Z3---4.15.1.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : GRA119+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n001.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 06:33:06 PM UTC 2026

% Result   : Unsatisfiable 0.30s 0.47s
% Output   : Proof 0.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRA119+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12  % Command    : run_E %s %d THM
% 0.16/0.33  % Computer : n001.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Mon May  4 21:32:05 EDT 2026
% 0.16/0.34  % CPUTime    : 
% 0.30/0.47  % SZS status Unsatisfiable
% 0.30/0.47  % SZS output start Proof
% 0.30/0.47  tff(c_type, type, (
% 0.30/0.47     c: $i)).
% 0.30/0.47  tff(f_type, type, (
% 0.30/0.47     f: $i > $i)).
% 0.30/0.47  tff(r_type, type, (
% 0.30/0.47     r: ( $i * $i ) > $o)).
% 0.30/0.47  tff(1,assumption,(f(c) = f(f(c))), introduced(assumption)).
% 0.30/0.47  tff(2,plain,
% 0.30/0.47      (f(f(c)) = f(c)),
% 0.30/0.47      inference(symmetry,[status(thm)],[1])).
% 0.30/0.47  tff(3,plain,
% 0.30/0.47      (f(f(f(c))) = f(f(c))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[2])).
% 0.30/0.47  tff(4,plain,
% 0.30/0.47      (f(f(c)) = f(f(f(c)))),
% 0.30/0.47      inference(symmetry,[status(thm)],[3])).
% 0.30/0.47  tff(5,assumption,(f(f(f(f(f(c))))) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.47  tff(6,plain,
% 0.30/0.47      (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[5])).
% 0.30/0.47  tff(7,plain,
% 0.30/0.47      ((~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(f(f(c))))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(8,axiom,(~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f64ck')).
% 0.30/0.47  tff(9,plain,
% 0.30/0.47      (~(f(f(f(f(f(f(c)))))) = f(f(f(f(c)))))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[8, 7])).
% 0.30/0.47  tff(10,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[9, 6])).
% 0.30/0.47  tff(11,plain,(~(f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(12,assumption,(f(f(c)) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.47  tff(13,plain,
% 0.30/0.47      (f(f(f(c))) = f(f(c))),
% 0.30/0.47      inference(symmetry,[status(thm)],[12])).
% 0.30/0.47  tff(14,plain,
% 0.30/0.47      (f(f(f(f(c)))) = f(f(f(c)))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[13])).
% 0.30/0.47  tff(15,plain,
% 0.30/0.47      (f(f(f(f(f(c))))) = f(f(f(f(c))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[14])).
% 0.30/0.47  tff(16,plain,
% 0.30/0.47      (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.30/0.47      inference(transitivity,[status(thm)],[15, 14])).
% 0.30/0.47  tff(17,assumption,(~(f(f(f(f(f(c))))) = f(f(f(c))))), introduced(assumption)).
% 0.30/0.47  tff(18,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[17, 16])).
% 0.30/0.47  tff(19,plain,((~(f(f(c)) = f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(20,plain,
% 0.30/0.47      (~(f(f(c)) = f(f(f(c))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[19, 11])).
% 0.30/0.47  tff(21,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[20, 4])).
% 0.30/0.47  tff(22,plain,(~(f(c) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(23,assumption,(c = f(c)), introduced(assumption)).
% 0.30/0.47  tff(24,plain,
% 0.30/0.47      (f(c) = c),
% 0.30/0.47      inference(symmetry,[status(thm)],[23])).
% 0.30/0.47  tff(25,plain,
% 0.30/0.47      (f(f(c)) = f(c)),
% 0.30/0.47      inference(monotonicity,[status(thm)],[24])).
% 0.30/0.47  tff(26,plain,
% 0.30/0.47      (f(c) = f(f(c))),
% 0.30/0.47      inference(symmetry,[status(thm)],[25])).
% 0.30/0.47  tff(27,assumption,(~(f(c) = f(f(c)))), introduced(assumption)).
% 0.30/0.47  tff(28,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[27, 26])).
% 0.30/0.47  tff(29,plain,((~(c = f(c))) | (f(c) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(30,plain,
% 0.30/0.47      (~(c = f(c))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[29, 22])).
% 0.30/0.47  tff(31,plain,
% 0.30/0.47      ((f(c) = c) <=> (c = f(c))),
% 0.30/0.47      inference(commutativity,[status(thm)],[])).
% 0.30/0.47  tff(32,assumption,(f(c) = c), introduced(assumption)).
% 0.30/0.47  tff(33,plain,
% 0.30/0.47      (c = f(c)),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.30/0.47  tff(34,assumption,(~(c = f(c))), introduced(assumption)).
% 0.30/0.47  tff(35,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.30/0.47  tff(36,plain,((~(f(c) = c)) | (c = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(37,plain,
% 0.30/0.47      (~(f(c) = c)),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[36, 30])).
% 0.30/0.47  tff(38,assumption,(f(f(f(f(c)))) = c), introduced(assumption)).
% 0.30/0.47  tff(39,plain,
% 0.30/0.47      (c = f(f(f(f(c))))),
% 0.30/0.47      inference(symmetry,[status(thm)],[38])).
% 0.30/0.47  tff(40,plain,
% 0.30/0.47      (f(c) = f(f(f(f(f(c)))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[39])).
% 0.30/0.47  tff(41,assumption,(f(c) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.47  tff(42,plain,
% 0.30/0.47      (f(f(c)) = f(f(f(f(f(f(c))))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[41])).
% 0.30/0.47  tff(43,plain,
% 0.30/0.47      (f(f(f(f(f(f(c)))))) = f(f(c))),
% 0.30/0.47      inference(symmetry,[status(thm)],[42])).
% 0.30/0.47  tff(44,plain,
% 0.30/0.47      ((~(f(f(f(f(f(f(c)))))) = f(f(c)))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(c))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(45,axiom,(~(f(f(f(f(f(f(c)))))) = f(f(c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f62ck')).
% 0.30/0.47  tff(46,plain,
% 0.30/0.47      (~(f(f(f(f(f(f(c)))))) = f(f(c)))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[45, 44])).
% 0.30/0.47  tff(47,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[46, 43])).
% 0.30/0.47  tff(48,plain,(~(f(c) = f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(49,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[48, 40])).
% 0.30/0.47  tff(50,plain,(~(f(f(f(f(c)))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(51,plain,
% 0.30/0.47      ((c = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = c)),
% 0.30/0.47      inference(commutativity,[status(thm)],[])).
% 0.30/0.47  tff(52,assumption,(c = f(f(f(f(c))))), introduced(assumption)).
% 0.30/0.47  tff(53,plain,
% 0.30/0.47      (f(f(f(f(c)))) = c),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[52, 51])).
% 0.30/0.47  tff(54,assumption,(~(f(f(f(f(c)))) = c)), introduced(assumption)).
% 0.30/0.47  tff(55,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[54, 53])).
% 0.30/0.47  tff(56,plain,((~(c = f(f(f(f(c)))))) | (f(f(f(f(c)))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(57,plain,
% 0.30/0.47      (~(c = f(f(f(f(c)))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[56, 50])).
% 0.30/0.47  tff(58,assumption,(~r(f(f(f(f(f(c))))), f(f(f(c))))), introduced(assumption)).
% 0.30/0.47  tff(59,assumption,(~r(f(f(f(c))), c)), introduced(assumption)).
% 0.30/0.47  tff(60,plain,
% 0.30/0.47      ((f(f(f(c))) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(f(f(c))))),
% 0.30/0.47      inference(commutativity,[status(thm)],[])).
% 0.30/0.47  tff(61,plain,
% 0.30/0.47      ((f(f(f(f(f(c))))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.47      inference(symmetry,[status(thm)],[60])).
% 0.30/0.47  tff(62,plain,
% 0.30/0.47      ((~(f(f(f(f(f(c))))) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[61])).
% 0.30/0.47  tff(63,plain,
% 0.30/0.47      (~(f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[17, 62])).
% 0.30/0.47  tff(64,assumption,(f(f(f(c))) = f(f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.47  tff(65,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[64, 63])).
% 0.30/0.47  tff(66,plain,((~(f(f(f(c))) = f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(67,plain,
% 0.30/0.47      (~(f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[66, 11])).
% 0.30/0.47  tff(68,assumption,(f(f(f(c))) = c), introduced(assumption)).
% 0.30/0.47  tff(69,plain,
% 0.30/0.47      (f(f(f(f(c)))) = f(c)),
% 0.30/0.47      inference(monotonicity,[status(thm)],[68])).
% 0.30/0.47  tff(70,plain,
% 0.30/0.47      (f(c) = f(f(f(f(c))))),
% 0.30/0.47      inference(symmetry,[status(thm)],[69])).
% 0.30/0.47  tff(71,assumption,(f(c) = f(f(f(f(c))))), introduced(assumption)).
% 0.30/0.47  tff(72,plain,
% 0.30/0.47      (f(f(c)) = f(f(f(f(f(c)))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[71])).
% 0.30/0.47  tff(73,plain,
% 0.30/0.47      (f(f(f(c))) = f(f(f(f(f(f(c))))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[72])).
% 0.30/0.47  tff(74,plain,
% 0.30/0.47      (f(f(f(f(f(f(c)))))) = f(f(f(c)))),
% 0.30/0.47      inference(symmetry,[status(thm)],[73])).
% 0.30/0.47  tff(75,plain,
% 0.30/0.47      ((~(f(f(f(f(f(f(c)))))) = f(f(f(c))))) <=> (~(f(f(f(f(f(f(c)))))) = f(f(f(c)))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(76,axiom,(~(f(f(f(f(f(f(c)))))) = f(f(f(c))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f63ck')).
% 0.30/0.47  tff(77,plain,
% 0.30/0.47      (~(f(f(f(f(f(f(c)))))) = f(f(f(c))))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[76, 75])).
% 0.30/0.47  tff(78,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[77, 74])).
% 0.30/0.47  tff(79,plain,(~(f(c) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(80,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[79, 70])).
% 0.30/0.47  tff(81,plain,(~(f(f(f(c))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(82,plain,
% 0.30/0.47      ((f(f(f(f(f(c))))) = c) <=> (c = f(f(f(f(f(c))))))),
% 0.30/0.47      inference(commutativity,[status(thm)],[])).
% 0.30/0.47  tff(83,plain,
% 0.30/0.47      ((~(f(f(f(f(f(c))))) = c)) <=> (~(c = f(f(f(f(f(c)))))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[82])).
% 0.30/0.47  tff(84,assumption,(f(f(f(f(f(c))))) = c), introduced(assumption)).
% 0.30/0.47  tff(85,plain,
% 0.30/0.47      (f(f(f(f(f(f(c)))))) = f(c)),
% 0.30/0.47      inference(monotonicity,[status(thm)],[84])).
% 0.30/0.47  tff(86,plain,
% 0.30/0.47      ((~(f(f(f(f(f(f(c)))))) = f(c))) <=> (~(f(f(f(f(f(f(c)))))) = f(c)))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(87,axiom,(~(f(f(f(f(f(f(c)))))) = f(c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f6ck')).
% 0.30/0.47  tff(88,plain,
% 0.30/0.47      (~(f(f(f(f(f(f(c)))))) = f(c))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[87, 86])).
% 0.30/0.47  tff(89,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[88, 85])).
% 0.30/0.47  tff(90,plain,(~(f(f(f(f(f(c))))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(91,plain,
% 0.30/0.47      (~(c = f(f(f(f(f(c))))))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[90, 83])).
% 0.30/0.47  tff(92,assumption,(~(f(f(f(c))) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.47  tff(93,plain,
% 0.30/0.47      (^[X: $i, Y: $i] : refl(((~r(X, Y)) | r(Y, X)) <=> ((~r(X, Y)) | r(Y, X)))),
% 0.30/0.47      inference(bind,[status(th)],[])).
% 0.30/0.47  tff(94,plain,
% 0.30/0.47      (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.47      inference(quant_intro,[status(thm)],[93])).
% 0.30/0.47  tff(95,plain,
% 0.30/0.47      (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(96,axiom,(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rsym')).
% 0.30/0.47  tff(97,plain,
% 0.30/0.47      (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[96, 95])).
% 0.30/0.47  tff(98,plain,(
% 0.30/0.47      ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.47      inference(skolemize,[status(sab)],[97])).
% 0.30/0.47  tff(99,plain,
% 0.30/0.47      (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[98, 94])).
% 0.30/0.47  tff(100,plain,
% 0.30/0.47      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(c)))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(c)))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(101,plain,
% 0.30/0.47      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(c)))))),
% 0.30/0.47      inference(quant_inst,[status(thm)],[])).
% 0.30/0.47  tff(102,plain,
% 0.30/0.47      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[101, 100])).
% 0.30/0.47  tff(103,plain,
% 0.30/0.47      (~r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[102, 99, 58])).
% 0.30/0.47  tff(104,assumption,(~(c = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.47  tff(105,assumption,(~r(c, f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.47  tff(106,assumption,(~(f(f(f(c))) = c)), introduced(assumption)).
% 0.30/0.47  tff(107,plain,
% 0.30/0.47      (^[X: $i, Y: $i, Z: $i] : refl((r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.30/0.47      inference(bind,[status(th)],[])).
% 0.30/0.47  tff(108,plain,
% 0.30/0.47      (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(quant_intro,[status(thm)],[107])).
% 0.30/0.47  tff(109,plain,
% 0.30/0.47      (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(110,plain,
% 0.30/0.47      (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((X = Y) | (X = Z)) <=> ((X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> (((X = Z) | (X = Y)) | (Y = Z)))), rewrite((((X = Z) | (X = Y)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y))), ((((X = Y) | (X = Z)) | (Y = Z)) <=> ((Y = Z) | (X = Z) | (X = Y)))), (((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) <=> (((Y = Z) | (X = Z) | (X = Y)) | r(X, Y)))), rewrite((((Y = Z) | (X = Z) | (X = Y)) | r(X, Y)) <=> (r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), (((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) <=> (r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> ((r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(X, Z)))), rewrite(((r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(X, Z)) <=> (r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) <=> (r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ((r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)))), rewrite(((r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y)) | r(Y, Z)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))), (((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))))),
% 0.30/0.47      inference(bind,[status(th)],[])).
% 0.30/0.47  tff(111,plain,
% 0.30/0.47      (![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(quant_intro,[status(thm)],[110])).
% 0.30/0.47  tff(112,axiom,(![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | r(X, Y)) | r(X, Z)) | r(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rn3acl')).
% 0.30/0.47  tff(113,plain,
% 0.30/0.47      (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[112, 111])).
% 0.30/0.47  tff(114,plain,
% 0.30/0.47      (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[113, 109])).
% 0.30/0.47  tff(115,plain,(
% 0.30/0.47      ![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(skolemize,[status(sab)],[114])).
% 0.30/0.47  tff(116,plain,
% 0.30/0.47      (![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[115, 108])).
% 0.30/0.47  tff(117,plain,
% 0.30/0.47      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(118,plain,
% 0.30/0.47      ((r(c, f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = c)) <=> (r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(119,plain,
% 0.30/0.47      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c))))))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[118])).
% 0.30/0.47  tff(120,plain,
% 0.30/0.47      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.47      inference(transitivity,[status(thm)],[119, 117])).
% 0.30/0.47  tff(121,plain,
% 0.30/0.47      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = c))),
% 0.30/0.47      inference(quant_inst,[status(thm)],[])).
% 0.30/0.47  tff(122,plain,
% 0.30/0.47      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c))))))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.30/0.47  tff(123,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[122, 116, 59, 106, 105, 104, 103, 92])).
% 0.30/0.47  tff(124,plain,((f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(125,plain,
% 0.30/0.47      ((f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[124, 91])).
% 0.30/0.47  tff(126,plain,
% 0.30/0.47      ((f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), c) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[125, 81])).
% 0.30/0.47  tff(127,plain,
% 0.30/0.47      (r(f(f(f(c))), c) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[126, 67])).
% 0.30/0.47  tff(128,plain,
% 0.30/0.47      (r(c, f(f(f(f(f(c))))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[127, 59, 58])).
% 0.30/0.47  tff(129,plain,
% 0.30/0.47      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(130,plain,
% 0.30/0.47      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c))),
% 0.30/0.47      inference(quant_inst,[status(thm)],[])).
% 0.30/0.47  tff(131,plain,
% 0.30/0.47      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), c)),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[130, 129])).
% 0.30/0.47  tff(132,plain,
% 0.30/0.47      (r(f(f(f(f(f(c))))), c)),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[131, 99, 128])).
% 0.30/0.47  tff(133,assumption,(f(c) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.47  tff(134,plain,
% 0.30/0.47      (f(f(c)) = f(f(f(f(c))))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[133])).
% 0.30/0.47  tff(135,plain,
% 0.30/0.47      (f(f(f(f(c)))) = f(f(c))),
% 0.30/0.47      inference(symmetry,[status(thm)],[134])).
% 0.30/0.47  tff(136,plain,
% 0.30/0.47      (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[135])).
% 0.30/0.47  tff(137,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[17, 136])).
% 0.30/0.47  tff(138,plain,((~(f(c) = f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(139,plain,
% 0.30/0.47      (~(f(c) = f(f(f(c))))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[138, 11])).
% 0.30/0.47  tff(140,assumption,(c = f(f(c))), introduced(assumption)).
% 0.30/0.47  tff(141,plain,
% 0.30/0.47      (f(c) = f(f(f(c)))),
% 0.30/0.47      inference(monotonicity,[status(thm)],[140])).
% 0.30/0.47  tff(142,assumption,(~(f(c) = f(f(f(c))))), introduced(assumption)).
% 0.30/0.47  tff(143,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[142, 141])).
% 0.30/0.47  tff(144,plain,((~(c = f(f(c)))) | (f(c) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(145,plain,
% 0.30/0.47      (~(c = f(f(c)))),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[144, 139])).
% 0.30/0.47  tff(146,plain,
% 0.30/0.47      ((f(f(c)) = c) <=> (c = f(f(c)))),
% 0.30/0.47      inference(commutativity,[status(thm)],[])).
% 0.30/0.47  tff(147,assumption,(f(f(c)) = c), introduced(assumption)).
% 0.30/0.47  tff(148,plain,
% 0.30/0.47      (c = f(f(c))),
% 0.30/0.47      inference(modus_ponens,[status(thm)],[147, 146])).
% 0.30/0.47  tff(149,assumption,(~(c = f(f(c)))), introduced(assumption)).
% 0.30/0.47  tff(150,plain,
% 0.30/0.47      ($false),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[149, 148])).
% 0.30/0.47  tff(151,plain,((~(f(f(c)) = c)) | (c = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.47  tff(152,plain,
% 0.30/0.47      (~(f(f(c)) = c)),
% 0.30/0.47      inference(unit_resolution,[status(thm)],[151, 145])).
