2 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v4, v0) | (v4 = v0)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[894])).
% 0.40/0.58 tff(896,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v4, v0) | r(v2, v0) | (v4 = v0) | (v2 = v0) | (v2 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v4, v0) | (v4 = v0))),
% 0.40/0.58 inference(transitivity,[status(thm)],[895, 893])).
% 0.40/0.58 tff(897,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v4) | r(v4, v0) | r(v2, v0) | (v4 = v0) | (v2 = v0) | (v2 = v4))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(898,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v4) | r(v2, v4) | (v2 = v0) | r(v2, v0) | r(v4, v0) | (v4 = v0)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.40/0.58 tff(899,plain,
% 0.40/0.58 (r(v2, v0)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[898, 73, 113, 10, 18, 804, 9])).
% 0.40/0.58 tff(900,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (~r(v2, v0)) | (v2 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v2)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (~r(v2, v0)) | (v2 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v2)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(901,plain,
% 0.40/0.58 (((~r(v1, v2)) | (~r(v2, v0)) | (~r(v1, v0)) | (v2 = v0) | (v1 = v0) | (v1 = v2)) <=> ((v1 = v2) | (~r(v2, v0)) | (v2 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v2)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(902,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v0)) | (~r(v1, v0)) | (v2 = v0) | (v1 = v0) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (~r(v2, v0)) | (v2 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v2))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[901])).
% 0.40/0.58 tff(903,plain,
% 0.40/0.58 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v0)) | (~r(v1, v0)) | (v2 = v0) | (v1 = v0) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (~r(v2, v0)) | (v2 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v2)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[902, 900])).
% 0.40/0.58 tff(904,plain,
% 0.40/0.58 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v0)) | (~r(v1, v0)) | (v2 = v0) | (v1 = v0) | (v1 = v2))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(905,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (~r(v2, v0)) | (v2 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v2))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.40/0.59 tff(906,plain,
% 0.40/0.59 (~r(v1, v0)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[905, 172, 99, 899, 18, 25, 892])).
% 0.40/0.59 tff(907,plain,
% 0.40/0.59 (r(v1, v4)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[555, 73, 8, 273, 792, 906, 25])).
% 0.40/0.59 tff(908,plain,
% 0.40/0.59 (r(v4, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[868, 701, 860])).
% 0.40/0.59 tff(909,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v1 = v5) | r(v0, v5) | r(v1, v0) | (v1 = v0) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | r(v0, v5) | r(v1, v0) | (v1 = v0) | r(v1, v5))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(910,plain,
% 0.40/0.59 ((r(v1, v0) | r(v0, v5) | r(v1, v5) | (v0 = v5) | (v1 = v5) | (v1 = v0)) <=> ((v0 = v5) | (v1 = v5) | r(v0, v5) | r(v1, v0) | (v1 = v0) | r(v1, v5))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(911,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v5) | r(v1, v5) | (v0 = v5) | (v1 = v5) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v1 = v5) | r(v0, v5) | r(v1, v0) | (v1 = v0) | r(v1, v5)))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[910])).
% 0.40/0.59 tff(912,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v5) | r(v1, v5) | (v0 = v5) | (v1 = v5) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | r(v0, v5) | r(v1, v0) | (v1 = v0) | r(v1, v5))),
% 0.40/0.59 inference(transitivity,[status(thm)],[911, 909])).
% 0.40/0.59 tff(913,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v5) | r(v1, v5) | (v0 = v5) | (v1 = v5) | (v1 = v0))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(914,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v1 = v5) | r(v0, v5) | r(v1, v0) | (v1 = v0) | r(v1, v5)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.40/0.59 tff(915,plain,
% 0.40/0.59 (r(v1, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[914, 73, 125, 32, 701, 549, 25])).
% 0.40/0.59 tff(916,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[402, 172, 273, 32, 46, 270, 915, 908])).
% 0.40/0.59 tff(917,plain,(r(v0, v5) | (~r(v1, v4)) | r(v1, v0) | r(v4, v0)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(918,plain,
% 0.40/0.59 (r(v0, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[917, 907, 906, 804])).
% 0.40/0.59 tff(919,plain,
% 0.40/0.59 (~r(v5, v2)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[227, 918, 800])).
% 0.40/0.59 tff(920,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(921,plain,
% 0.40/0.59 (((~r(v0, v5)) | (~r(v5, v3)) | (~r(v0, v3)) | (v5 = v3) | (v0 = v3) | (v0 = v5)) <=> ((v0 = v3) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(922,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v3)) | (~r(v0, v3)) | (v5 = v3) | (v0 = v3) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3)))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[921])).
