%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO617-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:41:58 AM UTC 2025
% Result : Unsatisfiable 3.04s 3.20s
% Output : Proof 3.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO617-1 : TPTP v9.0.0. Released v7.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:16:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.04/3.20 % SZS status Unsatisfiable
% 3.04/3.20 % SZS output start Proof
% 3.04/3.20 tff(le_type, type, (
% 3.04/3.20 le: ( $i * $i ) > $o)).
% 3.04/3.20 tff(max_type, type, (
% 3.04/3.20 max: ( $i * $i ) > $i)).
% 3.04/3.20 tff(s_type, type, (
% 3.04/3.20 s: $i > $i)).
% 3.04/3.20 tff(elem_0_type, type, (
% 3.04/3.20 elem_0: $i)).
% 3.04/3.20 tff(eq_type, type, (
% 3.04/3.20 eq: ( $i * $i ) > $o)).
% 3.04/3.20 tff(a1_type, type, (
% 3.04/3.20 a1: $i)).
% 3.04/3.20 tff(f_type, type, (
% 3.04/3.20 f: $i > $i)).
% 3.04/3.20 tff(a2_type, type, (
% 3.04/3.20 a2: $i)).
% 3.04/3.20 tff(a0_type, type, (
% 3.04/3.20 a0: $i)).
% 3.04/3.20 tff(1,plain,
% 3.04/3.20 (^[A: $i] : refl(le(A, A) <=> le(A, A))),
% 3.04/3.20 inference(bind,[status(th)],[])).
% 3.04/3.20 tff(2,plain,
% 3.04/3.20 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 3.04/3.20 inference(quant_intro,[status(thm)],[1])).
% 3.04/3.20 tff(3,plain,
% 3.04/3.20 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(4,axiom,(![A: $i] : le(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_01')).
% 3.04/3.20 tff(5,plain,
% 3.04/3.20 (![A: $i] : le(A, A)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.04/3.20 tff(6,plain,(
% 3.04/3.20 ![A: $i] : le(A, A)),
% 3.04/3.20 inference(skolemize,[status(sab)],[5])).
% 3.04/3.20 tff(7,plain,
% 3.04/3.20 (![A: $i] : le(A, A)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.04/3.20 tff(8,plain,
% 3.04/3.20 ((~![A: $i] : le(A, A)) | le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(9,plain,
% 3.04/3.20 (le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.04/3.20 tff(10,plain,
% 3.04/3.20 (^[B: $i, A: $i, C: $i] : refl(((~le(max(A, B), C)) | le(B, C)) <=> ((~le(max(A, B), C)) | le(B, C)))),
% 3.04/3.20 inference(bind,[status(th)],[])).
% 3.04/3.20 tff(11,plain,
% 3.04/3.20 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 3.04/3.20 inference(quant_intro,[status(thm)],[10])).
% 3.04/3.20 tff(12,plain,
% 3.04/3.20 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13,axiom,(![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_03')).
% 3.04/3.20 tff(14,plain,
% 3.04/3.20 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13, 12])).
% 3.04/3.20 tff(15,plain,(
% 3.04/3.20 ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 3.04/3.20 inference(skolemize,[status(sab)],[14])).
% 3.04/3.20 tff(16,plain,
% 3.04/3.20 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[15, 11])).
% 3.04/3.20 tff(17,plain,
% 3.04/3.20 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(18,plain,
% 3.04/3.20 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(19,plain,
% 3.04/3.20 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[18, 17])).
% 3.04/3.20 tff(20,plain,
% 3.04/3.20 (le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 3.04/3.20 tff(21,plain,
% 3.04/3.20 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(22,plain,
% 3.04/3.20 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(23,plain,
% 3.04/3.20 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[22, 21])).
% 3.04/3.20 tff(24,plain,
% 3.04/3.20 (le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[23, 16, 20])).
% 3.04/3.20 tff(25,plain,
% 3.04/3.20 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(26,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(27,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(elem!0, s(s(elem!0))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.05/3.21 tff(28,plain,
% 3.05/3.21 (le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[27, 16, 24])).
% 3.05/3.21 tff(29,plain,
% 3.05/3.21 (^[B: $i, A: $i, C: $i] : refl(((~le(max(A, B), C)) | le(A, C)) <=> ((~le(max(A, B), C)) | le(A, C)))),
% 3.05/3.21 inference(bind,[status(th)],[])).