% 0.30/0.47  tff(153,assumption,(~r(f(f(c)), c)), introduced(assumption)).
% 0.30/0.47  tff(154,assumption,(~r(f(f(c)), f(f(f(c))))), introduced(assumption)).
% 0.30/0.47  tff(155,assumption,(~r(f(c), f(f(c)))), introduced(assumption)).
% 0.30/0.47  tff(156,plain,
% 0.30/0.47      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(c))) | r(f(c), f(f(c))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(c))) | r(f(c), f(f(c))))),
% 0.30/0.47      inference(rewrite,[status(thm)],[])).
% 0.30/0.47  tff(157,plain,
% 0.30/0.47      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(c))) | r(f(c), f(f(c))))),
% 0.30/0.48      inference(quant_inst,[status(thm)],[])).
% 0.30/0.48  tff(158,plain,
% 0.30/0.48      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(c))) | r(f(c), f(f(c)))),
% 0.30/0.48      inference(modus_ponens,[status(thm)],[157, 156])).
% 0.30/0.48  tff(159,plain,
% 0.30/0.48      (~r(f(f(c)), f(c))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[158, 99, 155])).
% 0.30/0.48  tff(160,assumption,(f(f(c)) = f(c)), introduced(assumption)).
% 0.30/0.48  tff(161,plain,
% 0.30/0.48      (f(c) = f(f(c))),
% 0.30/0.48      inference(symmetry,[status(thm)],[160])).
% 0.30/0.48  tff(162,plain,
% 0.30/0.48      ($false),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[27, 161])).
% 0.30/0.48  tff(163,plain,((~(f(f(c)) = f(c))) | (f(c) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48  tff(164,plain,
% 0.30/0.48      (~(f(f(c)) = f(c))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[163, 27])).
% 0.30/0.48  tff(165,plain,
% 0.30/0.48      (~(c = f(c))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[29, 27])).
% 0.30/0.48  tff(166,plain,
% 0.30/0.48      ((f(f(f(c))) = c) <=> (c = f(f(f(c))))),
% 0.30/0.48      inference(commutativity,[status(thm)],[])).
% 0.30/0.48  tff(167,plain,
% 0.30/0.48      ((c = f(f(f(c)))) <=> (f(f(f(c))) = c)),
% 0.30/0.48      inference(symmetry,[status(thm)],[166])).
% 0.30/0.48  tff(168,assumption,(c = f(f(f(c)))), introduced(assumption)).
% 0.30/0.48  tff(169,plain,
% 0.30/0.48      (f(f(f(c))) = c),
% 0.30/0.48      inference(modus_ponens,[status(thm)],[168, 167])).
% 0.30/0.48  tff(170,plain,
% 0.30/0.48      ($false),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[106, 169])).
% 0.30/0.48  tff(171,plain,((~(c = f(f(f(c))))) | (f(f(f(c))) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48  tff(172,plain,
% 0.30/0.48      (~(c = f(f(f(c))))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[171, 81])).
% 0.30/0.48  tff(173,assumption,(~(f(f(c)) = c)), introduced(assumption)).
% 0.30/0.48  tff(174,assumption,(~(f(f(c)) = f(f(f(c))))), introduced(assumption)).
% 0.30/0.48  tff(175,assumption,(~r(c, f(f(f(c))))), introduced(assumption)).
% 0.30/0.48  tff(176,plain,
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% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(177,plain,
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% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(178,plain,
% 0.30/0.48      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | r(f(f(c)), c) | (c = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | (c = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), c) | (f(f(c)) = c)))),
% 0.30/0.48      inference(monotonicity,[status(thm)],[177])).
% 0.30/0.48  tff(179,plain,
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% 0.30/0.48      inference(transitivity,[status(thm)],[178, 176])).
% 0.30/0.48  tff(180,plain,
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% 0.30/0.48      inference(quant_inst,[status(thm)],[])).
% 0.30/0.48  tff(181,plain,
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% 0.30/0.48      inference(modus_ponens,[status(thm)],[180, 179])).
% 0.30/0.48  tff(182,plain,
% 0.30/0.48      ($false),
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% 0.30/0.48  tff(183,plain,(r(f(f(c)), f(f(f(c)))) | r(c, f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), c) | (f(f(c)) = c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48  tff(184,plain,
% 0.30/0.48      (r(f(f(c)), f(f(f(c)))) | r(c, f(f(f(c)))) | r(f(f(c)), c)),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[183, 20, 152])).
% 0.30/0.48  tff(185,plain,
% 0.30/0.48      (r(c, f(f(f(c))))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[184, 153, 154])).
% 0.30/0.48  tff(186,plain,
% 0.30/0.48      ((f(f(f(c))) = f(f(c))) <=> (f(f(c)) = f(f(f(c))))),
% 0.30/0.48      inference(commutativity,[status(thm)],[])).
% 0.30/0.48  tff(187,plain,
% 0.30/0.48      ((f(f(c)) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(c)))),
% 0.30/0.48      inference(symmetry,[status(thm)],[186])).
% 0.30/0.48  tff(188,plain,
% 0.30/0.48      ((~(f(f(c)) = f(f(f(c))))) <=> (~(f(f(f(c))) = f(f(c))))),
% 0.30/0.48      inference(monotonicity,[status(thm)],[187])).
% 0.30/0.48  tff(189,plain,
% 0.30/0.48      (~(f(f(f(c))) = f(f(c)))),
% 0.30/0.48      inference(modus_ponens,[status(thm)],[174, 188])).
% 0.30/0.48  tff(190,plain,
% 0.30/0.48      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(c)))) | r(f(f(c)), f(f(f(c)))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(c)))) | r(f(f(c)), f(f(f(c)))))),
% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(191,plain,
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% 0.30/0.48      inference(quant_inst,[status(thm)],[])).
% 0.30/0.48  tff(192,plain,
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% 0.30/0.48      inference(modus_ponens,[status(thm)],[191, 190])).
% 0.30/0.48  tff(193,plain,
% 0.30/0.48      (~r(f(f(f(c))), f(f(c)))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[192, 99, 154])).
% 0.30/0.48  tff(194,assumption,(~r(f(c), f(f(f(c))))), introduced(assumption)).
% 0.30/0.48  tff(195,plain,
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% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(196,plain,
% 0.30/0.48      ((r(f(f(f(c))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c))))) <=> ((f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))))),
% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(197,plain,
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% 0.30/0.48      inference(monotonicity,[status(thm)],[196])).
% 0.30/0.48  tff(198,plain,
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% 0.30/0.48      inference(transitivity,[status(thm)],[197, 195])).
% 0.30/0.48  tff(199,plain,
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% 0.30/0.48      inference(quant_inst,[status(thm)],[])).
% 0.30/0.48  tff(200,plain,
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% 0.30/0.48      inference(modus_ponens,[status(thm)],[199, 198])).
% 0.30/0.48  tff(201,plain,
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% 0.30/0.48  tff(202,plain,(r(f(f(c)), f(f(f(c)))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(c)) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.48  tff(203,plain,
% 0.30/0.48      (r(f(f(c)), f(f(f(c)))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(c))))),
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% 0.30/0.48  tff(204,plain,
% 0.30/0.48      (r(f(c), f(f(f(c))))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[203, 155, 154, 27])).
% 0.30/0.48  tff(205,plain,
% 0.30/0.48      (^[X: $i, Y: $i, Z: $i] : refl(((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)) <=> ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y)))),
% 0.30/0.48      inference(bind,[status(th)],[])).
% 0.30/0.48  tff(206,plain,
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% 0.30/0.48      inference(quant_intro,[status(thm)],[205])).
% 0.30/0.48  tff(207,plain,
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% 0.30/0.48      inference(rewrite,[status(thm)],[])).
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% 0.30/0.48      inference(bind,[status(th)],[])).
% 0.30/0.48  tff(209,plain,
% 0.30/0.48      (![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.48      inference(quant_intro,[status(thm)],[208])).
% 0.30/0.48  tff(210,axiom,(![X: $i, Y: $i, Z: $i] : ((((((X = Y) | (X = Z)) | (Y = Z)) | (~r(X, Y))) | (~r(X, Z))) | (~r(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rn3cl')).
% 0.30/0.48  tff(211,plain,
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% 0.30/0.48      inference(modus_ponens,[status(thm)],[210, 209])).
% 0.30/0.48  tff(212,plain,
% 0.30/0.48      (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.48      inference(modus_ponens,[status(thm)],[211, 207])).
% 0.30/0.48  tff(213,plain,(
% 0.30/0.48      ![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.48      inference(skolemize,[status(sab)],[212])).
% 0.30/0.48  tff(214,plain,
% 0.30/0.48      (![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))),
% 0.30/0.48      inference(modus_ponens,[status(thm)],[213, 206])).
% 0.30/0.48  tff(215,plain,
% 0.30/0.48      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (f(c) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(f(c), f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (f(c) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(f(c), f(f(f(c))))))),
% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(216,plain,
% 0.30/0.48      (((~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c))) <=> ((c = f(c)) | (f(c) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(f(c), f(f(f(c))))))),
% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(217,plain,
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% 0.30/0.48      inference(monotonicity,[status(thm)],[216])).
% 0.30/0.48  tff(218,plain,
% 0.30/0.48      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (f(c) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(f(c), f(f(f(c))))))),
% 0.30/0.48      inference(transitivity,[status(thm)],[217, 215])).
% 0.30/0.48  tff(219,plain,
% 0.30/0.48      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(c))) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))),
% 0.30/0.48      inference(quant_inst,[status(thm)],[])).
% 0.30/0.48  tff(220,plain,
% 0.30/0.48      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (f(c) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(c, f(c))) | (~r(f(c), f(f(f(c)))))),
% 0.30/0.48      inference(modus_ponens,[status(thm)],[219, 218])).
% 0.30/0.48  tff(221,plain,
% 0.30/0.48      (~r(c, f(c))),
% 0.30/0.48      inference(unit_resolution,[status(thm)],[220, 214, 165, 204, 139, 185, 172])).
% 0.30/0.48  tff(222,plain,
% 0.30/0.48      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(223,plain,
% 0.30/0.48      ((r(c, f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (c = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = c)) <=> (r(c, f(c)) | (c = f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.30/0.48      inference(rewrite,[status(thm)],[])).
% 0.30/0.48  tff(224,plain,
% 0.30/0.48      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (c = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (f(f(c)) = c)))),
% 0.30/0.48      inference(monotonicity,[status(thm)],[223])).
% 0.30/0.48  tff(225,plain,
% 0.30/0.48      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (c = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.30/0.49      inference(transitivity,[status(thm)],[224, 222])).
% 0.30/0.49  tff(226,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (c = f(c)) | (f(f(c)) = f(c)) | (f(f(c)) = c))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(227,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(c)) = f(c)) | r(f(f(c)), f(c)) | r(f(f(c)), c) | (f(f(c)) = c)),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[226, 225])).
% 0.30/0.49  tff(228,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[227, 116, 221, 165, 164, 153, 152, 159])).
% 0.30/0.49  tff(229,plain,(r(f(c), f(f(c))) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c)))) | (f(c) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(230,plain,
% 0.30/0.49      (r(f(c), f(f(c)))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[229, 27, 154, 153])).
% 0.30/0.49  tff(231,plain,
% 0.30/0.49      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(c)))) | r(f(f(c)), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(c)))) | r(f(f(c)), c))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(232,plain,
% 0.30/0.49      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(c)))) | r(f(f(c)), c))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(233,plain,
% 0.30/0.49      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(c)))) | r(f(f(c)), c)),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[232, 231])).
% 0.30/0.49  tff(234,plain,
% 0.30/0.49      (~r(c, f(f(c)))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[233, 99, 153])).
% 0.30/0.49  tff(235,assumption,(r(c, f(f(f(c))))), introduced(assumption)).
% 0.30/0.49  tff(236,plain,
% 0.30/0.49      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(c))))) | r(f(f(f(c))), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(c))))) | r(f(f(f(c))), c))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(237,plain,
% 0.30/0.49      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(c))))) | r(f(f(f(c))), c))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(238,plain,
% 0.30/0.49      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(c))))) | r(f(f(f(c))), c)),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[237, 236])).
% 0.30/0.49  tff(239,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[238, 99, 235, 59])).
% 0.30/0.49  tff(240,plain,(r(f(f(f(c))), c) | (~r(c, f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(241,plain,
% 0.30/0.49      (r(f(f(f(c))), c)),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[240, 185])).
% 0.30/0.49  tff(242,plain,
% 0.30/0.49      (~(f(f(f(c))) = f(f(c)))),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[20, 188])).
% 0.30/0.49  tff(243,assumption,(~r(f(f(f(f(c)))), f(f(c)))), introduced(assumption)).
% 0.30/0.49  tff(244,assumption,(f(f(f(f(c)))) = f(f(c))), introduced(assumption)).
% 0.30/0.49  tff(245,plain,
% 0.30/0.49      (f(f(c)) = f(f(f(f(c))))),
% 0.30/0.49      inference(symmetry,[status(thm)],[244])).
% 0.30/0.49  tff(246,plain,
% 0.30/0.49      (f(f(f(c))) = f(f(f(f(f(c)))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[245])).
% 0.30/0.49  tff(247,plain,
% 0.30/0.49      (f(f(f(f(f(c))))) = f(f(f(c)))),
% 0.30/0.49      inference(symmetry,[status(thm)],[246])).
% 0.30/0.49  tff(248,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[17, 247])).
% 0.30/0.49  tff(249,plain,((~(f(f(f(f(c)))) = f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(250,plain,
% 0.30/0.49      (~(f(f(f(f(c)))) = f(f(c)))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[249, 11])).
% 0.30/0.49  tff(251,assumption,(~r(f(f(f(c))), f(f(c)))), introduced(assumption)).
% 0.30/0.49  tff(252,assumption,(f(f(f(f(f(c))))) = f(f(f(f(c))))), introduced(assumption)).
% 0.30/0.49  tff(253,plain,
% 0.30/0.49      (f(f(f(f(f(f(c)))))) = f(f(f(f(f(c)))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[252])).
% 0.30/0.49  tff(254,plain,
% 0.30/0.49      (f(f(f(f(f(f(c)))))) = f(f(f(f(c))))),
% 0.30/0.49      inference(transitivity,[status(thm)],[253, 252])).
% 0.30/0.49  tff(255,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[9, 254])).
% 0.30/0.49  tff(256,plain,(~(f(f(f(f(f(c))))) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(257,assumption,(f(f(f(c))) = f(f(f(f(c))))), introduced(assumption)).
% 0.30/0.49  tff(258,plain,
% 0.30/0.49      (f(f(f(f(c)))) = f(f(f(f(f(c)))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[257])).
% 0.30/0.49  tff(259,plain,
% 0.30/0.49      (f(f(f(f(f(c))))) = f(f(f(f(c))))),
% 0.30/0.49      inference(symmetry,[status(thm)],[258])).
% 0.30/0.49  tff(260,assumption,(~(f(f(f(f(f(c))))) = f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.49  tff(261,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[260, 259])).
% 0.30/0.49  tff(262,plain,((~(f(f(f(c))) = f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(263,plain,
% 0.30/0.49      (~(f(f(f(c))) = f(f(f(f(c)))))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[262, 256])).
% 0.30/0.49  tff(264,plain,
% 0.30/0.49      ((f(f(f(f(c)))) = f(f(f(c)))) <=> (f(f(f(c))) = f(f(f(f(c)))))),
% 0.30/0.49      inference(commutativity,[status(thm)],[])).
% 0.30/0.49  tff(265,assumption,(f(f(f(f(c)))) = f(f(f(c)))), introduced(assumption)).
% 0.30/0.49  tff(266,plain,
% 0.30/0.49      (f(f(f(c))) = f(f(f(f(c))))),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[265, 264])).
% 0.30/0.49  tff(267,assumption,(~(f(f(f(c))) = f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.49  tff(268,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[267, 266])).
% 0.30/0.49  tff(269,plain,((~(f(f(f(f(c)))) = f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(270,plain,
% 0.30/0.49      (~(f(f(f(f(c)))) = f(f(f(c))))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[269, 263])).
% 0.30/0.49  tff(271,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(272,plain,
% 0.30/0.49      ((r(f(f(f(c))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c))))) <=> ((f(f(f(f(c)))) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(273,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[272])).
% 0.30/0.49  tff(274,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.49      inference(transitivity,[status(thm)],[273, 271])).
% 0.30/0.49  tff(275,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(276,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[275, 274])).
% 0.30/0.49  tff(277,plain,
% 0.30/0.49      (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[276, 116, 270, 251, 250, 243, 242])).
% 0.30/0.49  tff(278,assumption,(~r(c, f(f(c)))), introduced(assumption)).
% 0.30/0.49  tff(279,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(280,plain,
% 0.30/0.49      ((r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c)) <=> ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(281,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[280])).
% 0.30/0.49  tff(282,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.49      inference(transitivity,[status(thm)],[281, 279])).
% 0.30/0.49  tff(283,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), c) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(284,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[283, 282])).
% 0.30/0.49  tff(285,plain,
% 0.30/0.49      (r(f(f(f(f(c)))), c)),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[284, 116, 145, 50, 278, 250, 243])).
% 0.30/0.49  tff(286,assumption,(r(f(f(f(c))), c)), introduced(assumption)).
% 0.30/0.49  tff(287,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(288,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(289,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c))))),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[288, 287])).
% 0.30/0.49  tff(290,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[289, 214, 286, 81, 50, 285, 270, 277])).
% 0.30/0.49  tff(291,plain,(r(f(f(f(f(c)))), f(f(c))) | (~r(f(f(f(c))), c)) | r(f(f(f(c))), f(f(c))) | r(c, f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(292,plain,
% 0.30/0.49      (r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[291, 193, 241, 234])).
% 0.30/0.49  tff(293,assumption,(r(f(c), f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.49  tff(294,assumption,(r(f(f(f(f(c)))), f(f(c)))), introduced(assumption)).
% 0.30/0.49  tff(295,assumption,(r(f(c), f(f(c)))), introduced(assumption)).
% 0.30/0.49  tff(296,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(297,plain,
% 0.30/0.49      (((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c)))))) <=> ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.30/0.49      inference(rewrite,[status(thm)],[])).
% 0.30/0.49  tff(298,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(f(f(c))))))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[297])).
% 0.30/0.49  tff(299,plain,
% 0.30/0.49      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.30/0.49      inference(transitivity,[status(thm)],[298, 296])).
% 0.30/0.49  tff(300,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c))))))),
% 0.30/0.49      inference(quant_inst,[status(thm)],[])).
% 0.30/0.49  tff(301,plain,
% 0.30/0.49      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(c), f(f(f(f(c))))))),
% 0.30/0.49      inference(modus_ponens,[status(thm)],[300, 299])).
% 0.30/0.49  tff(302,plain,
% 0.30/0.49      ($false),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[301, 214, 27, 295, 79, 250, 294, 293])).