% 0.40/0.59 tff(923,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v3)) | (~r(v0, v3)) | (v5 = v3) | (v0 = v3) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3))),
% 0.40/0.59 inference(transitivity,[status(thm)],[922, 920])).
% 0.40/0.59 tff(924,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v5)) | (~r(v5, v3)) | (~r(v0, v3)) | (v5 = v3) | (v0 = v3) | (v0 = v5))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(925,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.40/0.59 tff(926,plain,
% 0.40/0.59 ((~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3)) | (v5 = v3)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[925, 172, 62, 125])).
% 0.40/0.59 tff(927,plain,
% 0.40/0.59 ((~r(v0, v5)) | (~r(v0, v3)) | (~r(v5, v3))),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[926, 183])).
% 0.40/0.59 tff(928,plain,
% 0.40/0.59 (~r(v5, v3)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[927, 918, 780])).
% 0.40/0.59 tff(929,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[218, 73, 928, 183, 919, 40, 55, 48])).
% 0.40/0.59 tff(930,plain,(r(v2, v4) | r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(931,plain,
% 0.40/0.59 (r(v2, v4)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[930, 48])).
% 0.40/0.59 tff(932,assumption,(r(v1, v2)), introduced(assumption)).
% 0.40/0.59 tff(933,plain,
% 0.40/0.59 (~r(v1, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[330, 172, 99, 32, 39, 2, 932])).
% 0.40/0.59 tff(934,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v4) | (v2 = v4) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v1, v2)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v4) | (v2 = v4) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v1, v2)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(935,plain,
% 0.40/0.59 (((~r(v1, v2)) | (~r(v2, v4)) | (~r(v1, v4)) | (v2 = v4) | (v1 = v4) | (v1 = v2)) <=> ((v1 = v2) | (v1 = v4) | (v2 = v4) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v1, v2)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(936,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v4)) | (~r(v1, v4)) | (v2 = v4) | (v1 = v4) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v2) | (v1 = v4) | (v2 = v4) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v1, v2))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[935])).
% 0.40/0.59 tff(937,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v4)) | (~r(v1, v4)) | (v2 = v4) | (v1 = v4) | (v1 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v4) | (v2 = v4) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v1, v2)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[936, 934])).
% 0.40/0.59 tff(938,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v2)) | (~r(v2, v4)) | (~r(v1, v4)) | (v2 = v4) | (v1 = v4) | (v1 = v2))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(939,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v2) | (v1 = v4) | (v2 = v4) | (~r(v2, v4)) | (~r(v1, v4)) | (~r(v1, v2))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.40/0.59 tff(940,plain,
% 0.40/0.59 (~r(v1, v4)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[939, 172, 99, 273, 113, 234, 932])).
% 0.40/0.59 tff(941,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[308, 73, 273, 32, 46, 940, 933, 858])).
% 0.40/0.59 tff(942,plain,((~r(v2, v5)) | (~r(v1, v2)) | (~r(v2, v4))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(943,plain,
% 0.40/0.59 (~r(v2, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[942, 892, 931])).
% 0.40/0.59 tff(944,plain,
% 0.40/0.59 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v2)) | r(v2, v5))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v2)) | r(v2, v5))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(945,plain,
% 0.40/0.59 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v5, v2)) | r(v2, v5))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(946,plain,
% 0.40/0.59 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v5, v2)) | r(v2, v5)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.40/0.59 tff(947,plain,
% 0.40/0.59 (~r(v5, v2)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[946, 89, 943])).
% 0.40/0.59 tff(948,plain,
% 0.40/0.59 (r(v3, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[888, 943, 48])).
% 0.40/0.59 tff(949,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v0, v5)) | (~r(v0, v3)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v0, v5)) | (~r(v0, v3)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(950,plain,
% 0.40/0.59 (((~r(v0, v3)) | (~r(v3, v5)) | (~r(v0, v5)) | (v3 = v5) | (v0 = v5) | (v0 = v3)) <=> ((v0 = v3) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v0, v5)) | (~r(v0, v3)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(951,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v5)) | (~r(v0, v5)) | (v3 = v5) | (v0 = v5) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v3) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v0, v5)) | (~r(v0, v3))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[950])).
% 0.40/0.59 tff(952,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v5)) | (~r(v0, v5)) | (v3 = v5) | (v0 = v5) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v0, v5)) | (~r(v0, v3)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[951, 949])).
% 0.40/0.59 tff(953,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v5)) | (~r(v0, v5)) | (v3 = v5) | (v0 = v5) | (v0 = v3))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(954,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v3) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v0, v5)) | (~r(v0, v3))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.40/0.59 tff(955,plain,
% 0.40/0.59 (~r(v0, v5)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[954, 172, 62, 125, 122, 948, 780])).