% 0.30/0.49  tff(303,plain,((~r(f(c), f(f(f(f(c)))))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.49  tff(304,plain,
% 0.30/0.49      (~r(f(c), f(f(f(f(c)))))),
% 0.30/0.49      inference(unit_resolution,[status(thm)],[303, 292, 230, 27])).
% 0.30/0.49  tff(305,plain,
% 0.30/0.49      ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.30/0.49      inference(commutativity,[status(thm)],[])).
% 0.30/0.49  tff(306,plain,
% 0.30/0.49      ((f(f(f(f(f(c))))) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.49      inference(symmetry,[status(thm)],[305])).
% 0.30/0.49  tff(307,plain,
% 0.30/0.49      ((~(f(f(f(f(f(c))))) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.49      inference(monotonicity,[status(thm)],[306])).
% 0.30/0.49  tff(308,plain,
% 0.30/0.50      (~(f(f(f(f(c)))) = f(f(f(f(f(c))))))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[256, 307])).
% 0.30/0.50  tff(309,assumption,(r(f(f(c)), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.50  tff(310,plain,
% 0.30/0.50      ((f(f(c)) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(f(c)))),
% 0.30/0.50      inference(commutativity,[status(thm)],[])).
% 0.30/0.50  tff(311,plain,
% 0.30/0.50      ((f(f(f(f(f(c))))) = f(f(c))) <=> (f(f(c)) = f(f(f(f(f(c))))))),
% 0.30/0.50      inference(symmetry,[status(thm)],[310])).
% 0.30/0.50  tff(312,plain,
% 0.30/0.50      ((~(f(f(f(f(f(c))))) = f(f(c)))) <=> (~(f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(monotonicity,[status(thm)],[311])).
% 0.30/0.50  tff(313,assumption,(f(f(f(f(f(c))))) = f(f(c))), introduced(assumption)).
% 0.30/0.50  tff(314,plain,
% 0.30/0.50      (f(f(f(f(f(f(c)))))) = f(f(f(c)))),
% 0.30/0.50      inference(monotonicity,[status(thm)],[313])).
% 0.30/0.50  tff(315,plain,
% 0.30/0.50      ($false),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[77, 314])).
% 0.30/0.50  tff(316,plain,(~(f(f(f(f(f(c))))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50  tff(317,plain,
% 0.30/0.50      (~(f(f(c)) = f(f(f(f(f(c))))))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[316, 312])).
% 0.30/0.50  tff(318,assumption,(r(f(f(f(f(c)))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.50  tff(319,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(320,plain,
% 0.30/0.50      (((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c)))) <=> ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(321,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c))))))),
% 0.30/0.50      inference(monotonicity,[status(thm)],[320])).
% 0.30/0.50  tff(322,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.50      inference(transitivity,[status(thm)],[321, 319])).
% 0.30/0.50  tff(323,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))))),
% 0.30/0.50      inference(quant_inst,[status(thm)],[])).
% 0.30/0.50  tff(324,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[323, 322])).
% 0.30/0.50  tff(325,plain,
% 0.30/0.50      ($false),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[324, 214, 250, 318, 309, 317, 308, 294])).
% 0.30/0.50  tff(326,plain,((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50  tff(327,plain,
% 0.30/0.50      (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[326, 292, 309])).
% 0.30/0.50  tff(328,plain,
% 0.30/0.50      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(329,plain,
% 0.30/0.50      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c))))),
% 0.30/0.50      inference(quant_inst,[status(thm)],[])).
% 0.30/0.50  tff(330,plain,
% 0.30/0.50      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(f(c)))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[329, 328])).
% 0.30/0.50  tff(331,plain,
% 0.30/0.50      (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[330, 99, 309])).
% 0.30/0.50  tff(332,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(333,plain,
% 0.30/0.50      (((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c))))))) <=> ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(334,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))))),
% 0.30/0.50      inference(monotonicity,[status(thm)],[333])).
% 0.30/0.50  tff(335,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.30/0.50      inference(transitivity,[status(thm)],[334, 332])).
% 0.30/0.50  tff(336,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(quant_inst,[status(thm)],[])).
% 0.30/0.50  tff(337,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[336, 335])).
% 0.30/0.50  tff(338,plain,
% 0.30/0.50      (~r(f(c), f(f(f(f(f(c))))))),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[337, 214, 27, 230, 48, 316, 331])).
% 0.30/0.50  tff(339,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(340,plain,
% 0.30/0.50      ((r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c)))))) <=> (r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(341,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))))),
% 0.30/0.50      inference(monotonicity,[status(thm)],[340])).
% 0.30/0.50  tff(342,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.30/0.50      inference(transitivity,[status(thm)],[341, 339])).
% 0.30/0.50  tff(343,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(f(c)))))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))))),
% 0.30/0.50      inference(quant_inst,[status(thm)],[])).
% 0.30/0.50  tff(344,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[343, 342])).
% 0.30/0.50  tff(345,plain,
% 0.30/0.50      ($false),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[344, 116, 338, 48, 79, 327, 308, 304])).
% 0.30/0.50  tff(346,plain,((~r(f(f(c)), f(f(f(f(f(c))))))) | (f(c) = f(f(c))) | r(f(f(c)), f(f(f(c)))) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50  tff(347,plain,
% 0.30/0.50      (~r(f(f(c)), f(f(f(f(f(c))))))),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[346, 27, 154, 153])).
% 0.30/0.50  tff(348,assumption,(~r(f(f(c)), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.50  tff(349,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(350,plain,
% 0.30/0.50      ((r(c, f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), c) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c)) <=> (r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(351,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), c) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c))))))))),
% 0.30/0.50      inference(monotonicity,[status(thm)],[350])).
% 0.30/0.50  tff(352,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), c) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(transitivity,[status(thm)],[351, 349])).
% 0.30/0.50  tff(353,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), c) | (c = f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(f(c)) = c))),
% 0.30/0.50      inference(quant_inst,[status(thm)],[])).
% 0.30/0.50  tff(354,plain,
% 0.30/0.50      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c))))))),
% 0.30/0.50      inference(modus_ponens,[status(thm)],[353, 352])).
% 0.30/0.50  tff(355,plain,
% 0.30/0.50      ($false),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[354, 116, 105, 91, 153, 152, 348, 317])).
% 0.30/0.50  tff(356,plain,(r(f(f(c)), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.50  tff(357,plain,
% 0.30/0.50      (r(c, f(f(f(f(f(c))))))),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[356, 347, 153])).
% 0.30/0.50  tff(358,plain,
% 0.30/0.50      (r(f(f(f(f(f(c))))), c)),
% 0.30/0.50      inference(unit_resolution,[status(thm)],[131, 99, 357])).
% 0.30/0.50  tff(359,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(360,plain,
% 0.30/0.50      (((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(f(c))))))) <=> ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.30/0.50      inference(rewrite,[status(thm)],[])).
% 0.30/0.50  tff(361,plain,
% 0.30/0.50      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c))))))))),
% 0.30/0.51      inference(monotonicity,[status(thm)],[360])).
% 0.30/0.51  tff(362,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.30/0.51      inference(transitivity,[status(thm)],[361, 359])).
% 0.30/0.51  tff(363,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(f(c)))))))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(364,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[363, 362])).
% 0.30/0.51  tff(365,plain,
% 0.30/0.51      (~r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[364, 214, 241, 81, 67, 90, 358])).
% 0.30/0.51  tff(366,plain,
% 0.30/0.51      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(367,plain,
% 0.30/0.51      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(368,plain,
% 0.30/0.51      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[367, 366])).
% 0.30/0.51  tff(369,plain,
% 0.30/0.51      (~r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[368, 99, 243])).
% 0.30/0.51  tff(370,assumption,(~r(f(f(c)), f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.51  tff(371,assumption,(f(f(c)) = f(f(f(f(c))))), introduced(assumption)).
% 0.30/0.51  tff(372,plain,
% 0.30/0.51      (f(f(f(f(c)))) = f(f(c))),
% 0.30/0.51      inference(symmetry,[status(thm)],[371])).
% 0.30/0.51  tff(373,plain,
% 0.30/0.51      ($false),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[250, 372])).
% 0.30/0.51  tff(374,plain,(~(f(f(c)) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51  tff(375,assumption,(~r(c, f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.51  tff(376,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(377,plain,
% 0.30/0.51      ((r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), c) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c)) <=> ((f(f(c)) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(378,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), c) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c)))))))),
% 0.30/0.51      inference(monotonicity,[status(thm)],[377])).
% 0.30/0.51  tff(379,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), c) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.51      inference(transitivity,[status(thm)],[378, 376])).
% 0.30/0.51  tff(380,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), c) | (c = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = c))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(381,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(c)), c) | (f(f(c)) = c) | r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[380, 379])).
% 0.30/0.51  tff(382,plain,
% 0.30/0.51      ($false),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[381, 116, 153, 152, 375, 57, 374, 370])).
% 0.30/0.51  tff(383,plain,(r(c, f(f(f(f(c))))) | r(f(f(c)), c) | r(f(f(c)), f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51  tff(384,plain,
% 0.30/0.51      (r(c, f(f(f(f(c)))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[383, 369, 153])).
% 0.30/0.51  tff(385,assumption,(r(c, f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.51  tff(386,assumption,(~r(f(f(f(f(c)))), c)), introduced(assumption)).
% 0.30/0.51  tff(387,plain,
% 0.30/0.51      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(388,plain,
% 0.30/0.51      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(389,plain,
% 0.30/0.51      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[388, 387])).
% 0.30/0.51  tff(390,plain,
% 0.30/0.51      ($false),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[389, 99, 386, 385])).
% 0.30/0.51  tff(391,plain,((~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51  tff(392,plain,
% 0.30/0.51      (r(f(f(f(f(c)))), c)),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[391, 384])).
% 0.30/0.51  tff(393,plain,
% 0.30/0.51      ((f(f(c)) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(f(c)))),
% 0.30/0.51      inference(commutativity,[status(thm)],[])).
% 0.30/0.51  tff(394,plain,
% 0.30/0.51      ((f(f(f(f(c)))) = f(f(c))) <=> (f(f(c)) = f(f(f(f(c)))))),
% 0.30/0.51      inference(symmetry,[status(thm)],[393])).
% 0.30/0.51  tff(395,plain,
% 0.30/0.51      ((~(f(f(f(f(c)))) = f(f(c)))) <=> (~(f(f(c)) = f(f(f(f(c))))))),
% 0.30/0.51      inference(monotonicity,[status(thm)],[394])).
% 0.30/0.51  tff(396,plain,
% 0.30/0.51      (~(f(f(c)) = f(f(f(f(c)))))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[250, 395])).
% 0.30/0.51  tff(397,assumption,(~r(f(f(f(c))), f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.51  tff(398,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(399,plain,
% 0.30/0.51      ((r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c))))) <=> (r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(400,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(c)))))))),
% 0.30/0.51      inference(monotonicity,[status(thm)],[399])).
% 0.30/0.51  tff(401,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.51      inference(transitivity,[status(thm)],[400, 398])).
% 0.30/0.51  tff(402,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(403,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[402, 401])).
% 0.30/0.51  tff(404,plain,
% 0.30/0.51      ($false),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[403, 116, 20, 154, 397, 267, 396, 369])).
% 0.30/0.51  tff(405,plain,(r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51  tff(406,plain,
% 0.30/0.51      (r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), f(f(f(f(c)))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[405, 263])).
% 0.30/0.51  tff(407,plain,
% 0.30/0.51      (r(f(f(f(c))), f(f(f(f(c)))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[406, 243, 154])).
% 0.30/0.51  tff(408,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(409,plain,
% 0.30/0.51      (((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c)))))) <=> ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(410,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 0.30/0.51      inference(monotonicity,[status(thm)],[409])).
% 0.30/0.51  tff(411,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.30/0.51      inference(transitivity,[status(thm)],[410, 408])).
% 0.30/0.51  tff(412,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(413,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[412, 411])).
% 0.30/0.51  tff(414,plain,
% 0.30/0.51      ($false),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[413, 214, 241, 81, 407, 263, 50, 392])).
% 0.30/0.51  tff(415,plain,(r(f(f(f(f(c)))), f(f(c))) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.51  tff(416,plain,
% 0.30/0.51      (r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[415, 153, 154])).
% 0.30/0.51  tff(417,plain,
% 0.30/0.51      (~r(f(c), f(f(f(f(c)))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[303, 230, 416, 27])).
% 0.30/0.51  tff(418,plain,
% 0.30/0.51      (~(f(c) = c)),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[36, 165])).
% 0.30/0.51  tff(419,assumption,(r(c, f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.51  tff(420,plain,
% 0.30/0.51      (r(f(f(f(f(f(c))))), c)),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[131, 99, 419])).
% 0.30/0.51  tff(421,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(422,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(c)))))),
% 0.30/0.51      inference(quant_inst,[status(thm)],[])).
% 0.30/0.51  tff(423,plain,
% 0.30/0.51      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(c))))),
% 0.30/0.51      inference(modus_ponens,[status(thm)],[422, 421])).
% 0.30/0.51  tff(424,plain,
% 0.30/0.51      (~r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[423, 214, 11, 286, 81, 90, 420])).
% 0.30/0.51  tff(425,plain,
% 0.30/0.51      (~(f(c) = c)),
% 0.30/0.51      inference(unit_resolution,[status(thm)],[36, 34])).
% 0.30/0.51  tff(426,assumption,(r(f(c), c)), introduced(assumption)).
% 0.30/0.51  tff(427,plain,
% 0.30/0.51      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(c) = f(f(f(c)))) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(c)))) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c))),
% 0.30/0.51      inference(rewrite,[status(thm)],[])).
% 0.30/0.51  tff(428,plain,
% 0.30/0.51      (((~r(f(f(f(c))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c))))) <=> ((f(c) = c) | (f(c) = f(f(f(c)))) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(429,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(c) = f(f(f(c)))) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c)))),
% 0.30/0.52      inference(monotonicity,[status(thm)],[428])).
% 0.30/0.52  tff(430,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(c)))) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c))),
% 0.30/0.52      inference(transitivity,[status(thm)],[429, 427])).
% 0.30/0.52  tff(431,plain,
% 0.30/0.52      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))),
% 0.30/0.52      inference(quant_inst,[status(thm)],[])).
% 0.30/0.52  tff(432,plain,
% 0.30/0.52      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(c)))) | (~r(f(c), c)) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c)),
% 0.30/0.52      inference(modus_ponens,[status(thm)],[431, 430])).
% 0.30/0.52  tff(433,plain,
% 0.30/0.52      (~r(f(c), f(f(f(c))))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[432, 214, 139, 286, 81, 426, 425])).
% 0.30/0.52  tff(434,plain,
% 0.30/0.52      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), c)) | r(c, f(c)))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), c)) | r(c, f(c)))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(435,plain,
% 0.30/0.52      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), c)) | r(c, f(c)))),
% 0.30/0.52      inference(quant_inst,[status(thm)],[])).
% 0.30/0.52  tff(436,plain,
% 0.30/0.52      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), c)) | r(c, f(c))),
% 0.30/0.52      inference(modus_ponens,[status(thm)],[435, 434])).
% 0.30/0.52  tff(437,plain,
% 0.30/0.52      (r(c, f(c))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[436, 99, 426])).
% 0.30/0.52  tff(438,assumption,(~(f(c) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.52  tff(439,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(440,plain,
% 0.30/0.52      ((r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(441,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c))))))))),
% 0.30/0.52      inference(monotonicity,[status(thm)],[440])).
% 0.30/0.52  tff(442,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(transitivity,[status(thm)],[441, 439])).
% 0.30/0.52  tff(443,plain,
% 0.30/0.52      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(quant_inst,[status(thm)],[])).
% 0.30/0.52  tff(444,plain,
% 0.30/0.52      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c))))))),
% 0.30/0.52      inference(modus_ponens,[status(thm)],[443, 442])).
% 0.30/0.52  tff(445,plain,
% 0.30/0.52      (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c))))))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[444, 116])).
% 0.30/0.52  tff(446,plain,
% 0.30/0.52      (r(f(c), f(f(f(f(f(c))))))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[445, 438, 194, 142, 17, 58])).
% 0.30/0.52  tff(447,plain,
% 0.30/0.52      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(c)))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(c)))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(448,plain,
% 0.30/0.52      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(c)))),
% 0.30/0.52      inference(quant_inst,[status(thm)],[])).
% 0.30/0.52  tff(449,plain,
% 0.30/0.52      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(f(f(c))))))) | r(f(f(f(f(f(c))))), f(c))),
% 0.30/0.52      inference(modus_ponens,[status(thm)],[448, 447])).
% 0.30/0.52  tff(450,plain,
% 0.30/0.52      (r(f(f(f(f(f(c))))), f(c))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[449, 99, 446])).
% 0.30/0.52  tff(451,assumption,(r(c, f(c))), introduced(assumption)).
% 0.30/0.52  tff(452,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(453,plain,
% 0.30/0.52      (((~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c))))))) <=> ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(454,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c))))))))),
% 0.30/0.52      inference(monotonicity,[status(thm)],[453])).
% 0.30/0.52  tff(455,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(transitivity,[status(thm)],[454, 452])).
% 0.30/0.52  tff(456,plain,
% 0.30/0.52      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(c))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.52      inference(quant_inst,[status(thm)],[])).
% 0.30/0.52  tff(457,plain,
% 0.30/0.52      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c))))))),
% 0.30/0.52      inference(modus_ponens,[status(thm)],[456, 455])).
% 0.30/0.52  tff(458,plain,
% 0.30/0.52      (f(f(f(f(f(c))))) = f(c)),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[457, 214, 451, 34, 419, 91, 450])).
% 0.30/0.52  tff(459,plain,
% 0.30/0.52      (f(c) = f(f(f(f(f(c)))))),
% 0.30/0.52      inference(symmetry,[status(thm)],[458])).
% 0.30/0.52  tff(460,plain,
% 0.30/0.52      ($false),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[438, 459])).
% 0.30/0.52  tff(461,plain,((f(c) = f(f(f(f(f(c)))))) | (~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(f(c))))))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52  tff(462,plain,
% 0.30/0.52      ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(f(c))))))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[461, 48])).
% 0.30/0.52  tff(463,plain,
% 0.30/0.52      ((~r(c, f(c))) | (c = f(c)) | (~r(c, f(f(f(f(f(c))))))) | r(f(c), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[462, 139, 11])).
% 0.30/0.52  tff(464,plain,
% 0.30/0.52      ($false),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[463, 437, 433, 419, 34, 424])).
% 0.30/0.52  tff(465,plain,((~r(f(c), c)) | (~r(c, f(f(f(f(f(c))))))) | (c = f(c)) | (~r(f(f(f(c))), c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.52  tff(466,plain,
% 0.30/0.52      (~r(f(c), c)),
% 0.30/0.52      inference(unit_resolution,[status(thm)],[465, 357, 165, 241])).
% 0.30/0.52  tff(467,assumption,(~r(f(c), f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.52  tff(468,assumption,(~(f(c) = c)), introduced(assumption)).
% 0.30/0.52  tff(469,assumption,(~r(f(c), c)), introduced(assumption)).
% 0.30/0.52  tff(470,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(471,plain,
% 0.30/0.52      ((r(f(f(f(f(c)))), c) | r(f(c), c) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(c)))))) <=> ((f(c) = c) | r(f(c), c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.30/0.52      inference(rewrite,[status(thm)],[])).
% 0.30/0.52  tff(472,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(c), c) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))))),
% 0.30/0.52      inference(monotonicity,[status(thm)],[471])).
% 0.30/0.52  tff(473,plain,
% 0.30/0.52      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(c), c) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.30/0.53      inference(transitivity,[status(thm)],[472, 470])).
% 0.30/0.53  tff(474,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(c), c) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(c) = c) | (f(c) = f(f(f(f(c))))))),
% 0.30/0.53      inference(quant_inst,[status(thm)],[])).
% 0.30/0.53  tff(475,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))),
% 0.30/0.53      inference(modus_ponens,[status(thm)],[474, 473])).
% 0.30/0.53  tff(476,plain,
% 0.30/0.53      ($false),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[475, 116, 50, 386, 79, 469, 468, 467])).
% 0.30/0.53  tff(477,plain,(r(f(c), c) | r(f(f(f(f(c)))), c) | (f(c) = c) | r(f(c), f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53  tff(478,plain,
% 0.30/0.53      (r(f(f(f(f(c)))), c)),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[477, 466, 418, 417])).
% 0.30/0.53  tff(479,assumption,(~r(f(f(f(c))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.53  tff(480,assumption,(~(f(f(f(f(c)))) = f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.53  tff(481,assumption,(~r(f(f(f(f(c)))), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.30/0.53  tff(482,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(483,plain,
% 0.30/0.53      ((r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))) <=> (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(484,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))))),
% 0.30/0.53      inference(monotonicity,[status(thm)],[483])).
% 0.30/0.53  tff(485,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.30/0.53      inference(transitivity,[status(thm)],[484, 482])).
% 0.30/0.53  tff(486,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.30/0.53      inference(quant_inst,[status(thm)],[])).
% 0.30/0.53  tff(487,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.53      inference(modus_ponens,[status(thm)],[486, 485])).
% 0.30/0.53  tff(488,plain,
% 0.30/0.53      (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[487, 116, 92, 481])).
% 0.30/0.53  tff(489,plain,
% 0.30/0.53      (r(f(f(f(c))), f(f(f(f(c)))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[488, 267, 480, 479])).
% 0.30/0.53  tff(490,assumption,(r(f(f(f(f(c)))), c)), introduced(assumption)).
% 0.30/0.53  tff(491,plain,
% 0.30/0.53      ((f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[413, 214, 286, 81, 54, 490])).
% 0.30/0.53  tff(492,plain,
% 0.30/0.53      ($false),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[491, 489, 267])).
% 0.30/0.53  tff(493,plain,((f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53  tff(494,plain,
% 0.30/0.53      ((f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[493, 50])).
% 0.30/0.53  tff(495,plain,
% 0.30/0.53      ((f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[494, 67])).
% 0.30/0.53  tff(496,plain,
% 0.30/0.53      ((~r(f(f(f(c))), c)) | (~r(f(f(f(f(c)))), c)) | r(f(f(f(c))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[495, 263, 308])).
% 0.30/0.53  tff(497,plain,
% 0.30/0.53      (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[496, 478, 241, 365])).
% 0.30/0.53  tff(498,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(499,plain,
% 0.30/0.53      (((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))) <=> ((~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(500,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(f(f(f(c)))))))))),
% 0.30/0.53      inference(monotonicity,[status(thm)],[499])).
% 0.30/0.53  tff(501,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))))),
% 0.30/0.53      inference(transitivity,[status(thm)],[500, 498])).
% 0.30/0.53  tff(502,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.30/0.53      inference(quant_inst,[status(thm)],[])).
% 0.30/0.53  tff(503,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (~r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.30/0.53      inference(modus_ponens,[status(thm)],[502, 501])).
% 0.30/0.53  tff(504,plain,
% 0.30/0.53      ($false),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[503, 214, 90, 50, 478, 497, 308, 358])).
% 0.30/0.53  tff(505,plain,((f(c) = f(f(c))) | r(f(f(c)), c) | r(f(f(c)), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.53  tff(506,plain,
% 0.30/0.53      (r(f(f(c)), f(f(f(c))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[505, 153, 22])).
% 0.30/0.53  tff(507,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(508,plain,
% 0.30/0.53      ((r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c)))))) <=> ((f(f(f(f(c)))) = f(f(c))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(509,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.53      inference(monotonicity,[status(thm)],[508])).
% 0.30/0.53  tff(510,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.53      inference(transitivity,[status(thm)],[509, 507])).
% 0.30/0.53  tff(511,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(c, f(f(c))) | r(c, f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))),
% 0.30/0.53      inference(quant_inst,[status(thm)],[])).
% 0.30/0.53  tff(512,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(c, f(f(c))) | (c = f(f(c))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.53      inference(modus_ponens,[status(thm)],[511, 510])).
% 0.30/0.53  tff(513,plain,
% 0.30/0.53      (r(c, f(f(f(f(c)))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[512, 116, 145, 234, 57, 250, 243])).
% 0.30/0.53  tff(514,plain,
% 0.30/0.53      (r(f(f(f(f(c)))), c)),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[284, 116, 145, 50, 234, 250, 243])).
% 0.30/0.53  tff(515,plain,
% 0.30/0.53      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), c)) | r(c, f(f(f(c)))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), c)) | r(c, f(f(f(c)))))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(516,plain,
% 0.30/0.53      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), c)) | r(c, f(f(f(c)))))),
% 0.30/0.53      inference(quant_inst,[status(thm)],[])).
% 0.30/0.53  tff(517,plain,
% 0.30/0.53      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), c)) | r(c, f(f(f(c))))),
% 0.30/0.53      inference(modus_ponens,[status(thm)],[516, 515])).
% 0.30/0.53  tff(518,plain,
% 0.30/0.53      (~r(f(f(f(c))), c)),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[517, 99, 175])).
% 0.30/0.53  tff(519,plain,
% 0.30/0.53      (~r(c, f(f(f(f(c)))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[391, 386])).
% 0.30/0.53  tff(520,plain,
% 0.30/0.53      (r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[383, 519, 153])).
% 0.30/0.53  tff(521,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(522,plain,
% 0.30/0.53      ((r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c)))))) <=> (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c))),
% 0.30/0.53      inference(rewrite,[status(thm)],[])).
% 0.30/0.53  tff(523,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c)))),
% 0.30/0.53      inference(monotonicity,[status(thm)],[522])).
% 0.30/0.53  tff(524,plain,
% 0.30/0.53      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c))),
% 0.30/0.53      inference(transitivity,[status(thm)],[523, 521])).
% 0.30/0.53  tff(525,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.30/0.53      inference(quant_inst,[status(thm)],[])).
% 0.30/0.53  tff(526,plain,
% 0.30/0.53      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c)),
% 0.30/0.53      inference(modus_ponens,[status(thm)],[525, 524])).
% 0.30/0.53  tff(527,plain,
% 0.30/0.53      (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c)),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[526, 116])).
% 0.30/0.53  tff(528,plain,
% 0.30/0.53      (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), c)),
% 0.30/0.53      inference(unit_resolution,[status(thm)],[527, 81, 50])).
% 0.30/0.54  tff(529,plain,
% 0.30/0.54      (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(f(c))), c) | r(f(f(f(f(c)))), c)),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[528, 263])).
% 0.30/0.54  tff(530,plain,
% 0.30/0.54      (r(f(f(f(c))), f(f(f(f(c)))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[529, 386, 59])).
% 0.30/0.54  tff(531,plain,
% 0.30/0.54      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(532,plain,
% 0.30/0.54      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(533,plain,
% 0.30/0.54      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(f(c)))) | r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[532, 531])).
% 0.30/0.54  tff(534,plain,
% 0.30/0.54      (r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[533, 99, 294])).
% 0.30/0.54  tff(535,assumption,(~(f(f(f(f(c)))) = f(f(c)))), introduced(assumption)).
% 0.30/0.54  tff(536,plain,
% 0.30/0.54      (~(f(f(c)) = f(f(f(f(c)))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[535, 395])).
% 0.30/0.54  tff(537,assumption,(r(f(f(f(c))), f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.54  tff(538,assumption,(r(f(f(c)), f(f(f(c))))), introduced(assumption)).
% 0.30/0.54  tff(539,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(540,plain,
% 0.30/0.54      (((~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c))))) <=> ((f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(541,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 0.30/0.54      inference(monotonicity,[status(thm)],[540])).
% 0.30/0.54  tff(542,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.30/0.54      inference(transitivity,[status(thm)],[541, 539])).
% 0.30/0.54  tff(543,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(544,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[543, 542])).
% 0.30/0.54  tff(545,plain,
% 0.30/0.54      ($false),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[544, 214, 174, 538, 537, 267, 536, 534])).
% 0.30/0.54  tff(546,plain,((~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54  tff(547,plain,
% 0.30/0.54      ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[546, 250, 20])).
% 0.30/0.54  tff(548,plain,
% 0.30/0.54      ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[547, 263])).
% 0.30/0.54  tff(549,plain,
% 0.30/0.54      (~r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[548, 530, 506])).
% 0.30/0.54  tff(550,plain,
% 0.30/0.54      ($false),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[368, 99, 549, 520])).
% 0.30/0.54  tff(551,plain,(r(f(f(f(f(c)))), c) | r(f(f(c)), c) | r(f(f(f(c))), c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54  tff(552,plain,
% 0.30/0.54      (r(f(f(f(f(c)))), c)),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[551, 59, 153])).
% 0.30/0.54  tff(553,plain,
% 0.30/0.54      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), c)) | r(c, f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), c)) | r(c, f(f(f(f(c))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(554,plain,
% 0.30/0.54      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), c)) | r(c, f(f(f(f(c))))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(555,plain,
% 0.30/0.54      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), c)) | r(c, f(f(f(f(c)))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[554, 553])).
% 0.30/0.54  tff(556,plain,
% 0.30/0.54      ($false),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[555, 99, 490, 375])).
% 0.30/0.54  tff(557,plain,(r(c, f(f(f(f(c))))) | (~r(f(f(f(f(c)))), c))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54  tff(558,plain,
% 0.30/0.54      (r(c, f(f(f(f(c)))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[557, 552])).
% 0.30/0.54  tff(559,assumption,(~r(f(f(f(f(f(c))))), f(f(f(f(c)))))), introduced(assumption)).
% 0.30/0.54  tff(560,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(561,plain,
% 0.30/0.54      ((r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(c))))))) <=> ((f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(562,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c)))))))),
% 0.30/0.54      inference(monotonicity,[status(thm)],[561])).
% 0.30/0.54  tff(563,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))))),
% 0.30/0.54      inference(transitivity,[status(thm)],[562, 560])).
% 0.30/0.54  tff(564,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(c))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(565,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(c)) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c)))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[564, 563])).
% 0.30/0.54  tff(566,plain,
% 0.30/0.54      ($false),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[565, 116, 559, 256, 348, 317, 374, 370])).
% 0.30/0.54  tff(567,plain,(r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54  tff(568,plain,
% 0.30/0.54      (r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[567, 348, 370])).
% 0.30/0.54  tff(569,plain,
% 0.30/0.54      (r(c, f(f(f(f(f(c))))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[356, 348, 153])).
% 0.30/0.54  tff(570,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(571,plain,
% 0.30/0.54      (((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(f(f(f(c))))))) <=> ((c = f(f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(572,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c))))))))),
% 0.30/0.54      inference(monotonicity,[status(thm)],[571])).
% 0.30/0.54  tff(573,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))))),
% 0.30/0.54      inference(transitivity,[status(thm)],[572, 570])).
% 0.30/0.54  tff(574,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(f(f(f(c)))))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(575,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c))))))),
% 0.30/0.54      inference(modus_ponens,[status(thm)],[574, 573])).
% 0.30/0.54  tff(576,plain,
% 0.30/0.54      ($false),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[575, 214, 569, 91, 568, 385, 57, 256])).
% 0.30/0.54  tff(577,plain,(r(f(f(c)), f(f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | r(f(f(c)), f(f(f(f(c))))) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.54  tff(578,plain,
% 0.30/0.54      (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.30/0.54      inference(unit_resolution,[status(thm)],[577, 369, 558, 153])).
% 0.30/0.54  tff(579,assumption,(r(f(f(f(f(f(c))))), f(f(f(c))))), introduced(assumption)).
% 0.30/0.54  tff(580,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(581,plain,
% 0.30/0.54      (((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c))))))) <=> ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.54      inference(rewrite,[status(thm)],[])).
% 0.30/0.54  tff(582,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))))),
% 0.30/0.54      inference(monotonicity,[status(thm)],[581])).
% 0.30/0.54  tff(583,plain,
% 0.30/0.54      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.54      inference(transitivity,[status(thm)],[582, 580])).
% 0.30/0.54  tff(584,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.30/0.54      inference(quant_inst,[status(thm)],[])).
% 0.30/0.54  tff(585,plain,
% 0.30/0.54      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))),
% 0.30/0.55      inference(modus_ponens,[status(thm)],[584, 583])).
% 0.30/0.55  tff(586,plain,
% 0.30/0.55      ($false),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[585, 214, 579, 11, 20, 538, 309, 317])).
% 0.30/0.55  tff(587,plain,((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(c)), f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55  tff(588,plain,
% 0.30/0.55      (~r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[587, 578, 506])).
% 0.30/0.55  tff(589,plain,
% 0.30/0.55      (~(c = f(f(f(c))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[171, 106])).
% 0.30/0.55  tff(590,plain,
% 0.30/0.55      (~r(c, f(f(f(c))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[238, 99, 59])).
% 0.30/0.55  tff(591,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(592,plain,
% 0.30/0.55      ((r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | r(c, f(c)) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c))) <=> (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(593,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | r(c, f(c)) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))))),
% 0.30/0.55      inference(monotonicity,[status(thm)],[592])).
% 0.30/0.55  tff(594,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | r(c, f(c)) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))))),
% 0.30/0.55      inference(transitivity,[status(thm)],[593, 591])).
% 0.30/0.55  tff(595,plain,
% 0.30/0.55      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | r(c, f(f(f(c)))) | r(c, f(c)) | (f(c) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(c)))),
% 0.30/0.55      inference(quant_inst,[status(thm)],[])).
% 0.30/0.55  tff(596,plain,
% 0.30/0.55      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c))))),
% 0.30/0.55      inference(modus_ponens,[status(thm)],[595, 594])).
% 0.30/0.55  tff(597,plain,
% 0.30/0.55      (r(c, f(c)) | (c = f(c))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[596, 116, 194, 142, 590, 589])).
% 0.30/0.55  tff(598,plain,
% 0.30/0.55      (r(c, f(c))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[597, 34])).
% 0.30/0.55  tff(599,plain,
% 0.30/0.55      (~(f(f(f(c))) = f(f(f(f(f(c))))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[66, 17])).
% 0.30/0.55  tff(600,plain,
% 0.30/0.55      (r(c, f(f(f(f(f(c))))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[125, 58, 106, 599, 59])).
% 0.30/0.55  tff(601,plain,
% 0.30/0.55      ($false),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[461, 600, 58, 48, 34, 194, 142, 598, 17])).
% 0.30/0.55  tff(602,plain,(r(f(f(f(f(f(c))))), f(f(f(c)))) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(c))) = c) | r(f(f(f(c))), c)), inference(lemma,lemma(discharge,[]))).
% 0.30/0.55  tff(603,plain,
% 0.30/0.55      (r(f(f(f(f(f(c))))), f(f(f(c)))) | (c = f(c)) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(c))), c)),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[602, 81])).
% 0.30/0.55  tff(604,plain,
% 0.30/0.55      (r(f(f(f(f(f(c))))), f(f(f(c)))) | (c = f(c)) | r(f(c), f(f(f(c)))) | r(f(f(f(c))), c)),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[603, 11, 139])).
% 0.30/0.55  tff(605,plain,
% 0.30/0.55      (r(f(c), f(f(f(c))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[604, 588, 59, 30])).
% 0.30/0.55  tff(606,plain,
% 0.30/0.55      (~(f(f(c)) = f(c))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[163, 22])).
% 0.30/0.55  tff(607,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | r(f(c), f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(608,plain,
% 0.30/0.55      ((r(f(f(f(f(c)))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c)))))) <=> ((f(c) = f(f(c))) | r(f(c), f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(609,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | r(f(c), f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.30/0.55      inference(monotonicity,[status(thm)],[608])).
% 0.30/0.55  tff(610,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.30/0.55      inference(transitivity,[status(thm)],[609, 607])).
% 0.30/0.55  tff(611,plain,
% 0.30/0.55      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(c))))))),
% 0.30/0.55      inference(quant_inst,[status(thm)],[])).
% 0.30/0.55  tff(612,plain,
% 0.30/0.55      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.30/0.55      inference(modus_ponens,[status(thm)],[611, 610])).
% 0.30/0.55  tff(613,plain,
% 0.30/0.55      (r(f(c), f(f(f(f(c)))))),
% 0.30/0.55      inference(unit_resolution,[status(thm)],[612, 116, 22, 155, 79, 250, 243])).
% 0.30/0.55  tff(614,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(615,plain,
% 0.30/0.55      (((~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(c))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c))) <=> ((c = f(c)) | (~r(c, f(c))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.30/0.55      inference(rewrite,[status(thm)],[])).
% 0.30/0.55  tff(616,plain,
% 0.30/0.55      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(c))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(c, f(c))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))))),
% 0.40/0.55      inference(monotonicity,[status(thm)],[615])).
% 0.40/0.55  tff(617,plain,
% 0.40/0.55      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(c))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.40/0.55      inference(transitivity,[status(thm)],[616, 614])).
% 0.40/0.55  tff(618,plain,
% 0.40/0.55      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(c))) | (f(c) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(c)))),
% 0.40/0.55      inference(quant_inst,[status(thm)],[])).
% 0.40/0.55  tff(619,plain,
% 0.40/0.55      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(c, f(c))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))),
% 0.40/0.55      inference(modus_ponens,[status(thm)],[618, 617])).
% 0.40/0.55  tff(620,plain,
% 0.40/0.55      (~r(c, f(c))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[619, 214, 30, 79, 385, 57, 613])).
% 0.40/0.55  tff(621,plain,
% 0.40/0.55      ($false),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[227, 116, 620, 30, 606, 153, 152, 159])).