% 0.40/0.59 tff(956,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | r(v0, v5) | r(v0, v2) | (v5 = v2) | r(v5, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | r(v0, v5) | r(v0, v2) | (v5 = v2) | r(v5, v2))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(957,plain,
% 0.40/0.59 ((r(v0, v5) | r(v5, v2) | r(v0, v2) | (v5 = v2) | (v0 = v2) | (v0 = v5)) <=> ((v0 = v2) | (v0 = v5) | r(v0, v5) | r(v0, v2) | (v5 = v2) | r(v5, v2))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(958,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v5) | r(v5, v2) | r(v0, v2) | (v5 = v2) | (v0 = v2) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v5) | r(v0, v5) | r(v0, v2) | (v5 = v2) | r(v5, v2)))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[957])).
% 0.40/0.59 tff(959,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v5) | r(v5, v2) | r(v0, v2) | (v5 = v2) | (v0 = v2) | (v0 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | r(v0, v5) | r(v0, v2) | (v5 = v2) | r(v5, v2))),
% 0.40/0.59 inference(transitivity,[status(thm)],[958, 956])).
% 0.40/0.59 tff(960,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v5) | r(v5, v2) | r(v0, v2) | (v5 = v2) | (v0 = v2) | (v0 = v5))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(961,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v5) | r(v0, v5) | r(v0, v2) | (v5 = v2) | r(v5, v2)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.40/0.59 tff(962,plain,
% 0.40/0.59 (r(v0, v2)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[961, 73, 17, 125, 955, 947, 40])).
% 0.40/0.59 tff(963,plain,
% 0.40/0.59 (~r(v0, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[369, 172, 24, 17, 891, 100, 962])).
% 0.40/0.59 tff(964,plain,
% 0.40/0.59 (~r(v1, v4)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[939, 172, 99, 273, 113, 931, 892])).
% 0.40/0.59 tff(965,plain,
% 0.40/0.59 (~r(v4, v1)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[760, 89, 964])).
% 0.40/0.59 tff(966,plain,
% 0.40/0.59 (r(v2, v0)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[844, 962])).
% 0.40/0.59 tff(967,plain,
% 0.40/0.59 (~r(v0, v4)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[453, 966, 931])).
% 0.40/0.59 tff(968,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(969,plain,
% 0.40/0.59 ((r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1) | (v0 = v1) | (v0 = v4)) <=> ((v0 = v1) | (v0 = v4) | r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(970,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v1) | (v0 = v4) | r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1)))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[969])).
% 0.40/0.59 tff(971,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1) | (v0 = v1) | (v0 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1))),
% 0.40/0.59 inference(transitivity,[status(thm)],[970, 968])).
% 0.40/0.59 tff(972,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1) | (v0 = v1) | (v0 = v4))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(973,plain,
% 0.40/0.59 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v1) | (v0 = v4) | r(v0, v4) | r(v4, v1) | r(v0, v1) | (v4 = v1)),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[972, 971])).
% 0.40/0.59 tff(974,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[973, 73, 24, 8, 967, 965, 591, 963])).
% 0.40/0.59 tff(975,plain,(r(v3, v2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(976,plain,
% 0.40/0.59 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(977,plain,
% 0.40/0.60 (((~r(v0, v3)) | (~r(v3, v2)) | (~r(v0, v2)) | (v3 = v2) | (v0 = v2) | (v0 = v3)) <=> ((v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(978,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v2)) | (~r(v0, v2)) | (v3 = v2) | (v0 = v2) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[977])).
% 0.40/0.60 tff(979,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v2)) | (~r(v0, v2)) | (v3 = v2) | (v0 = v2) | (v0 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[978, 976])).
% 0.40/0.60 tff(980,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v0, v3)) | (~r(v3, v2)) | (~r(v0, v2)) | (v3 = v2) | (v0 = v2) | (v0 = v3))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(981,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v0 = v3) | (~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.40/0.60 tff(982,plain,
% 0.40/0.60 ((~r(v0, v3)) | (~r(v0, v2)) | (v3 = v2) | (~r(v3, v2))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[981, 172, 17, 62])).
% 0.40/0.60 tff(983,plain,
% 0.40/0.60 ((~r(v0, v3)) | (~r(v0, v2)) | (~r(v3, v2))),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[982, 55])).
% 0.40/0.60 tff(984,plain,
% 0.40/0.60 (~r(v0, v2)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[983, 975, 780])).
% 0.40/0.60 tff(985,plain,
% 0.40/0.60 (~r(v2, v0)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[678, 89, 984])).
% 0.40/0.60 tff(986,plain,
% 0.40/0.60 ($false),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[774, 73, 8, 113, 10, 985, 18, 11])).