% 0.40/0.55  tff(622,plain,(r(f(c), f(f(c))) | r(f(f(c)), c) | (~r(c, f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55  tff(623,plain,
% 0.40/0.55      (r(f(c), f(f(c)))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[622, 243, 558, 153])).
% 0.40/0.55  tff(624,plain,
% 0.40/0.55      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))))),
% 0.40/0.55      inference(rewrite,[status(thm)],[])).
% 0.40/0.55  tff(625,plain,
% 0.40/0.55      (((~r(f(f(c)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(c)))) <=> ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))))),
% 0.40/0.55      inference(rewrite,[status(thm)],[])).
% 0.40/0.55  tff(626,plain,
% 0.40/0.55      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c)))))))),
% 0.40/0.55      inference(monotonicity,[status(thm)],[625])).
% 0.40/0.55  tff(627,plain,
% 0.40/0.55      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))))),
% 0.40/0.55      inference(transitivity,[status(thm)],[626, 624])).
% 0.40/0.55  tff(628,plain,
% 0.40/0.55      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(c))))),
% 0.40/0.55      inference(quant_inst,[status(thm)],[])).
% 0.40/0.55  tff(629,plain,
% 0.40/0.55      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c)))))),
% 0.40/0.55      inference(modus_ponens,[status(thm)],[628, 627])).
% 0.40/0.55  tff(630,plain,
% 0.40/0.55      ($false),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[629, 214, 22, 623, 605, 139, 20, 506])).
% 0.40/0.55  tff(631,plain,(r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(c))), c) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55  tff(632,plain,
% 0.40/0.55      (r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[631, 518, 153])).
% 0.40/0.55  tff(633,assumption,(f(f(f(c))) = f(f(c))), introduced(assumption)).
% 0.40/0.55  tff(634,plain,
% 0.40/0.55      (f(f(c)) = f(f(f(c)))),
% 0.40/0.55      inference(symmetry,[status(thm)],[633])).
% 0.40/0.55  tff(635,plain,
% 0.40/0.55      ($false),
% 0.40/0.55      inference(unit_resolution,[status(thm)],[20, 634])).
% 0.40/0.55  tff(636,plain,(~(f(f(f(c))) = f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.55  tff(637,plain,
% 0.40/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | r(f(f(c)), c) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.55      inference(rewrite,[status(thm)],[])).
% 0.40/0.55  tff(638,plain,
% 0.40/0.55      ((r(f(f(c)), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(c))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c)))) <=> (r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.55      inference(rewrite,[status(thm)],[])).
% 0.40/0.55  tff(639,plain,
% 0.40/0.55      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(c))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | r(f(f(c)), c) | (f(f(c)) = c)))),
% 0.40/0.56      inference(monotonicity,[status(thm)],[638])).
% 0.40/0.56  tff(640,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(c))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.56      inference(transitivity,[status(thm)],[639, 637])).
% 0.40/0.56  tff(641,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(f(f(c))), c) | r(f(f(f(c))), f(f(c))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(642,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | r(f(f(f(c))), f(f(c))) | (f(f(f(c))) = f(f(c))) | r(f(f(c)), c) | (f(f(c)) = c)),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[641, 640])).
% 0.40/0.56  tff(643,plain,
% 0.40/0.56      (r(f(f(f(c))), f(f(c)))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[642, 116, 518, 81, 153, 152, 636])).
% 0.40/0.56  tff(644,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(645,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(646,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(c))))),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[645, 644])).
% 0.40/0.56  tff(647,plain,
% 0.40/0.56      (~r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[646, 214, 270, 643, 250, 632, 636])).
% 0.40/0.56  tff(648,plain,
% 0.40/0.56      (r(f(f(f(f(c)))), c)),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[551, 518, 153])).
% 0.40/0.56  tff(649,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(650,plain,
% 0.40/0.56      ((r(c, f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = c)) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(651,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c)))),
% 0.40/0.56      inference(monotonicity,[status(thm)],[650])).
% 0.40/0.56  tff(652,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))),
% 0.40/0.56      inference(transitivity,[status(thm)],[651, 649])).
% 0.40/0.56  tff(653,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = c))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(654,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(c, f(f(f(c)))) | (c = f(f(f(c)))) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c)),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[653, 652])).
% 0.40/0.56  tff(655,plain,
% 0.40/0.56      (r(f(f(f(f(f(c))))), c)),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[654, 116, 58, 11, 175, 172, 90])).
% 0.40/0.56  tff(656,assumption,(~r(f(f(f(f(c)))), f(f(f(c))))), introduced(assumption)).
% 0.40/0.56  tff(657,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(658,plain,
% 0.40/0.56      ((r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(659,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.40/0.56      inference(monotonicity,[status(thm)],[658])).
% 0.40/0.56  tff(660,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.56      inference(transitivity,[status(thm)],[659, 657])).
% 0.40/0.56  tff(661,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(662,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[661, 660])).
% 0.40/0.56  tff(663,plain,
% 0.40/0.56      (r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[662, 116, 58, 11, 270, 656, 256])).
% 0.40/0.56  tff(664,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(665,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(666,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[665, 664])).
% 0.40/0.56  tff(667,plain,
% 0.40/0.56      ($false),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[666, 214, 90, 50, 490, 663, 256, 655])).
% 0.40/0.56  tff(668,plain,(r(f(f(f(f(f(c))))), f(f(f(c)))) | (~r(f(f(f(f(c)))), c)) | r(f(f(f(f(c)))), f(f(f(c)))) | r(c, f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.56  tff(669,plain,
% 0.40/0.56      (r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[668, 648, 647, 175])).
% 0.40/0.56  tff(670,plain,
% 0.40/0.56      (~r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[587, 669, 506])).
% 0.40/0.56  tff(671,plain,
% 0.40/0.56      (r(c, f(f(f(f(f(c))))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[356, 670, 153])).
% 0.40/0.56  tff(672,plain,
% 0.40/0.56      (r(f(f(c)), f(f(f(f(c)))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[533, 99, 632])).
% 0.40/0.56  tff(673,plain,
% 0.40/0.56      (r(c, f(f(f(f(c)))))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[557, 648])).
% 0.40/0.56  tff(674,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(675,plain,
% 0.40/0.56      (((~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c)))) <=> ((~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 0.40/0.56      inference(rewrite,[status(thm)],[])).
% 0.40/0.56  tff(676,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c))))))))),
% 0.40/0.56      inference(monotonicity,[status(thm)],[675])).
% 0.40/0.56  tff(677,plain,
% 0.40/0.56      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c)))))))),
% 0.40/0.56      inference(transitivity,[status(thm)],[676, 674])).
% 0.40/0.56  tff(678,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(c)))))) | (~r(c, f(f(f(f(c)))))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))))),
% 0.40/0.56      inference(quant_inst,[status(thm)],[])).
% 0.40/0.56  tff(679,plain,
% 0.40/0.56      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(c)) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(c)), f(f(f(f(c))))))),
% 0.40/0.56      inference(modus_ponens,[status(thm)],[678, 677])).
% 0.40/0.56  tff(680,plain,
% 0.40/0.56      (~r(c, f(f(c)))),
% 0.40/0.56      inference(unit_resolution,[status(thm)],[679, 214, 145, 673, 57, 374, 672])).
% 0.40/0.57  tff(681,assumption,(~(f(f(f(f(f(c))))) = f(f(c)))), introduced(assumption)).
% 0.40/0.57  tff(682,plain,
% 0.40/0.57      (~(f(f(c)) = f(f(f(c))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[19, 17])).
% 0.40/0.57  tff(683,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(684,plain,
% 0.40/0.57      (((~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))) <=> ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(685,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))))),
% 0.40/0.57      inference(monotonicity,[status(thm)],[684])).
% 0.40/0.57  tff(686,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(transitivity,[status(thm)],[685, 683])).
% 0.40/0.57  tff(687,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(688,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[687, 686])).
% 0.40/0.57  tff(689,plain,
% 0.40/0.57      ((~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[688, 214, 579, 17, 682, 538])).
% 0.40/0.57  tff(690,plain,
% 0.40/0.57      (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[689, 681])).
% 0.40/0.57  tff(691,assumption,(~r(f(c), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.40/0.57  tff(692,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(693,plain,
% 0.40/0.57      ((r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c))))))) <=> ((f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(694,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))))),
% 0.40/0.57      inference(monotonicity,[status(thm)],[693])).
% 0.40/0.57  tff(695,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.57      inference(transitivity,[status(thm)],[694, 692])).
% 0.40/0.57  tff(696,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(697,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[696, 695])).
% 0.40/0.57  tff(698,plain,
% 0.40/0.57      ($false),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[697, 116, 27, 155, 691, 48, 690, 681])).
% 0.40/0.57  tff(699,plain,((f(f(f(f(f(c))))) = f(f(c))) | (f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(c)), f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57  tff(700,plain,
% 0.40/0.57      ((f(c) = f(f(c))) | r(f(c), f(f(c))) | r(f(c), f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(c)), f(f(f(c)))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[699, 316, 11])).
% 0.40/0.57  tff(701,plain,
% 0.40/0.57      (r(f(c), f(f(f(f(f(c))))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[700, 155, 538, 579, 22])).
% 0.40/0.57  tff(702,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(703,plain,
% 0.40/0.57      (((~r(c, f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = c)) <=> ((f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(704,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c))))))))),
% 0.40/0.57      inference(monotonicity,[status(thm)],[703])).
% 0.40/0.57  tff(705,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.57      inference(transitivity,[status(thm)],[704, 702])).
% 0.40/0.57  tff(706,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), c)) | (c = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = c))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(707,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c))))))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[706, 705])).
% 0.40/0.57  tff(708,plain,
% 0.40/0.57      (~r(f(c), c)),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[707, 214, 701, 48, 419, 91, 37])).
% 0.40/0.57  tff(709,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(c, f(f(c))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(c, f(f(c))) | (c = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(710,plain,
% 0.40/0.57      ((r(c, f(f(c))) | r(f(c), f(f(c))) | r(f(c), c) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c)) <=> ((f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(c, f(f(c))) | (c = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(711,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(c), f(f(c))) | r(f(c), c) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(c, f(f(c))) | (c = f(f(c)))))),
% 0.40/0.57      inference(monotonicity,[status(thm)],[710])).
% 0.40/0.57  tff(712,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(c), f(f(c))) | r(f(c), c) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(c, f(f(c))) | (c = f(f(c))))),
% 0.40/0.57      inference(transitivity,[status(thm)],[711, 709])).
% 0.40/0.57  tff(713,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(c))) | r(f(c), f(f(c))) | r(f(c), c) | (c = f(f(c))) | (f(c) = f(f(c))) | (f(c) = c))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(714,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(c, f(f(c))) | (c = f(f(c)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[713, 712])).
% 0.40/0.57  tff(715,plain,
% 0.40/0.57      ($false),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[714, 116, 22, 155, 145, 278, 708, 37])).
% 0.40/0.57  tff(716,plain,(r(f(c), f(f(c))) | r(c, f(f(c))) | (~r(c, f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57  tff(717,plain,
% 0.40/0.57      (r(f(c), f(f(c)))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[716, 680, 671, 506, 669])).
% 0.40/0.57  tff(718,plain,
% 0.40/0.57      (~r(f(c), f(f(f(f(c)))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[303, 717, 632, 22])).
% 0.40/0.57  tff(719,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(720,plain,
% 0.40/0.57      (((~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c))))) <=> ((~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(721,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c)))))),
% 0.40/0.57      inference(monotonicity,[status(thm)],[720])).
% 0.40/0.57  tff(722,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))))),
% 0.40/0.57      inference(transitivity,[status(thm)],[721, 719])).
% 0.40/0.57  tff(723,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), f(f(c)))) | (~r(f(c), f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c))) | (f(c) = f(f(c))) | (f(c) = f(f(f(c)))))),
% 0.40/0.57      inference(quant_inst,[status(thm)],[])).
% 0.40/0.57  tff(724,plain,
% 0.40/0.57      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), f(f(c)))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(c))) = f(f(c)))),
% 0.40/0.57      inference(modus_ponens,[status(thm)],[723, 722])).
% 0.40/0.57  tff(725,plain,
% 0.40/0.57      (~r(f(c), f(f(f(c))))),
% 0.40/0.57      inference(unit_resolution,[status(thm)],[724, 214, 22, 717, 139, 643, 636])).
% 0.40/0.57  tff(726,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(727,plain,
% 0.40/0.57      ((r(f(f(f(f(c)))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c)))))) <=> (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.40/0.57      inference(rewrite,[status(thm)],[])).
% 0.40/0.57  tff(728,plain,
% 0.40/0.57      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))))),
% 0.40/0.58      inference(monotonicity,[status(thm)],[727])).
% 0.40/0.58  tff(729,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c))))))),
% 0.40/0.58      inference(transitivity,[status(thm)],[728, 726])).
% 0.40/0.58  tff(730,plain,
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% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(731,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | r(f(c), f(f(f(f(c)))))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[730, 729])).
% 0.40/0.58  tff(732,plain,
% 0.40/0.58      ($false),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[731, 116, 725, 139, 79, 270, 647, 718])).
% 0.40/0.58  tff(733,plain,(r(c, f(f(f(c)))) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58  tff(734,plain,
% 0.40/0.58      (r(c, f(f(f(c))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[733, 153])).
% 0.40/0.58  tff(735,plain,
% 0.40/0.58      (r(f(f(f(c))), c)),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[240, 734])).
% 0.40/0.58  tff(736,plain,
% 0.40/0.58      (~r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[289, 214, 735, 81, 50, 514, 270])).
% 0.40/0.58  tff(737,plain,
% 0.40/0.58      (r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[662, 116, 58, 11, 270, 736, 256])).
% 0.40/0.58  tff(738,plain,
% 0.40/0.58      (~r(c, f(f(f(f(f(c))))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[575, 214, 91, 737, 513, 57, 256])).
% 0.40/0.58  tff(739,plain,
% 0.40/0.58      (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[577, 369, 513, 153])).
% 0.40/0.58  tff(740,plain,
% 0.40/0.58      (r(f(c), f(f(c)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[622, 513, 243, 153])).
% 0.40/0.58  tff(741,assumption,(r(f(c), f(f(f(f(f(c))))))), introduced(assumption)).
% 0.40/0.58  tff(742,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(743,plain,
% 0.40/0.58      (((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(c)))) <=> ((f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(744,plain,
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% 0.40/0.58      inference(monotonicity,[status(thm)],[743])).
% 0.40/0.58  tff(745,plain,
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% 0.40/0.58      inference(transitivity,[status(thm)],[744, 742])).
% 0.40/0.58  tff(746,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(c))))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(747,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(c)), f(f(f(f(f(c))))))) | (f(f(c)) = f(f(f(f(f(c))))))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[746, 745])).
% 0.40/0.58  tff(748,plain,
% 0.40/0.58      ($false),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[747, 214, 22, 295, 741, 48, 309, 317])).
% 0.40/0.58  tff(749,plain,((~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c)))) | (~r(f(f(c)), f(f(f(f(f(c)))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58  tff(750,plain,
% 0.40/0.58      (~r(f(c), f(f(f(f(f(c))))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[749, 740, 739])).
% 0.40/0.58  tff(751,plain,
% 0.40/0.58      ((f(f(f(c))) = f(c)) <=> (f(c) = f(f(f(c))))),
% 0.40/0.58      inference(commutativity,[status(thm)],[])).
% 0.40/0.58  tff(752,assumption,(f(f(f(c))) = f(c)), introduced(assumption)).
% 0.40/0.58  tff(753,plain,
% 0.40/0.58      (f(c) = f(f(f(c)))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[752, 751])).
% 0.40/0.58  tff(754,plain,
% 0.40/0.58      ($false),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[139, 753])).
% 0.40/0.58  tff(755,plain,(~(f(f(f(c))) = f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58  tff(756,plain,
% 0.40/0.58      (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(c))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[445, 48])).
% 0.40/0.58  tff(757,plain,
% 0.40/0.58      (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(c), f(f(f(c)))) | r(f(c), f(f(f(f(f(c))))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[756, 139, 11])).
% 0.40/0.58  tff(758,plain,
% 0.40/0.58      (r(f(c), f(f(f(c))))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[757, 750, 58])).
% 0.40/0.58  tff(759,assumption,(~r(f(f(f(c))), f(c))), introduced(assumption)).
% 0.40/0.58  tff(760,assumption,(r(f(c), f(f(f(c))))), introduced(assumption)).
% 0.40/0.58  tff(761,plain,
% 0.40/0.58      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(762,plain,
% 0.40/0.58      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c)))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(763,plain,
% 0.40/0.58      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[762, 761])).
% 0.40/0.58  tff(764,plain,
% 0.40/0.58      ($false),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[763, 99, 760, 759])).
% 0.40/0.58  tff(765,plain,((~r(f(c), f(f(f(c))))) | r(f(f(f(c))), f(c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58  tff(766,plain,
% 0.40/0.58      (r(f(f(f(c))), f(c))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[765, 758])).
% 0.40/0.58  tff(767,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(768,plain,
% 0.40/0.58      (((~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c)) <=> ((c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(769,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c))))),
% 0.40/0.58      inference(monotonicity,[status(thm)],[768])).
% 0.40/0.58  tff(770,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c)))),
% 0.40/0.58      inference(transitivity,[status(thm)],[769, 767])).
% 0.40/0.58  tff(771,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(c))) | (~r(f(f(f(c))), f(c))) | (~r(f(f(f(c))), c)) | (c = f(c)) | (f(f(f(c))) = f(c)) | (f(f(f(c))) = c))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(772,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[771, 770])).
% 0.40/0.58  tff(773,plain,
% 0.40/0.58      ((c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(c))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[772, 214])).
% 0.40/0.58  tff(774,plain,
% 0.40/0.58      ((c = f(c)) | (~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = f(c))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[773, 81])).
% 0.40/0.58  tff(775,plain,
% 0.40/0.58      (~r(c, f(c))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[774, 766, 755, 30, 735])).
% 0.40/0.58  tff(776,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(777,plain,
% 0.40/0.58      ((r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c))) <=> (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(778,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c))))))))),
% 0.40/0.58      inference(monotonicity,[status(thm)],[777])).
% 0.40/0.58  tff(779,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.58      inference(transitivity,[status(thm)],[778, 776])).
% 0.40/0.58  tff(780,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(c), f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | r(c, f(c)) | (f(c) = f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))) | (c = f(c)))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(781,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c))))))),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[780, 779])).
% 0.40/0.58  tff(782,plain,
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% 0.40/0.58      inference(unit_resolution,[status(thm)],[781, 116, 775, 30, 750, 48, 738, 91])).
% 0.40/0.58  tff(783,plain,(r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58  tff(784,plain,
% 0.40/0.58      (r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[783, 58, 153])).
% 0.40/0.58  tff(785,plain,
% 0.40/0.58      (~r(f(c), c)),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[465, 419, 30, 735])).
% 0.40/0.58  tff(786,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(f(f(c)), c) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(787,plain,
% 0.40/0.58      ((r(f(f(c)), c) | r(f(c), c) | r(f(c), f(f(c))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c)))) <=> ((f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.58      inference(rewrite,[status(thm)],[])).
% 0.40/0.58  tff(788,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(c), c) | r(f(c), f(f(c))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(f(f(c)), c) | (f(f(c)) = c)))),
% 0.40/0.58      inference(monotonicity,[status(thm)],[787])).
% 0.40/0.58  tff(789,plain,
% 0.40/0.58      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(c), c) | r(f(c), f(f(c))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(f(f(c)), c) | (f(f(c)) = c))),
% 0.40/0.58      inference(transitivity,[status(thm)],[788, 786])).
% 0.40/0.58  tff(790,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), c) | r(f(c), c) | r(f(c), f(f(c))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c))))),
% 0.40/0.58      inference(quant_inst,[status(thm)],[])).
% 0.40/0.58  tff(791,plain,
% 0.40/0.58      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | r(f(c), f(f(c))) | r(f(c), c) | r(f(f(c)), c) | (f(f(c)) = c)),
% 0.40/0.58      inference(modus_ponens,[status(thm)],[790, 789])).
% 0.40/0.58  tff(792,plain,
% 0.40/0.58      (r(f(c), f(f(c)))),
% 0.40/0.58      inference(unit_resolution,[status(thm)],[791, 116, 22, 153, 152, 785, 37])).
% 0.40/0.58  tff(793,plain,
% 0.40/0.58      (~r(f(c), f(f(f(f(c)))))),
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% 0.40/0.58  tff(794,plain,
% 0.40/0.58      (r(f(f(f(f(c)))), c)),
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% 0.40/0.58  tff(795,plain,
% 0.40/0.58      (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
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% 0.40/0.58  tff(796,plain,
% 0.40/0.58      ($false),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[503, 214, 90, 50, 794, 795, 308, 420])).
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% 0.40/0.59  tff(798,plain,
% 0.40/0.59      (~r(c, f(f(f(f(f(c))))))),
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% 0.40/0.59  tff(799,plain,
% 0.40/0.59      (r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[356, 798, 153])).
% 0.40/0.59  tff(800,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(801,plain,
% 0.40/0.59      ((r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c)) <=> ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(802,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))))),
% 0.40/0.59      inference(monotonicity,[status(thm)],[801])).
% 0.40/0.59  tff(803,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(transitivity,[status(thm)],[802, 800])).
% 0.40/0.59  tff(804,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c))),
% 0.40/0.59      inference(quant_inst,[status(thm)],[])).
% 0.40/0.59  tff(805,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (c = f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.59      inference(modus_ponens,[status(thm)],[804, 803])).
% 0.40/0.59  tff(806,plain,
% 0.40/0.59      ((f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c)),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[805, 116, 105, 91, 481, 480])).
% 0.40/0.59  tff(807,plain,
% 0.40/0.59      (r(f(f(f(f(c)))), c)),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[806, 54])).
% 0.40/0.59  tff(808,plain,
% 0.40/0.59      ($false),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[493, 807, 54, 481, 267, 480, 479, 92, 286])).
% 0.40/0.59  tff(809,plain,((f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | r(c, f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59  tff(810,plain,
% 0.40/0.59      (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[809, 50])).
% 0.40/0.59  tff(811,plain,
% 0.40/0.59      (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[810, 67])).
% 0.40/0.59  tff(812,plain,
% 0.40/0.59      (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | r(c, f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[811, 263, 308])).
% 0.40/0.59  tff(813,plain,
% 0.40/0.59      (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[812, 798, 735, 103])).
% 0.40/0.59  tff(814,plain,
% 0.40/0.59      ($false),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[326, 813, 799, 784])).
% 0.40/0.59  tff(815,plain,(r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59  tff(816,plain,
% 0.40/0.59      (r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[815, 153])).
% 0.40/0.59  tff(817,plain,
% 0.40/0.59      (~r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[587, 816, 506])).
% 0.40/0.59  tff(818,plain,
% 0.40/0.59      (r(c, f(f(f(f(f(c))))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[356, 817, 153])).
% 0.40/0.59  tff(819,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(820,plain,
% 0.40/0.59      (((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(f(c))))))) <=> ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(821,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c))))))))),
% 0.40/0.59      inference(monotonicity,[status(thm)],[820])).
% 0.40/0.59  tff(822,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(transitivity,[status(thm)],[821, 819])).
% 0.40/0.59  tff(823,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (c = f(f(f(c)))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.59      inference(quant_inst,[status(thm)],[])).
% 0.40/0.59  tff(824,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(c, f(f(f(c))))) | (c = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c))))))),
% 0.40/0.59      inference(modus_ponens,[status(thm)],[823, 822])).
% 0.40/0.59  tff(825,plain,
% 0.40/0.59      ($false),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[824, 214, 816, 11, 734, 172, 818, 91])).
% 0.40/0.59  tff(826,plain,(r(f(f(c)), c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59  tff(827,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(828,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.59      inference(quant_inst,[status(thm)],[])).
% 0.40/0.59  tff(829,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(f(c))))), c)) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(f(c))))) = c) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.40/0.59      inference(modus_ponens,[status(thm)],[828, 827])).
% 0.40/0.59  tff(830,plain,
% 0.40/0.59      (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[829, 214, 90, 316, 826, 152, 132])).
% 0.40/0.59  tff(831,plain,
% 0.40/0.59      (~r(c, f(f(f(c))))),
% 0.40/0.59      inference(unit_resolution,[status(thm)],[240, 59])).
% 0.40/0.59  tff(832,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(833,plain,
% 0.40/0.59      ((r(f(f(c)), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c)))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.59      inference(rewrite,[status(thm)],[])).
% 0.40/0.59  tff(834,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))))),
% 0.40/0.59      inference(monotonicity,[status(thm)],[833])).
% 0.40/0.59  tff(835,plain,
% 0.40/0.59      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.59      inference(transitivity,[status(thm)],[834, 832])).
% 0.40/0.59  tff(836,plain,
% 0.40/0.59      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(c)), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(c)) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))))),
% 0.40/0.60      inference(quant_inst,[status(thm)],[])).
% 0.40/0.60  tff(837,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c)))),
% 0.40/0.60      inference(modus_ponens,[status(thm)],[836, 835])).
% 0.40/0.60  tff(838,plain,
% 0.40/0.60      (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[837, 116, 58, 11, 20, 316, 154])).
% 0.40/0.60  tff(839,plain,
% 0.40/0.60      (r(f(f(c)), c)),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[184, 175, 154])).
% 0.40/0.60  tff(840,plain,
% 0.40/0.60      ($false),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[829, 214, 90, 316, 839, 152, 655, 838])).
% 0.40/0.60  tff(841,plain,(r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | r(c, f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.60  tff(842,plain,
% 0.40/0.60      (r(f(f(c)), f(f(f(c))))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[841, 831, 58])).
% 0.40/0.60  tff(843,plain,
% 0.40/0.60      (r(f(c), f(f(f(c))))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[604, 59, 58, 30])).
% 0.40/0.60  tff(844,plain,
% 0.40/0.60      (~r(f(c), f(f(c)))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[629, 214, 22, 843, 139, 20, 842])).
% 0.40/0.60  tff(845,assumption,(~r(f(f(f(f(f(c))))), f(f(c)))), introduced(assumption)).
% 0.40/0.60  tff(846,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(847,plain,
% 0.40/0.60      ((r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))) <=> ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(848,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c)))))),
% 0.40/0.60      inference(monotonicity,[status(thm)],[847])).
% 0.40/0.60  tff(849,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c))))),
% 0.40/0.60      inference(transitivity,[status(thm)],[848, 846])).
% 0.40/0.60  tff(850,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.40/0.60      inference(quant_inst,[status(thm)],[])).
% 0.40/0.60  tff(851,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | r(f(f(f(f(f(c))))), f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.60      inference(modus_ponens,[status(thm)],[850, 849])).
% 0.40/0.60  tff(852,plain,
% 0.40/0.60      (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[851, 116, 316, 250, 308, 243, 845])).
% 0.40/0.60  tff(853,plain,
% 0.40/0.60      (r(f(c), f(f(f(f(f(c))))))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[697, 116, 22, 155, 48, 316, 845])).
% 0.40/0.60  tff(854,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(855,plain,
% 0.40/0.60      (((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c)))))) <=> ((f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(856,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))))),
% 0.40/0.60      inference(monotonicity,[status(thm)],[855])).
% 0.40/0.60  tff(857,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.40/0.60      inference(transitivity,[status(thm)],[856, 854])).
% 0.40/0.60  tff(858,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(c))))))),
% 0.40/0.60      inference(quant_inst,[status(thm)],[])).
% 0.40/0.60  tff(859,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))),
% 0.40/0.60      inference(modus_ponens,[status(thm)],[858, 857])).
% 0.40/0.60  tff(860,plain,
% 0.40/0.60      ($false),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[859, 214, 853, 48, 79, 852, 308, 613])).
% 0.40/0.60  tff(861,plain,(r(f(f(f(f(c)))), f(f(c))) | r(f(c), f(f(c))) | r(f(f(f(f(f(c))))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.60  tff(862,plain,
% 0.40/0.60      (r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[861, 844, 830])).
% 0.40/0.60  tff(863,plain,
% 0.40/0.60      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), c)) | r(c, f(f(c))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), c)) | r(c, f(f(c))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(864,plain,
% 0.40/0.60      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(c)), c)) | r(c, f(f(c))))),
% 0.40/0.60      inference(quant_inst,[status(thm)],[])).
% 0.40/0.60  tff(865,plain,
% 0.40/0.60      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(c)), c)) | r(c, f(f(c)))),
% 0.40/0.60      inference(modus_ponens,[status(thm)],[864, 863])).
% 0.40/0.60  tff(866,plain,
% 0.40/0.60      (r(c, f(f(c)))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[865, 99, 826])).
% 0.40/0.60  tff(867,plain,
% 0.40/0.60      (~r(f(f(f(c))), f(f(f(f(c)))))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[548, 862, 842])).
% 0.40/0.60  tff(868,plain,
% 0.40/0.60      (r(f(f(f(f(c)))), c)),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[529, 867, 59])).
% 0.40/0.60  tff(869,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(870,plain,
% 0.40/0.60      (((~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), c)) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c)) <=> ((~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(871,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), c)) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c))))))),
% 0.40/0.60      inference(monotonicity,[status(thm)],[870])).
% 0.40/0.60  tff(872,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), c)) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.40/0.60      inference(transitivity,[status(thm)],[871, 869])).
% 0.40/0.60  tff(873,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(c)))), f(f(c)))) | (~r(f(f(f(f(c)))), c)) | (c = f(f(c))) | (f(f(f(f(c)))) = f(f(c))) | (f(f(f(f(c)))) = c))),
% 0.40/0.60      inference(quant_inst,[status(thm)],[])).
% 0.40/0.60  tff(874,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (~r(f(f(f(f(c)))), c)) | (f(f(f(f(c)))) = c) | (c = f(f(c))) | (~r(f(f(f(f(c)))), f(f(c))))),
% 0.40/0.60      inference(modus_ponens,[status(thm)],[873, 872])).
% 0.40/0.60  tff(875,plain,
% 0.40/0.60      ($false),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[874, 214, 145, 50, 868, 866, 250, 862])).
% 0.40/0.60  tff(876,plain,(r(f(f(f(c))), c) | r(f(f(f(f(f(c))))), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.60  tff(877,plain,
% 0.40/0.60      (r(f(f(f(c))), c)),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[876, 58])).
% 0.40/0.60  tff(878,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), c)) | (f(f(c)) = c) | (~r(f(f(c)), f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), c)) | (f(f(c)) = c) | (~r(f(f(c)), f(f(f(c))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(879,plain,
% 0.40/0.60      (((~r(f(f(f(c))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c))))) <=> ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), c)) | (f(f(c)) = c) | (~r(f(f(c)), f(f(f(c))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(880,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), c)) | (f(f(c)) = c) | (~r(f(f(c)), f(f(f(c)))))))),
% 0.40/0.60      inference(monotonicity,[status(thm)],[879])).
% 0.40/0.60  tff(881,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), c)) | (f(f(c)) = c) | (~r(f(f(c)), f(f(f(c))))))),
% 0.40/0.60      inference(transitivity,[status(thm)],[880, 878])).
% 0.40/0.60  tff(882,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (~r(f(f(c)), c)) | (~r(f(f(c)), f(f(f(c))))) | (f(f(f(c))) = c) | (f(f(c)) = c) | (f(f(c)) = f(f(f(c)))))),
% 0.40/0.60      inference(quant_inst,[status(thm)],[])).
% 0.40/0.60  tff(883,plain,
% 0.40/0.60      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(c)) = f(f(f(c)))) | (~r(f(f(c)), c)) | (f(f(c)) = c) | (~r(f(f(c)), f(f(f(c)))))),
% 0.40/0.60      inference(modus_ponens,[status(thm)],[882, 881])).
% 0.40/0.60  tff(884,plain,
% 0.40/0.60      (~r(f(f(c)), f(f(f(c))))),
% 0.40/0.60      inference(unit_resolution,[status(thm)],[883, 214, 877, 81, 20, 826, 152])).
% 0.40/0.60  tff(885,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(886,plain,
% 0.40/0.60      ((r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c))))))) <=> (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.40/0.60      inference(rewrite,[status(thm)],[])).
% 0.40/0.60  tff(887,plain,
% 0.40/0.60      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c))))))))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[886])).
% 0.40/0.61  tff(888,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(transitivity,[status(thm)],[887, 885])).
% 0.40/0.61  tff(889,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | (f(f(c)) = f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(890,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | r(f(f(c)), f(f(f(c)))) | (f(f(c)) = f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))) | (f(f(c)) = f(f(f(f(f(c))))))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[889, 888])).
% 0.40/0.61  tff(891,plain,
% 0.40/0.61      ($false),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[890, 116, 58, 11, 20, 884, 348, 317])).
% 0.40/0.61  tff(892,plain,(r(f(f(f(f(f(c))))), f(f(f(c)))) | r(f(f(c)), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61  tff(893,plain,
% 0.40/0.61      (r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[892, 348])).
% 0.40/0.61  tff(894,plain,
% 0.40/0.61      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(895,plain,
% 0.40/0.61      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(896,plain,
% 0.40/0.61      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[895, 894])).
% 0.40/0.61  tff(897,plain,
% 0.40/0.61      (r(f(f(f(c))), f(f(f(f(f(c))))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[896, 99, 893])).
% 0.40/0.61  tff(898,plain,
% 0.40/0.61      (r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[567, 369, 348])).
% 0.40/0.61  tff(899,assumption,(r(f(f(f(f(f(c))))), f(f(f(f(c)))))), introduced(assumption)).
% 0.40/0.61  tff(900,plain,
% 0.40/0.61      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(901,plain,
% 0.40/0.61      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(902,plain,
% 0.40/0.61      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[901, 900])).
% 0.40/0.61  tff(903,plain,
% 0.40/0.61      ($false),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[902, 99, 899, 481])).
% 0.40/0.61  tff(904,plain,((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61  tff(905,plain,
% 0.40/0.61      (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[904, 898])).
% 0.40/0.61  tff(906,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(907,plain,
% 0.40/0.61      (((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c)))))) <=> ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(908,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[907])).
% 0.40/0.61  tff(909,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.40/0.61      inference(transitivity,[status(thm)],[908, 906])).
% 0.40/0.61  tff(910,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(911,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(f(c))))))) | (f(f(f(c))) = f(f(f(f(f(c)))))) | (f(f(f(c))) = f(f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(c))), f(f(f(f(c))))))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[910, 909])).
% 0.40/0.61  tff(912,plain,
% 0.40/0.61      (~r(f(f(f(c))), f(f(f(f(c)))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[911, 214, 67, 263, 905, 308, 897])).
% 0.40/0.61  tff(913,plain,
% 0.40/0.61      (r(f(f(f(f(c)))), c)),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[529, 912, 59])).
% 0.40/0.61  tff(914,plain,
% 0.40/0.61      (r(c, f(f(f(f(c)))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[557, 913])).
% 0.40/0.61  tff(915,plain,
% 0.40/0.61      (~r(c, f(f(f(f(f(c))))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[575, 214, 91, 898, 914, 57, 256])).
% 0.40/0.61  tff(916,plain,
% 0.40/0.61      ((f(f(f(f(f(c))))) = f(c)) <=> (f(c) = f(f(f(f(f(c))))))),
% 0.40/0.61      inference(commutativity,[status(thm)],[])).
% 0.40/0.61  tff(917,plain,
% 0.40/0.61      ((f(c) = f(f(f(f(f(c)))))) <=> (f(f(f(f(f(c))))) = f(c))),
% 0.40/0.61      inference(symmetry,[status(thm)],[916])).
% 0.40/0.61  tff(918,plain,
% 0.40/0.61      ((~(f(c) = f(f(f(f(f(c))))))) <=> (~(f(f(f(f(f(c))))) = f(c)))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[917])).
% 0.40/0.61  tff(919,plain,
% 0.40/0.61      (~(f(f(f(f(f(c))))) = f(c))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[48, 918])).
% 0.40/0.61  tff(920,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | r(f(f(f(c))), c) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | r(f(f(f(c))), c) | (f(f(f(c))) = c))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(921,plain,
% 0.40/0.61      ((r(f(f(f(c))), c) | r(f(c), c) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c))))) <=> ((f(c) = c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | r(f(f(f(c))), c) | (f(f(f(c))) = c))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(922,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(f(c), c) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | r(f(f(f(c))), c) | (f(f(f(c))) = c)))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[921])).
% 0.40/0.61  tff(923,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(f(c), c) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | r(f(f(f(c))), c) | (f(f(f(c))) = c))),
% 0.40/0.61      inference(transitivity,[status(thm)],[922, 920])).
% 0.40/0.61  tff(924,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(f(c), c) | r(f(c), f(f(f(c)))) | (f(f(f(c))) = c) | (f(c) = c) | (f(c) = f(f(f(c)))))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(925,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), f(f(f(c)))) | (f(c) = f(f(f(c)))) | r(f(c), c) | r(f(f(f(c))), c) | (f(f(f(c))) = c)),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[924, 923])).
% 0.40/0.61  tff(926,plain,
% 0.40/0.61      ($false),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[925, 116, 194, 139, 59, 81, 469, 468])).
% 0.40/0.61  tff(927,plain,(r(f(c), c) | r(f(c), f(f(f(c)))) | r(f(f(f(c))), c) | (f(c) = c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61  tff(928,plain,
% 0.40/0.61      (r(f(c), f(f(f(c))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[927, 469, 59, 37])).