% 0.40/0.60 tff(987,plain,(r(v0, v4) | r(v2, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.60 tff(988,plain,
% 0.40/0.60 (r(v0, v4)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[987, 10])).
% 0.40/0.60 tff(989,plain,
% 0.40/0.60 (r(v4, v0)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[259, 89, 988])).
% 0.40/0.60 tff(990,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v3 = v4) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v4)) | (~r(v3, v4)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v3 = v4) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v4)) | (~r(v3, v4)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(991,plain,
% 0.40/0.60 (((~r(v3, v0)) | (~r(v0, v4)) | (~r(v3, v4)) | (v0 = v4) | (v3 = v4) | (v3 = v0)) <=> ((v0 = v4) | (v3 = v4) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v4)) | (~r(v3, v4)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(992,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v4)) | (~r(v3, v4)) | (v0 = v4) | (v3 = v4) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v4) | (v3 = v4) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v4)) | (~r(v3, v4))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[991])).
% 0.40/0.60 tff(993,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v4)) | (~r(v3, v4)) | (v0 = v4) | (v3 = v4) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v3 = v4) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v4)) | (~r(v3, v4)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[992, 990])).
% 0.40/0.60 tff(994,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v4)) | (~r(v3, v4)) | (v0 = v4) | (v3 = v4) | (v3 = v0))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(995,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v4) | (v3 = v4) | (~r(v3, v0)) | (v3 = v0) | (~r(v0, v4)) | (~r(v3, v4))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.40/0.60 tff(996,plain,
% 0.40/0.60 (~r(v3, v4)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[995, 172, 8, 150, 776, 63, 988])).
% 0.40/0.60 tff(997,plain,
% 0.40/0.60 (((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v3)) | r(v3, v4))) <=> ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v3)) | r(v3, v4))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(998,plain,
% 0.40/0.60 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(v4, v3)) | r(v3, v4))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(999,plain,
% 0.40/0.60 ((~![Y: $i, X: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(v4, v3)) | r(v3, v4)),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.40/0.60 tff(1000,plain,
% 0.40/0.60 (~r(v4, v3)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[999, 89, 996])).
% 0.40/0.60 tff(1001,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v2 = v5) | r(v0, v5) | (v2 = v0) | r(v2, v0) | r(v2, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v2 = v5) | r(v0, v5) | (v2 = v0) | r(v2, v0) | r(v2, v5))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(1002,plain,
% 0.40/0.60 ((r(v2, v0) | r(v0, v5) | r(v2, v5) | (v0 = v5) | (v2 = v5) | (v2 = v0)) <=> ((v0 = v5) | (v2 = v5) | r(v0, v5) | (v2 = v0) | r(v2, v0) | r(v2, v5))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(1003,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v5) | r(v2, v5) | (v0 = v5) | (v2 = v5) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v2 = v5) | r(v0, v5) | (v2 = v0) | r(v2, v0) | r(v2, v5)))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[1002])).
% 0.40/0.60 tff(1004,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v5) | r(v2, v5) | (v0 = v5) | (v2 = v5) | (v2 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v2 = v5) | r(v0, v5) | (v2 = v0) | r(v2, v0) | r(v2, v5))),
% 0.40/0.60 inference(transitivity,[status(thm)],[1003, 1001])).
% 0.40/0.60 tff(1005,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v2, v0) | r(v0, v5) | r(v2, v5) | (v0 = v5) | (v2 = v5) | (v2 = v0))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(1006,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v2 = v5) | r(v0, v5) | (v2 = v0) | r(v2, v0) | r(v2, v5)),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.40/0.60 tff(1007,plain,
% 0.40/0.60 (r(v2, v5)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[1006, 73, 125, 39, 701, 985, 18])).
% 0.40/0.60 tff(1008,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (v3 = v2) | (~r(v3, v2)) | (~r(v2, v5)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (v3 = v2) | (~r(v3, v2)) | (~r(v2, v5)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(1009,plain,
% 0.40/0.60 (((~r(v3, v2)) | (~r(v2, v5)) | (~r(v3, v5)) | (v2 = v5) | (v3 = v5) | (v3 = v2)) <=> ((v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (v3 = v2) | (~r(v3, v2)) | (~r(v2, v5)))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(1010,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v5)) | (~r(v3, v5)) | (v2 = v5) | (v3 = v5) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (v3 = v2) | (~r(v3, v2)) | (~r(v2, v5))))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[1009])).
% 0.40/0.60 tff(1011,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v5)) | (~r(v3, v5)) | (v2 = v5) | (v3 = v5) | (v3 = v2))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (v3 = v2) | (~r(v3, v2)) | (~r(v2, v5)))),
% 0.40/0.60 inference(transitivity,[status(thm)],[1010, 1008])).