% 0.40/0.61  tff(929,plain,
% 0.40/0.61      (r(f(f(f(f(f(c))))), f(f(f(c))))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[127, 105, 59])).
% 0.40/0.61  tff(930,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(931,plain,
% 0.40/0.61      (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(c))) <=> ((f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(932,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c)))))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[931])).
% 0.40/0.61  tff(933,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c))))),
% 0.40/0.61      inference(transitivity,[status(thm)],[932, 930])).
% 0.40/0.61  tff(934,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(c)))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(935,plain,
% 0.40/0.61      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | (~r(f(f(f(f(f(c))))), f(c)))),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[934, 933])).
% 0.40/0.61  tff(936,plain,
% 0.40/0.61      (~r(f(f(f(f(f(c))))), f(c))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[935, 214, 929, 11, 928, 139, 919])).
% 0.40/0.61  tff(937,plain,
% 0.40/0.61      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(c))) | r(f(c), c))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(c))) | r(f(c), c))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(938,plain,
% 0.40/0.61      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(c, f(c))) | r(f(c), c))),
% 0.40/0.61      inference(quant_inst,[status(thm)],[])).
% 0.40/0.61  tff(939,plain,
% 0.40/0.61      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(c, f(c))) | r(f(c), c)),
% 0.40/0.61      inference(modus_ponens,[status(thm)],[938, 937])).
% 0.40/0.61  tff(940,plain,
% 0.40/0.61      (~r(c, f(c))),
% 0.40/0.61      inference(unit_resolution,[status(thm)],[939, 99, 469])).
% 0.40/0.61  tff(941,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(942,plain,
% 0.40/0.61      ((r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c))))))) <=> (r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(rewrite,[status(thm)],[])).
% 0.40/0.61  tff(943,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c))))))))),
% 0.40/0.61      inference(monotonicity,[status(thm)],[942])).
% 0.40/0.61  tff(944,plain,
% 0.40/0.61      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.61      inference(transitivity,[status(thm)],[943, 941])).
% 0.40/0.62  tff(945,plain,
% 0.40/0.62      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(c)) | r(c, f(c)) | r(c, f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(c)) | (c = f(c)) | (c = f(f(f(f(f(c)))))))),
% 0.40/0.62      inference(quant_inst,[status(thm)],[])).
% 0.40/0.62  tff(946,plain,
% 0.40/0.62      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(c, f(f(f(f(f(c)))))) | (c = f(f(f(f(f(c))))))),
% 0.40/0.62      inference(modus_ponens,[status(thm)],[945, 944])).
% 0.40/0.62  tff(947,plain,
% 0.40/0.62      ($false),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[946, 116, 940, 30, 105, 91, 936, 919])).
% 0.40/0.62  tff(948,plain,(r(f(c), c) | r(c, f(f(f(f(f(c)))))) | r(f(f(f(c))), c)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62  tff(949,plain,
% 0.40/0.62      (r(f(c), c)),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[948, 915, 59])).
% 0.40/0.62  tff(950,plain,
% 0.40/0.62      (r(f(f(c)), f(f(f(c))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[406, 912, 243])).
% 0.40/0.62  tff(951,plain,
% 0.40/0.62      (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[688, 214, 893, 11, 20, 316, 950])).
% 0.40/0.62  tff(952,plain,
% 0.40/0.62      (r(f(c), f(f(c)))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[861, 951, 243])).
% 0.40/0.62  tff(953,assumption,(r(f(f(c)), c)), introduced(assumption)).
% 0.40/0.62  tff(954,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(f(c)) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(f(c)) = c))),
% 0.40/0.62      inference(rewrite,[status(thm)],[])).
% 0.40/0.62  tff(955,plain,
% 0.40/0.62      (((~r(f(f(c)), c)) | (~r(f(c), c)) | (~r(f(c), f(f(c)))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c)))) <=> ((f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(f(c)) = c))),
% 0.40/0.62      inference(rewrite,[status(thm)],[])).
% 0.40/0.62  tff(956,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(c), c)) | (~r(f(c), f(f(c)))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(f(c)) = c)))),
% 0.40/0.62      inference(monotonicity,[status(thm)],[955])).
% 0.40/0.62  tff(957,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(c), c)) | (~r(f(c), f(f(c)))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(f(c)) = c))),
% 0.40/0.62      inference(transitivity,[status(thm)],[956, 954])).
% 0.40/0.62  tff(958,plain,
% 0.40/0.62      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(c), c)) | (~r(f(c), f(f(c)))) | (f(f(c)) = c) | (f(c) = c) | (f(c) = f(f(c))))),
% 0.40/0.62      inference(quant_inst,[status(thm)],[])).
% 0.40/0.62  tff(959,plain,
% 0.40/0.62      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(c))) | (f(c) = c) | (~r(f(c), f(f(c)))) | (~r(f(c), c)) | (~r(f(f(c)), c)) | (f(f(c)) = c)),
% 0.40/0.62      inference(modus_ponens,[status(thm)],[958, 957])).
% 0.40/0.62  tff(960,plain,
% 0.40/0.62      ($false),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[959, 214, 27, 295, 953, 152, 426, 418])).
% 0.40/0.62  tff(961,plain,((~r(f(c), c)) | (f(c) = f(f(c))) | (~r(f(c), f(f(c)))) | (~r(f(f(c)), c))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62  tff(962,plain,
% 0.40/0.62      ($false),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[961, 952, 949, 22, 826])).
% 0.40/0.62  tff(963,plain,(r(f(f(f(f(c)))), f(f(c))) | r(f(f(f(c))), c) | r(f(f(c)), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62  tff(964,plain,
% 0.40/0.62      (r(f(f(f(f(c)))), f(f(c)))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[963, 59, 348])).
% 0.40/0.62  tff(965,plain,
% 0.40/0.62      (~r(f(f(f(f(c)))), c)),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[874, 214, 145, 50, 866, 250, 964])).
% 0.40/0.62  tff(966,plain,
% 0.40/0.62      (r(f(f(f(c))), f(f(f(f(c)))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[529, 965, 59])).
% 0.40/0.62  tff(967,plain,
% 0.40/0.62      (~r(f(f(c)), f(f(f(c))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[548, 966, 964])).
% 0.40/0.62  tff(968,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.62      inference(rewrite,[status(thm)],[])).
% 0.40/0.62  tff(969,plain,
% 0.40/0.62      ((r(f(f(f(c))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c))))) <=> (r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.62      inference(rewrite,[status(thm)],[])).
% 0.40/0.62  tff(970,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.40/0.62      inference(monotonicity,[status(thm)],[969])).
% 0.40/0.62  tff(971,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.40/0.62      inference(transitivity,[status(thm)],[970, 968])).
% 0.40/0.62  tff(972,plain,
% 0.40/0.62      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(c))), c) | r(f(f(f(f(c)))), c) | r(f(f(f(f(c)))), f(f(f(c)))) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(f(c)))))),
% 0.40/0.62      inference(quant_inst,[status(thm)],[])).
% 0.40/0.62  tff(973,plain,
% 0.40/0.62      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(c))), c) | (f(f(f(c))) = c) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.62      inference(modus_ponens,[status(thm)],[972, 971])).
% 0.40/0.62  tff(974,plain,
% 0.40/0.62      (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[973, 116, 59, 81, 50, 965, 270])).
% 0.40/0.62  tff(975,plain,
% 0.40/0.62      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))))),
% 0.40/0.62      inference(rewrite,[status(thm)],[])).
% 0.40/0.62  tff(976,plain,
% 0.40/0.62      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(c)), f(f(f(f(f(c)))))))),
% 0.40/0.62      inference(quant_inst,[status(thm)],[])).
% 0.40/0.62  tff(977,plain,
% 0.40/0.62      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | r(f(f(c)), f(f(f(f(f(c))))))),
% 0.40/0.62      inference(modus_ponens,[status(thm)],[976, 975])).
% 0.40/0.62  tff(978,plain,
% 0.40/0.62      (~r(f(f(f(f(f(c))))), f(f(c)))),
% 0.40/0.62      inference(unit_resolution,[status(thm)],[977, 99, 348])).
% 0.40/0.62  tff(979,plain,
% 0.40/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.48/0.62      inference(rewrite,[status(thm)],[])).
% 0.48/0.62  tff(980,plain,
% 0.48/0.62      (((~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c)))))) <=> ((~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.48/0.62      inference(rewrite,[status(thm)],[])).
% 0.48/0.62  tff(981,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c))))))),
% 0.48/0.62      inference(monotonicity,[status(thm)],[980])).
% 0.48/0.62  tff(982,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c)))))),
% 0.48/0.62      inference(transitivity,[status(thm)],[981, 979])).
% 0.48/0.62  tff(983,plain,
% 0.48/0.62      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(c))))))),
% 0.48/0.62      inference(quant_inst,[status(thm)],[])).
% 0.48/0.62  tff(984,plain,
% 0.48/0.62      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (f(f(f(f(c)))) = f(f(c))) | (c = f(f(f(f(c))))) | (c = f(f(c))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(c))))),
% 0.48/0.62      inference(modus_ponens,[status(thm)],[983, 982])).
% 0.48/0.62  tff(985,plain,
% 0.48/0.62      (~r(c, f(f(f(f(c)))))),
% 0.48/0.62      inference(unit_resolution,[status(thm)],[984, 214, 145, 866, 57, 250, 964])).
% 0.48/0.62  tff(986,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.48/0.62      inference(rewrite,[status(thm)],[])).
% 0.48/0.62  tff(987,plain,
% 0.48/0.62      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.48/0.62      inference(quant_inst,[status(thm)],[])).
% 0.48/0.62  tff(988,plain,
% 0.48/0.62      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.48/0.62      inference(modus_ponens,[status(thm)],[987, 986])).
% 0.48/0.62  tff(989,plain,
% 0.48/0.62      (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.48/0.62      inference(unit_resolution,[status(thm)],[988, 214, 893, 11, 270, 974, 256])).
% 0.48/0.62  tff(990,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.48/0.62      inference(rewrite,[status(thm)],[])).
% 0.48/0.62  tff(991,plain,
% 0.48/0.62      ((r(c, f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c)) <=> (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.48/0.62      inference(rewrite,[status(thm)],[])).
% 0.48/0.62  tff(992,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))))),
% 0.48/0.62      inference(monotonicity,[status(thm)],[991])).
% 0.48/0.62  tff(993,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.48/0.62      inference(transitivity,[status(thm)],[992, 990])).
% 0.48/0.62  tff(994,plain,
% 0.48/0.62      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (c = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c))),
% 0.48/0.62      inference(quant_inst,[status(thm)],[])).
% 0.48/0.62  tff(995,plain,
% 0.48/0.62      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = c) | r(c, f(f(f(f(c))))) | (c = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), c) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.48/0.62      inference(modus_ponens,[status(thm)],[994, 993])).
% 0.48/0.62  tff(996,plain,
% 0.48/0.62      (r(f(f(f(f(f(c))))), c)),
% 0.48/0.62      inference(unit_resolution,[status(thm)],[995, 116, 90, 989, 985, 57, 256])).
% 0.48/0.62  tff(997,assumption,(r(f(f(f(f(c)))), f(f(f(c))))), introduced(assumption)).
% 0.48/0.62  tff(998,plain,
% 0.48/0.62      (r(f(c), f(f(f(c))))),
% 0.48/0.62      inference(unit_resolution,[status(thm)],[203, 155, 154, 22])).
% 0.48/0.62  tff(999,assumption,(~(f(f(f(f(c)))) = f(f(f(c))))), introduced(assumption)).
% 0.48/0.62  tff(1000,assumption,(~(f(c) = f(f(f(f(c)))))), introduced(assumption)).
% 0.48/0.62  tff(1001,plain,
% 0.48/0.62      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.48/0.62      inference(rewrite,[status(thm)],[])).
% 0.48/0.62  tff(1002,plain,
% 0.48/0.62      (((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c)))))) <=> ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1003,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))))),
% 0.48/0.63      inference(monotonicity,[status(thm)],[1002])).
% 0.48/0.63  tff(1004,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))))),
% 0.48/0.63      inference(transitivity,[status(thm)],[1003, 1001])).
% 0.48/0.63  tff(1005,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(c)))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(c))))))),
% 0.48/0.63      inference(quant_inst,[status(thm)],[])).
% 0.48/0.63  tff(1006,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))),
% 0.48/0.63      inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.48/0.63  tff(1007,plain,
% 0.48/0.63      ((f(f(f(f(c)))) = f(f(f(c)))) | (f(c) = f(f(f(f(c))))) | (~r(f(c), f(f(f(f(c))))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1006, 214, 760, 142, 997])).
% 0.48/0.63  tff(1008,plain,
% 0.48/0.63      (~r(f(c), f(f(f(f(c)))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1007, 1000, 999])).
% 0.48/0.63  tff(1009,plain,
% 0.48/0.63      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1010,plain,
% 0.48/0.63      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c))))))),
% 0.48/0.63      inference(quant_inst,[status(thm)],[])).
% 0.48/0.63  tff(1011,plain,
% 0.48/0.63      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(f(c)))), f(c))) | r(f(c), f(f(f(f(c)))))),
% 0.48/0.63      inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.48/0.63  tff(1012,plain,
% 0.48/0.63      (~r(f(f(f(f(c)))), f(c))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1011, 99, 1008])).
% 0.48/0.63  tff(1013,plain,
% 0.48/0.63      ((f(c) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(c))),
% 0.48/0.63      inference(commutativity,[status(thm)],[])).
% 0.48/0.63  tff(1014,plain,
% 0.48/0.63      ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(c)))),
% 0.48/0.63      inference(monotonicity,[status(thm)],[1013])).
% 0.48/0.63  tff(1015,plain,
% 0.48/0.63      (~(f(f(f(f(c)))) = f(c))),
% 0.48/0.63      inference(modus_ponens,[status(thm)],[1000, 1014])).
% 0.48/0.63  tff(1016,assumption,(~r(c, f(c))), introduced(assumption)).
% 0.48/0.63  tff(1017,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1018,plain,
% 0.48/0.63      ((r(c, f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), c) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = c)) <=> (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1019,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), c) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c))))),
% 0.48/0.63      inference(monotonicity,[status(thm)],[1018])).
% 0.48/0.63  tff(1020,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), c) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.48/0.63      inference(transitivity,[status(thm)],[1019, 1017])).
% 0.48/0.63  tff(1021,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(c, f(c)) | r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(c)))), c) | (c = f(c)) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(c)))) = c))),
% 0.48/0.63      inference(quant_inst,[status(thm)],[])).
% 0.48/0.63  tff(1022,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c))),
% 0.48/0.63      inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.48/0.63  tff(1023,plain,
% 0.48/0.63      ($false),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1022, 116, 1016, 34, 54, 386, 1015, 1012])).
% 0.48/0.63  tff(1024,plain,((f(c) = f(f(f(f(c))))) | r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63  tff(1025,plain,
% 0.48/0.63      (r(c, f(c)) | (c = f(c)) | (f(f(f(f(c)))) = c) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1024, 79])).
% 0.48/0.63  tff(1026,plain,
% 0.48/0.63      (r(c, f(c)) | (c = f(c)) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(c) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1025, 50])).
% 0.48/0.63  tff(1027,plain,
% 0.48/0.63      (r(c, f(c)) | (c = f(c)) | r(f(f(f(f(c)))), c) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1026, 139])).
% 0.48/0.63  tff(1028,plain,
% 0.48/0.63      (r(c, f(c)) | (c = f(c)) | r(f(f(f(f(c)))), c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1027, 270])).
% 0.48/0.63  tff(1029,plain,
% 0.48/0.63      (r(c, f(c))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1028, 998, 386, 30, 997])).
% 0.48/0.63  tff(1030,plain,
% 0.48/0.63      (r(f(c), c)),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[939, 99, 1029])).
% 0.48/0.63  tff(1031,assumption,(r(f(f(f(f(f(c))))), c)), introduced(assumption)).
% 0.48/0.63  tff(1032,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(c), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1033,plain,
% 0.48/0.63      (((~r(f(f(f(f(f(c))))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c))))))) <=> ((f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1034,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(c), f(f(f(f(f(c)))))))))),
% 0.48/0.63      inference(monotonicity,[status(thm)],[1033])).
% 0.48/0.63  tff(1035,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.63      inference(transitivity,[status(thm)],[1034, 1032])).
% 0.48/0.63  tff(1036,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), c)) | (~r(f(c), c)) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))),
% 0.48/0.63      inference(quant_inst,[status(thm)],[])).
% 0.48/0.63  tff(1037,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), c)) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(c), f(f(f(f(f(c)))))))),
% 0.48/0.63      inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.48/0.63  tff(1038,plain,
% 0.48/0.63      ($false),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1037, 214, 853, 48, 90, 1031, 1030, 37])).
% 0.48/0.63  tff(1039,plain,(r(f(c), f(f(c))) | (~r(f(f(f(f(f(c))))), c)) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(f(c)))), c) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(c)), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63  tff(1040,plain,
% 0.48/0.63      (r(f(c), f(f(c)))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1039, 996, 978, 965, 974, 967])).
% 0.48/0.63  tff(1041,plain,
% 0.48/0.63      (~r(f(c), c)),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[961, 1040, 22, 826])).
% 0.48/0.63  tff(1042,plain,
% 0.48/0.63      (~r(f(c), f(f(f(f(c)))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[303, 1040, 964, 22])).
% 0.48/0.63  tff(1043,plain,
% 0.48/0.63      ($false),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[477, 1042, 1041, 37, 965])).
% 0.48/0.63  tff(1044,plain,(r(f(f(f(c))), c) | r(f(f(c)), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63  tff(1045,plain,
% 0.48/0.63      (r(f(f(f(c))), c)),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1044, 348])).
% 0.48/0.63  tff(1046,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.63  tff(1047,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c))))),
% 0.48/0.63      inference(quant_inst,[status(thm)],[])).
% 0.48/0.63  tff(1048,plain,
% 0.48/0.63      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(c))), c)) | (~r(f(f(f(c))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(c)))),
% 0.48/0.63      inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.48/0.63  tff(1049,plain,
% 0.48/0.63      (~r(f(f(f(c))), f(f(c)))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[1048, 214, 1045, 81, 826, 152, 636])).
% 0.48/0.63  tff(1050,plain,
% 0.48/0.63      (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.63      inference(unit_resolution,[status(thm)],[276, 116, 270, 251, 250, 243, 636])).
% 0.48/0.63  tff(1051,plain,
% 0.48/0.63      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.63      inference(rewrite,[status(thm)],[])).
% 0.48/0.64  tff(1052,plain,
% 0.48/0.64      (((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(f(f(c))))))) <=> ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
% 0.48/0.64  tff(1053,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c)))))))),
% 0.48/0.64      inference(monotonicity,[status(thm)],[1052])).
% 0.48/0.64  tff(1054,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.64      inference(transitivity,[status(thm)],[1053, 1051])).