% 0.40/0.60 tff(1012,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v2)) | (~r(v2, v5)) | (~r(v3, v5)) | (v2 = v5) | (v3 = v5) | (v3 = v2))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(1013,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v2 = v5) | (v3 = v5) | (~r(v3, v5)) | (v3 = v2) | (~r(v3, v2)) | (~r(v2, v5))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.40/0.60 tff(1014,plain,
% 0.40/0.60 (~r(v3, v5)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[1013, 172, 39, 122, 55, 975, 1007])).
% 0.40/0.60 tff(1015,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v5) | (v4 = v5) | r(v3, v5) | r(v4, v3) | r(v4, v5) | (v4 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | (v4 = v5) | r(v3, v5) | r(v4, v3) | r(v4, v5) | (v4 = v3))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(1016,plain,
% 0.40/0.60 ((r(v4, v3) | r(v3, v5) | r(v4, v5) | (v3 = v5) | (v4 = v5) | (v4 = v3)) <=> ((v3 = v5) | (v4 = v5) | r(v3, v5) | r(v4, v3) | r(v4, v5) | (v4 = v3))),
% 0.40/0.60 inference(rewrite,[status(thm)],[])).
% 0.40/0.60 tff(1017,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v3, v5) | r(v4, v5) | (v3 = v5) | (v4 = v5) | (v4 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v3 = v5) | (v4 = v5) | r(v3, v5) | r(v4, v3) | r(v4, v5) | (v4 = v3)))),
% 0.40/0.60 inference(monotonicity,[status(thm)],[1016])).
% 0.40/0.60 tff(1018,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v3, v5) | r(v4, v5) | (v3 = v5) | (v4 = v5) | (v4 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | (v4 = v5) | r(v3, v5) | r(v4, v3) | r(v4, v5) | (v4 = v3))),
% 0.40/0.60 inference(transitivity,[status(thm)],[1017, 1015])).
% 0.40/0.60 tff(1019,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v4, v3) | r(v3, v5) | r(v4, v5) | (v3 = v5) | (v4 = v5) | (v4 = v3))),
% 0.40/0.60 inference(quant_inst,[status(thm)],[])).
% 0.40/0.60 tff(1020,plain,
% 0.40/0.60 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v3 = v5) | (v4 = v5) | r(v3, v5) | r(v4, v3) | r(v4, v5) | (v4 = v3)),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.40/0.60 tff(1021,plain,
% 0.40/0.60 (r(v4, v5)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[1020, 73, 122, 46, 1014, 1000, 268])).
% 0.40/0.60 tff(1022,plain,
% 0.40/0.60 (~r(v5, v0)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[644, 89, 701])).
% 0.40/0.60 tff(1023,plain,
% 0.40/0.60 (r(v5, v2)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[337, 89, 1007])).
% 0.40/0.60 tff(1024,plain,
% 0.40/0.60 (~r(v5, v3)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[419, 89, 1014])).
% 0.40/0.60 tff(1025,plain,
% 0.40/0.60 (r(v1, v2)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[673, 89, 363])).
% 0.40/0.60 tff(1026,assumption,(r(v5, v2)), introduced(assumption)).
% 0.40/0.60 tff(1027,plain,
% 0.40/0.60 (r(v2, v5)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[946, 89, 1026])).
% 0.40/0.60 tff(1028,plain,
% 0.40/0.60 (~r(v1, v5)),
% 0.40/0.60 inference(unit_resolution,[status(thm)],[330, 172, 99, 32, 39, 1027, 1025])).
% 0.40/0.60 tff(1029,plain,
% 0.40/0.60 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | r(v5, v3) | (v5 = v3) | r(v1, v3) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | r(v5, v3) | (v5 = v3) | r(v1, v3) | r(v1, v5))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1030,plain,
% 0.40/0.61 ((r(v1, v5) | r(v5, v3) | r(v1, v3) | (v5 = v3) | (v1 = v3) | (v1 = v5)) <=> ((v1 = v3) | (v1 = v5) | r(v5, v3) | (v5 = v3) | r(v1, v3) | r(v1, v5))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1031,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v5, v3) | r(v1, v3) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v5) | r(v5, v3) | (v5 = v3) | r(v1, v3) | r(v1, v5)))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1030])).
% 0.40/0.61 tff(1032,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v5, v3) | r(v1, v3) | (v5 = v3) | (v1 = v3) | (v1 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | r(v5, v3) | (v5 = v3) | r(v1, v3) | r(v1, v5))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1031, 1029])).
% 0.40/0.61 tff(1033,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v5, v3) | r(v1, v3) | (v5 = v3) | (v1 = v3) | (v1 = v5))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1034,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v5) | r(v5, v3) | (v5 = v3) | r(v1, v3) | r(v1, v5)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 0.40/0.61 tff(1035,plain,
% 0.40/0.61 (r(v1, v3)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1034, 73, 276, 32, 115, 183, 1028])).
% 0.40/0.61 tff(1036,plain,
% 0.40/0.61 (r(v3, v0)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[415, 115])).
% 0.40/0.61 tff(1037,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v3)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v3)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1038,plain,
% 0.40/0.61 (((~r(v1, v3)) | (~r(v3, v0)) | (~r(v1, v0)) | (v3 = v0) | (v1 = v0) | (v1 = v3)) <=> ((v1 = v3) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v3)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1039,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v0)) | (~r(v1, v0)) | (v3 = v0) | (v1 = v0) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v3))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1038])).
% 0.40/0.61 tff(1040,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v0)) | (~r(v1, v0)) | (v3 = v0) | (v1 = v0) | (v1 = v3))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v3)))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1039, 1037])).
% 0.40/0.61 tff(1041,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v1, v3)) | (~r(v3, v0)) | (~r(v1, v0)) | (v3 = v0) | (v1 = v0) | (v1 = v3))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1042,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (~r(v3, v0)) | (v3 = v0) | (~r(v1, v0)) | (v1 = v0) | (~r(v1, v3))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.40/0.61 tff(1043,plain,
% 0.40/0.61 ((~r(v1, v0)) | (v1 = v0)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1042, 172, 276, 1036, 63, 1035])).
% 0.40/0.61 tff(1044,plain,
% 0.40/0.61 (~r(v1, v0)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1043, 25])).
% 0.40/0.61 tff(1045,plain,
% 0.40/0.61 ((~r(v5, v1)) | (v5 = v1)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[490, 172, 363, 100, 1026, 40])).
% 0.40/0.61 tff(1046,plain,
% 0.40/0.61 (~r(v5, v1)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1045, 33])).
% 0.40/0.61 tff(1047,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v5, v1) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v5, v1) | (v5 = v1))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1048,plain,
% 0.40/0.61 ((r(v5, v1) | r(v1, v0) | r(v5, v0) | (v1 = v0) | (v5 = v0) | (v5 = v1)) <=> ((v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v5, v1) | (v5 = v1))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1049,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v1, v0) | r(v5, v0) | (v1 = v0) | (v5 = v0) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v5, v1) | (v5 = v1)))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1048])).
% 0.40/0.61 tff(1050,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v1, v0) | r(v5, v0) | (v1 = v0) | (v5 = v0) | (v5 = v1))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v5, v1) | (v5 = v1))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1049, 1047])).
% 0.40/0.61 tff(1051,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v5, v1) | r(v1, v0) | r(v5, v0) | (v1 = v0) | (v5 = v0) | (v5 = v1))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1052,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v5, v1) | (v5 = v1)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 0.40/0.61 tff(1053,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1052, 73, 421, 161, 1046, 33, 1044, 25])).
% 0.40/0.61 tff(1054,plain,((~r(v2, v1)) | r(v5, v0) | r(v5, v3) | (~r(v5, v2))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(1055,plain,
% 0.40/0.61 (~r(v2, v1)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1054, 1024, 1023, 1022])).
% 0.40/0.61 tff(1056,plain,
% 0.40/0.61 (r(v1, v4)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[395, 1055, 10])).
% 0.40/0.61 tff(1057,plain,
% 0.40/0.61 (~r(v1, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[402, 172, 273, 32, 46, 1056, 1021])).
% 0.40/0.61 tff(1058,plain,
% 0.40/0.61 (~r(v1, v0)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[291, 172, 273, 1056, 989, 9, 25])).
% 0.40/0.61 tff(1059,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v1, v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v1, v5))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1060,plain,
% 0.40/0.61 ((r(v1, v5) | r(v5, v0) | r(v1, v0) | (v5 = v0) | (v1 = v0) | (v1 = v5)) <=> ((v1 = v5) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v1, v5))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1061,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v5, v0) | r(v1, v0) | (v5 = v0) | (v1 = v0) | (v1 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v5) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v1, v5)))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1060])).
% 0.40/0.61 tff(1062,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v5, v0) | r(v1, v0) | (v5 = v0) | (v1 = v0) | (v1 = v5))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v1, v5))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1061, 1059])).
% 0.40/0.61 tff(1063,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v5) | r(v5, v0) | r(v1, v0) | (v5 = v0) | (v1 = v0) | (v1 = v5))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1064,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v5) | (v5 = v0) | r(v5, v0) | r(v1, v0) | (v1 = v0) | r(v1, v5)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.40/0.61 tff(1065,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1064, 73, 32, 1022, 161, 1058, 25, 1057])).