% 0.48/0.64  tff(1055,plain,
% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))))),
% 0.48/0.64      inference(quant_inst,[status(thm)],[])).
% 0.48/0.64  tff(1056,plain,
% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(f(f(c)))))) | (~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.64      inference(modus_ponens,[status(thm)],[1055, 1054])).
% 0.48/0.64  tff(1057,plain,
% 0.48/0.64      ($false),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1056, 214, 579, 11, 270, 1050, 852, 308])).
% 0.48/0.64  tff(1058,plain,(r(f(f(f(f(c)))), f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(f(c))), f(f(c)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64  tff(1059,plain,
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% 0.48/0.64      inference(unit_resolution,[status(thm)],[1058, 893, 978, 1049])).
% 0.48/0.64  tff(1060,plain,
% 0.48/0.64      (~r(f(f(c)), f(f(f(c))))),
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% 0.48/0.64  tff(1061,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
% 0.48/0.64  tff(1062,plain,
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% 0.48/0.64      inference(rewrite,[status(thm)],[])).
% 0.48/0.64  tff(1063,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c)))))))))),
% 0.48/0.64      inference(monotonicity,[status(thm)],[1062])).
% 0.48/0.64  tff(1064,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))))),
% 0.48/0.64      inference(transitivity,[status(thm)],[1063, 1061])).
% 0.48/0.64  tff(1065,plain,
% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))))),
% 0.48/0.64      inference(quant_inst,[status(thm)],[])).
% 0.48/0.64  tff(1066,plain,
% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(f(f(f(f(c))))) = f(f(f(c)))) | (f(c) = f(f(f(c)))) | (f(c) = f(f(f(f(f(c)))))) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(c), f(f(f(f(f(c)))))))),
% 0.48/0.64      inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.48/0.64  tff(1067,plain,
% 0.48/0.64      ($false),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1066, 214, 579, 11, 998, 853, 139, 48])).
% 0.48/0.64  tff(1068,plain,(r(f(c), f(f(c))) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | r(f(f(f(f(f(c))))), f(f(c))) | r(f(f(c)), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64  tff(1069,plain,
% 0.48/0.64      (r(f(c), f(f(c)))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1068, 893, 978, 1060])).
% 0.48/0.64  tff(1070,plain,
% 0.48/0.64      (~r(f(c), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[961, 1069, 22, 826])).
% 0.48/0.64  tff(1071,plain,
% 0.48/0.64      (~r(f(c), f(f(f(f(c)))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[303, 1059, 1069, 22])).
% 0.48/0.64  tff(1072,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[477, 1071, 37, 1070])).
% 0.48/0.64  tff(1073,plain,
% 0.48/0.64      ($false),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[874, 214, 145, 50, 1072, 866, 250, 1059])).
% 0.48/0.64  tff(1074,plain,(r(f(f(c)), f(f(f(f(f(c))))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64  tff(1075,plain,
% 0.48/0.64      (r(f(f(f(f(f(c))))), f(f(c)))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[330, 99, 1074])).
% 0.48/0.64  tff(1076,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
% 0.48/0.64  tff(1077,plain,
% 0.48/0.64      (((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c))))))) <=> ((~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
% 0.48/0.64  tff(1078,plain,
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% 0.48/0.64      inference(monotonicity,[status(thm)],[1077])).
% 0.48/0.64  tff(1079,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))),
% 0.48/0.64      inference(transitivity,[status(thm)],[1078, 1076])).
% 0.48/0.64  tff(1080,plain,
% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))) | (c = f(f(f(f(f(c)))))))),
% 0.48/0.64      inference(quant_inst,[status(thm)],[])).
% 0.48/0.64  tff(1081,plain,
% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (~r(c, f(f(f(f(f(c))))))) | (c = f(f(f(f(f(c)))))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c)))),
% 0.48/0.64      inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.48/0.64  tff(1082,plain,
% 0.48/0.64      (~r(c, f(f(f(f(f(c))))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1081, 214, 91, 316, 145, 866, 1075])).
% 0.48/0.64  tff(1083,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), f(f(f(f(f(c)))))) | r(f(f(f(c))), f(f(f(f(f(c)))))) | (~r(f(f(f(c))), c))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[812, 1082])).
% 0.48/0.64  tff(1084,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), f(f(f(f(f(c))))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1083, 103, 877])).
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% 0.48/0.64      ((~r(f(f(f(f(c)))), f(f(f(f(f(c))))))) | (~r(f(f(f(f(c)))), f(f(c))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[326, 1074])).
% 0.48/0.64  tff(1086,plain,
% 0.48/0.64      (~r(f(f(f(f(c)))), f(f(c)))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1085, 1084])).
% 0.48/0.64  tff(1087,plain,
% 0.48/0.64      (~r(f(f(f(c))), f(f(c)))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1048, 214, 877, 81, 826, 152, 636])).
% 0.48/0.64  tff(1088,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[276, 116, 270, 1087, 250, 1086, 636])).
% 0.48/0.64  tff(1089,plain,
% 0.48/0.64      (~r(f(c), f(f(f(f(c)))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1006, 214, 204, 139, 79, 999, 997])).
% 0.48/0.64  tff(1090,plain,
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% 0.48/0.64      inference(unit_resolution,[status(thm)],[612, 116, 27, 155, 79, 250, 243, 1089])).
% 0.48/0.64  tff(1091,plain,(r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(c)), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64  tff(1092,plain,
% 0.48/0.64      (r(f(c), f(f(c))) | (f(c) = f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(c)), f(f(f(c))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1091, 270])).
% 0.48/0.64  tff(1093,plain,
% 0.48/0.64      (r(f(c), f(f(c))) | r(f(f(f(f(c)))), f(f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | r(f(f(c)), f(f(f(c))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1092, 22])).
% 0.48/0.64  tff(1094,plain,
% 0.48/0.64      (r(f(c), f(f(c)))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1093, 1088, 884, 1086])).
% 0.48/0.64  tff(1095,plain,
% 0.48/0.64      ((~r(f(c), f(f(f(f(f(c))))))) | (~r(f(c), f(f(c))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[749, 1074])).
% 0.48/0.64  tff(1096,plain,
% 0.48/0.64      (~r(f(c), f(f(f(f(f(c))))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1095, 1094])).
% 0.48/0.64  tff(1097,plain,
% 0.48/0.64      (r(f(c), f(f(f(c))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[757, 1096, 58])).
% 0.48/0.64  tff(1098,plain,
% 0.48/0.64      (r(f(f(f(c))), f(c))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[765, 1097])).
% 0.48/0.64  tff(1099,plain,
% 0.48/0.64      ((~r(f(f(f(c))), f(c))) | (~r(c, f(c))) | (~r(f(f(f(c))), c))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[774, 755, 30])).
% 0.48/0.64  tff(1100,plain,
% 0.48/0.64      (~r(c, f(c))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1099, 1098, 877])).
% 0.48/0.64  tff(1101,plain,
% 0.48/0.64      (r(c, f(c)) | r(f(f(f(f(c)))), c) | (~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1028, 30])).
% 0.48/0.64  tff(1102,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1101, 1100, 1088, 1097])).
% 0.48/0.64  tff(1103,plain,
% 0.48/0.64      (r(c, f(f(f(f(c)))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[557, 1102])).
% 0.48/0.64  tff(1104,plain,
% 0.48/0.64      (r(f(f(f(c))), f(f(f(f(c)))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[406, 1086, 884])).
% 0.48/0.64  tff(1105,plain,
% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
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% 0.48/0.64      (((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c)) <=> ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
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% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c))))))))),
% 0.48/0.64      inference(monotonicity,[status(thm)],[1106])).
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% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | (~r(f(f(f(c))), c)) | (c = f(f(f(f(c))))) | (f(f(f(c))) = f(f(f(f(c))))) | (f(f(f(c))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(f(c))), c)) | (f(f(f(c))) = c) | (f(f(f(c))) = f(f(f(f(c))))) | (c = f(f(f(f(c))))) | (~r(c, f(f(f(f(c)))))) | (~r(f(f(f(c))), f(f(f(f(c)))))))),
% 0.48/0.64      inference(transitivity,[status(thm)],[1107, 1105])).
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% 0.48/0.64      inference(quant_inst,[status(thm)],[])).
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% 0.48/0.64      inference(modus_ponens,[status(thm)],[1109, 1108])).
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% 0.48/0.64  tff(1114,plain,
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% 0.48/0.64      inference(unit_resolution,[status(thm)],[1113, 1112])).
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% 0.48/0.64  tff(1116,plain,
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% 0.48/0.64  tff(1119,plain,
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% 0.48/0.64      inference(unit_resolution,[status(thm)],[935, 214, 1112, 11, 760, 139, 919])).
% 0.48/0.64  tff(1120,plain,
% 0.48/0.64      (r(f(f(f(c))), f(c))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[765, 760])).
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% 0.48/0.64  tff(1122,plain,
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% 0.48/0.64      inference(unit_resolution,[status(thm)],[781, 116, 30, 1121, 48, 1082, 91])).
% 0.48/0.64  tff(1123,plain,
% 0.48/0.64      (~r(f(f(f(c))), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1099, 1122, 1120])).
% 0.48/0.64  tff(1124,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), f(f(c)))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[405, 397, 154, 267])).
% 0.48/0.64  tff(1125,plain,
% 0.48/0.64      (r(f(f(c)), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[184, 590, 154])).
% 0.48/0.64  tff(1126,plain,
% 0.48/0.64      (r(f(f(f(f(c)))), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[528, 397, 59, 267])).
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% 0.48/0.64      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(f(c)), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(c))))),
% 0.48/0.64      inference(rewrite,[status(thm)],[])).
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% 0.48/0.64      inference(quant_inst,[status(thm)],[])).
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% 0.48/0.64      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(f(f(c)), c)) | (~r(f(f(f(f(c)))), c)) | (~r(f(f(f(f(c)))), f(f(c)))) | (f(f(c)) = c) | (f(f(f(f(c)))) = c) | (f(f(f(f(c)))) = f(f(c)))),
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% 0.48/0.64      ($false),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1129, 214, 50, 1126, 1125, 152, 250, 1124])).
% 0.48/0.64  tff(1131,plain,(r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | (f(f(f(c))) = f(f(f(f(c))))) | r(f(f(f(c))), c)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.64  tff(1132,plain,
% 0.48/0.64      (r(f(f(f(c))), f(f(f(f(c))))) | r(f(f(c)), f(f(f(c)))) | r(f(f(f(c))), c)),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1131, 263])).
% 0.48/0.64  tff(1133,plain,
% 0.48/0.64      (r(f(f(f(c))), f(f(f(f(c)))))),
% 0.48/0.64      inference(unit_resolution,[status(thm)],[1132, 1123, 1114])).
% 0.48/0.64  tff(1134,plain,
% 0.48/0.64      (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1135,plain,
% 0.48/0.65      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(1136,plain,
% 0.48/0.65      ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(f(f(f(c))), f(f(f(f(c)))))) | r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.48/0.65  tff(1137,plain,
% 0.48/0.65      (r(f(f(f(f(c)))), f(f(f(c))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1136, 99, 1133])).
% 0.48/0.65  tff(1138,plain,
% 0.48/0.65      ((~r(f(f(f(f(f(c))))), f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[988, 214, 579, 11, 999, 997])).
% 0.48/0.65  tff(1139,plain,
% 0.48/0.65      (~r(f(f(f(f(f(c))))), f(f(f(f(c)))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1138, 260])).
% 0.48/0.65  tff(1140,assumption,(~r(f(f(f(f(c)))), f(c))), introduced(assumption)).
% 0.48/0.65  tff(1141,plain,
% 0.48/0.65      ((f(f(f(f(c)))) = f(c)) <=> (f(c) = f(f(f(f(c)))))),
% 0.48/0.65      inference(commutativity,[status(thm)],[])).
% 0.48/0.65  tff(1142,plain,
% 0.48/0.65      ((f(c) = f(f(f(f(c))))) <=> (f(f(f(f(c)))) = f(c))),
% 0.48/0.65      inference(symmetry,[status(thm)],[1141])).
% 0.48/0.65  tff(1143,plain,
% 0.48/0.65      ((~(f(c) = f(f(f(f(c)))))) <=> (~(f(f(f(f(c)))) = f(c)))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[1142])).
% 0.48/0.65  tff(1144,plain,
% 0.48/0.65      (~(f(f(f(f(c)))) = f(c))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[79, 1143])).
% 0.48/0.65  tff(1145,assumption,(~r(f(f(f(f(f(c))))), f(c))), introduced(assumption)).
% 0.48/0.65  tff(1146,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1147,plain,
% 0.48/0.65      ((r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))) <=> (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1148,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c))))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[1147])).
% 0.48/0.65  tff(1149,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c)))),
% 0.48/0.65      inference(transitivity,[status(thm)],[1148, 1146])).
% 0.48/0.65  tff(1150,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(c)))), f(c)) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | (f(f(f(f(f(c))))) = f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(1151,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(c)) | r(f(f(f(f(f(c))))), f(c)) | (f(f(f(f(f(c))))) = f(f(f(f(c))))) | (f(f(f(f(c)))) = f(c)) | r(f(f(f(f(c)))), f(c))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.48/0.65  tff(1152,plain,
% 0.48/0.65      (r(f(f(f(f(f(c))))), f(f(f(f(c))))) | (f(f(f(f(f(c))))) = f(f(f(f(c)))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1151, 116, 1145, 919, 1144, 1140])).
% 0.48/0.65  tff(1153,plain,
% 0.48/0.65      ($false),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1152, 1139, 260])).
% 0.48/0.65  tff(1154,plain,((f(f(f(f(f(c))))) = f(f(f(f(c))))) | r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (~r(f(f(f(f(c)))), f(f(f(c)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65  tff(1155,plain,
% 0.48/0.65      (r(f(f(f(f(f(c))))), f(c)) | r(f(f(f(f(c)))), f(c)) | (~r(f(f(f(f(f(c))))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1154, 256, 270])).
% 0.48/0.65  tff(1156,plain,
% 0.48/0.65      (r(f(f(f(f(c)))), f(c))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1155, 1137, 1112, 1119])).
% 0.48/0.65  tff(1157,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1158,plain,
% 0.48/0.65      (((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c))) <=> ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1159,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c)))))))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[1158])).
% 0.48/0.65  tff(1160,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c))))))),
% 0.48/0.65      inference(transitivity,[status(thm)],[1159, 1157])).
% 0.48/0.65  tff(1161,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(f(c), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(f(f(c))))) | (~r(f(f(f(f(c)))), f(c))) | (f(c) = f(f(f(c)))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(1162,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = f(f(f(c)))) | (~r(f(c), f(f(f(c))))) | (f(f(f(f(c)))) = f(f(f(c)))) | (f(f(f(f(c)))) = f(c)) | (~r(f(f(f(f(c)))), f(c))) | (~r(f(f(f(f(c)))), f(f(f(c)))))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[1161, 1160])).
% 0.48/0.65  tff(1163,plain,
% 0.48/0.65      ($false),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1162, 214, 760, 139, 270, 1137, 1156, 1118])).
% 0.48/0.65  tff(1164,plain,(~r(f(c), f(f(f(c))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65  tff(1165,plain,
% 0.48/0.65      (r(f(f(c)), f(f(f(c)))) | r(f(c), f(f(c))) | r(f(c), f(f(f(c))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[203, 22])).
% 0.48/0.65  tff(1166,plain,
% 0.48/0.65      (r(f(c), f(f(c)))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1165, 1164, 1114])).
% 0.48/0.65  tff(1167,plain,
% 0.48/0.65      ((~r(f(c), c)) | (~r(f(c), f(f(c))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[961, 22, 826])).
% 0.48/0.65  tff(1168,plain,
% 0.48/0.65      (~r(f(c), c)),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1167, 1166])).
% 0.48/0.65  tff(1169,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1170,plain,
% 0.48/0.65      (((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c)) <=> ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1171,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c)))))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[1170])).
% 0.48/0.65  tff(1172,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c))))),
% 0.48/0.65      inference(transitivity,[status(thm)],[1171, 1169])).
% 0.48/0.65  tff(1173,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | ((~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (c = f(f(c))) | (f(f(f(f(f(c))))) = f(f(c))) | (f(f(f(f(f(c))))) = c))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(1174,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : ((~r(Y, Z)) | (~r(X, Z)) | (~r(X, Y)) | (Y = Z) | (X = Z) | (X = Y))) | (~r(c, f(f(c)))) | (~r(f(f(f(f(f(c))))), c)) | (f(f(f(f(f(c))))) = c) | (~r(f(f(f(f(f(c))))), f(f(c)))) | (f(f(f(f(f(c))))) = f(f(c))) | (c = f(f(c)))),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.48/0.65  tff(1175,plain,
% 0.48/0.65      (~r(f(f(f(f(f(c))))), c)),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1174, 214, 90, 316, 145, 866, 1075])).
% 0.48/0.65  tff(1176,plain,
% 0.48/0.65      (~r(f(c), f(f(f(f(f(c))))))),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1095, 1166])).
% 0.48/0.65  tff(1177,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), c) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), c) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1178,plain,
% 0.48/0.65      ((r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c))))))) <=> ((f(c) = c) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), c) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))),
% 0.48/0.65      inference(rewrite,[status(thm)],[])).
% 0.48/0.65  tff(1179,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | ((f(c) = c) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), c) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c)))),
% 0.48/0.65      inference(monotonicity,[status(thm)],[1178])).
% 0.48/0.65  tff(1180,plain,
% 0.48/0.65      (((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), c) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c))),
% 0.48/0.65      inference(transitivity,[status(thm)],[1179, 1177])).
% 0.48/0.65  tff(1181,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (r(f(f(f(f(f(c))))), c) | r(f(c), c) | r(f(c), f(f(f(f(f(c)))))) | (f(f(f(f(f(c))))) = c) | (f(c) = c) | (f(c) = f(f(f(f(f(c)))))))),
% 0.48/0.65      inference(quant_inst,[status(thm)],[])).
% 0.48/0.65  tff(1182,plain,
% 0.48/0.65      ((~![X: $i, Y: $i, Z: $i] : (r(Y, Z) | r(X, Z) | r(X, Y) | (Y = Z) | (X = Z) | (X = Y))) | (f(c) = c) | r(f(c), f(f(f(f(f(c)))))) | (f(c) = f(f(f(f(f(c)))))) | r(f(c), c) | (f(f(f(f(f(c))))) = c) | r(f(f(f(f(f(c))))), c)),
% 0.48/0.65      inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.48/0.65  tff(1183,plain,
% 0.48/0.65      ($false),
% 0.48/0.65      inference(unit_resolution,[status(thm)],[1182, 116, 1176, 48, 90, 1175, 1168, 37])).
% 0.48/0.65  % SZS output end Proof
% 0.48/0.66  % E exiting
%------------------------------------------------------------------------------