% 0.40/0.61 tff(1066,plain,(r(v0, v5) | r(v2, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(1067,plain,
% 0.40/0.61 (r(v0, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1066, 10])).
% 0.40/0.61 tff(1068,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v4 = v5) | (~r(v0, v5)) | (~r(v4, v0)) | (~r(v4, v5)) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v4 = v5) | (~r(v0, v5)) | (~r(v4, v0)) | (~r(v4, v5)) | (v4 = v0))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1069,plain,
% 0.40/0.61 (((~r(v4, v0)) | (~r(v0, v5)) | (~r(v4, v5)) | (v0 = v5) | (v4 = v5) | (v4 = v0)) <=> ((v0 = v5) | (v4 = v5) | (~r(v0, v5)) | (~r(v4, v0)) | (~r(v4, v5)) | (v4 = v0))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1070,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v0)) | (~r(v0, v5)) | (~r(v4, v5)) | (v0 = v5) | (v4 = v5) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v4 = v5) | (~r(v0, v5)) | (~r(v4, v0)) | (~r(v4, v5)) | (v4 = v0)))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1069])).
% 0.40/0.61 tff(1071,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v0)) | (~r(v0, v5)) | (~r(v4, v5)) | (v0 = v5) | (v4 = v5) | (v4 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v4 = v5) | (~r(v0, v5)) | (~r(v4, v0)) | (~r(v4, v5)) | (v4 = v0))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1070, 1068])).
% 0.40/0.61 tff(1072,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v4, v0)) | (~r(v0, v5)) | (~r(v4, v5)) | (v0 = v5) | (v4 = v5) | (v4 = v0))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1073,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v4 = v5) | (~r(v0, v5)) | (~r(v4, v0)) | (~r(v4, v5)) | (v4 = v0)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.40/0.61 tff(1074,plain,
% 0.40/0.61 (~r(v4, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1073, 172, 125, 46, 1067, 989, 9])).
% 0.40/0.61 tff(1075,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v3, v0)) | (~r(v0, v5)) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v3, v0)) | (~r(v0, v5)) | (v3 = v0))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1076,plain,
% 0.40/0.61 (((~r(v3, v0)) | (~r(v0, v5)) | (~r(v3, v5)) | (v0 = v5) | (v3 = v5) | (v3 = v0)) <=> ((v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v3, v0)) | (~r(v0, v5)) | (v3 = v0))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1077,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v5)) | (~r(v3, v5)) | (v0 = v5) | (v3 = v5) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v3, v0)) | (~r(v0, v5)) | (v3 = v0)))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1076])).
% 0.40/0.61 tff(1078,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v5)) | (~r(v3, v5)) | (v0 = v5) | (v3 = v5) | (v3 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v3, v0)) | (~r(v0, v5)) | (v3 = v0))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1077, 1075])).
% 0.40/0.61 tff(1079,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(v3, v0)) | (~r(v0, v5)) | (~r(v3, v5)) | (v0 = v5) | (v3 = v5) | (v3 = v0))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1080,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : ((~r(X, Y)) | (~r(Y, Z)) | (~r(X, Z)) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v5) | (v3 = v5) | (~r(v3, v5)) | (~r(v3, v0)) | (~r(v0, v5)) | (v3 = v0)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.40/0.61 tff(1081,plain,
% 0.40/0.61 (~r(v3, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1080, 172, 125, 122, 776, 1067, 63])).
% 0.40/0.61 tff(1082,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1020, 73, 122, 46, 1081, 1000, 268, 1074])).
% 0.40/0.61 tff(1083,plain,(r(v2, v4)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(1084,plain,
% 0.40/0.61 ((~r(v4, v5)) | (~r(v2, v5))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[857, 1083])).
% 0.40/0.61 tff(1085,plain,
% 0.40/0.61 (~r(v4, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1084, 2])).
% 0.40/0.61 tff(1086,plain,
% 0.40/0.61 ((~r(v2, v4)) | (~r(v3, v4))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[242, 975])).
% 0.40/0.61 tff(1087,plain,
% 0.40/0.61 (~r(v3, v4)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1086, 1083])).
% 0.40/0.61 tff(1088,plain,
% 0.40/0.61 (~r(v4, v3)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[999, 89, 1087])).
% 0.40/0.61 tff(1089,plain,
% 0.40/0.61 (~r(v3, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1013, 172, 39, 122, 55, 975, 2])).
% 0.40/0.61 tff(1090,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[1020, 73, 122, 46, 1089, 1088, 268, 1085])).
% 0.40/0.61 tff(1091,plain,(~r(v2, v5)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(1092,plain,
% 0.40/0.61 (r(v1, v5)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[413, 73, 99, 32, 39, 1091, 1])).
% 0.40/0.61 tff(1093,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v1 = v2) | r(v0, v2) | r(v1, v0) | (v1 = v0) | r(v1, v2))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v1 = v2) | r(v0, v2) | r(v1, v0) | (v1 = v0) | r(v1, v2))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1094,plain,
% 0.40/0.61 ((r(v1, v0) | r(v0, v2) | r(v1, v2) | (v0 = v2) | (v1 = v2) | (v1 = v0)) <=> ((v0 = v2) | (v1 = v2) | r(v0, v2) | r(v1, v0) | (v1 = v0) | r(v1, v2))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(1095,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v2) | r(v1, v2) | (v0 = v2) | (v1 = v2) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v0 = v2) | (v1 = v2) | r(v0, v2) | r(v1, v0) | (v1 = v0) | r(v1, v2)))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[1094])).
% 0.40/0.61 tff(1096,plain,
% 0.40/0.61 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v2) | r(v1, v2) | (v0 = v2) | (v1 = v2) | (v1 = v0))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v1 = v2) | r(v0, v2) | r(v1, v0) | (v1 = v0) | r(v1, v2))),
% 0.40/0.61 inference(transitivity,[status(thm)],[1095, 1093])).
% 0.40/0.61 tff(1097,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v0) | r(v0, v2) | r(v1, v2) | (v0 = v2) | (v1 = v2) | (v1 = v0))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(1098,plain,
% 0.40/0.61 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v0 = v2) | (v1 = v2) | r(v0, v2) | r(v1, v0) | (v1 = v0) | r(v1, v2)),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.40/0.62 tff(1099,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[1098, 73, 17, 99, 984, 549, 25, 1])).
% 0.40/0.62 tff(1100,plain,(r(v1, v2) | r(v1, v0)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(1101,plain,
% 0.40/0.62 (r(v1, v0)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[1100, 1])).
% 0.40/0.62 tff(1102,plain,
% 0.40/0.62 (r(v0, v5)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[709, 73, 17, 125, 39, 984, 1091])).
% 0.40/0.62 tff(1103,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[718, 172, 125, 32, 1102, 1101, 25, 1092])).
% 0.40/0.62 tff(1104,plain,(r(v1, v2)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(1105,plain,
% 0.40/0.62 (r(v2, v3)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[594, 89, 975])).
% 0.40/0.62 tff(1106,plain,
% 0.40/0.62 (~r(v1, v3)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[692, 172, 99, 276, 54, 1105, 1104])).
% 0.40/0.62 tff(1107,plain,
% 0.40/0.62 (~r(v1, v4)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[939, 172, 99, 273, 113, 1083, 1104])).
% 0.40/0.62 tff(1108,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | r(v1, v4) | r(v4, v3) | (v4 = v3) | r(v1, v3))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | r(v1, v4) | r(v4, v3) | (v4 = v3) | r(v1, v3))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(1109,plain,
% 0.40/0.62 ((r(v1, v4) | r(v4, v3) | r(v1, v3) | (v4 = v3) | (v1 = v3) | (v1 = v4)) <=> ((v1 = v3) | (v1 = v4) | r(v1, v4) | r(v4, v3) | (v4 = v3) | r(v1, v3))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(1110,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v3) | r(v1, v3) | (v4 = v3) | (v1 = v3) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | ((v1 = v3) | (v1 = v4) | r(v1, v4) | r(v4, v3) | (v4 = v3) | r(v1, v3)))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[1109])).
% 0.40/0.62 tff(1111,plain,
% 0.40/0.62 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v3) | r(v1, v3) | (v4 = v3) | (v1 = v3) | (v1 = v4))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | r(v1, v4) | r(v4, v3) | (v4 = v3) | r(v1, v3))),
% 0.40/0.62 inference(transitivity,[status(thm)],[1110, 1108])).
% 0.40/0.62 tff(1112,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (r(v1, v4) | r(v4, v3) | r(v1, v3) | (v4 = v3) | (v1 = v3) | (v1 = v4))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(1113,plain,
% 0.40/0.62 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y) | r(Y, Z) | r(X, Z) | (Y = Z) | (X = Z) | (X = Y))) | (v1 = v3) | (v1 = v4) | r(v1, v4) | r(v4, v3) | (v4 = v3) | r(v1, v3)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.40/0.62 tff(1114,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[1113, 73, 276, 273, 1107, 1088, 268, 1106])).
% 0.40/0.62 % SZS output end Proof
% 0.40/0.62 % E exiting
%------------------------------------------------------------------------------