% 3.05/3.21 tff(30,plain,
% 3.05/3.21 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 3.05/3.21 inference(quant_intro,[status(thm)],[29])).
% 3.05/3.21 tff(31,plain,
% 3.05/3.21 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(32,axiom,(![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_02')).
% 3.05/3.21 tff(33,plain,
% 3.05/3.21 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[32, 31])).
% 3.05/3.21 tff(34,plain,(
% 3.05/3.21 ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 3.05/3.21 inference(skolemize,[status(sab)],[33])).
% 3.05/3.21 tff(35,plain,
% 3.05/3.21 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[34, 30])).
% 3.05/3.21 tff(36,plain,
% 3.05/3.21 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(37,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(38,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[37, 36])).
% 3.05/3.21 tff(39,plain,
% 3.05/3.21 (le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[38, 35, 20])).
% 3.05/3.21 tff(40,plain,
% 3.05/3.21 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(41,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(42,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[41, 40])).
% 3.05/3.21 tff(43,plain,
% 3.05/3.21 (le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[42, 35, 39])).
% 3.05/3.21 tff(44,assumption,(eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)), introduced(assumption)).
% 3.05/3.21 tff(45,assumption,(~eq(f(s(elem!0)), a1)), introduced(assumption)).
% 3.05/3.21 tff(46,assumption,(~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)), introduced(assumption)).
% 3.05/3.21 tff(47,assumption,(~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)), introduced(assumption)).
% 3.05/3.21 tff(48,assumption,(eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)), introduced(assumption)).
% 3.05/3.21 tff(49,plain,
% 3.05/3.21 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(50,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(51,plain,
% 3.05/3.21 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[50, 49])).
% 3.05/3.21 tff(52,plain,
% 3.05/3.21 (le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[51, 35, 9])).
% 3.05/3.21 tff(53,plain,
% 3.05/3.21 (^[A0: $i, A1: $i] : refl(((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))))),
% 3.05/3.21 inference(bind,[status(th)],[])).
% 3.05/3.21 tff(54,plain,
% 3.05/3.21 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(quant_intro,[status(thm)],[53])).
% 3.05/3.21 tff(55,plain,
% 3.05/3.21 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(56,plain,
% 3.05/3.21 (^[A0: $i, A1: $i] : trans(monotonicity(rewrite(((~eq(f(A0), a1)) | (~eq(f(A1), a1))) <=> ((~eq(f(A1), a1)) | (~eq(f(A0), a1)))), ((((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1))) <=> (((~eq(f(A1), a1)) | (~eq(f(A0), a1))) | (~le(s(A0), A1))))), rewrite((((~eq(f(A1), a1)) | (~eq(f(A0), a1))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))), ((((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))))),
% 3.05/3.21 inference(bind,[status(th)],[])).
% 3.05/3.21 tff(57,plain,
% 3.05/3.21 (![A0: $i, A1: $i] : (((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(quant_intro,[status(thm)],[56])).
% 3.05/3.21 tff(58,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_06')).
% 3.05/3.21 tff(59,plain,
% 3.05/3.21 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[58, 57])).
% 3.05/3.21 tff(60,plain,
% 3.05/3.21 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[59, 55])).
% 3.05/3.21 tff(61,plain,(
% 3.05/3.21 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(skolemize,[status(sab)],[60])).
% 3.05/3.21 tff(62,plain,
% 3.05/3.21 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[61, 54])).
% 3.05/3.21 tff(63,plain,
% 3.05/3.21 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(64,plain,
% 3.05/3.21 (((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1))) <=> ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(65,plain,
% 3.05/3.21 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))))),
% 3.05/3.21 inference(monotonicity,[status(thm)],[64])).
% 3.05/3.21 tff(66,plain,
% 3.05/3.21 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.21 inference(transitivity,[status(thm)],[65, 63])).
% 3.05/3.21 tff(67,plain,
% 3.05/3.21 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)))),
% 3.05/3.21 inference(quant_inst,[status(thm)],[])).
% 3.05/3.21 tff(68,plain,
% 3.05/3.21 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[67, 66])).
% 3.05/3.21 tff(69,plain,
% 3.05/3.21 ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1))),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[68, 62, 52])).
% 3.05/3.21 tff(70,plain,
% 3.05/3.21 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)),
% 3.05/3.21 inference(unit_resolution,[status(thm)],[69, 48])).
% 3.05/3.21 tff(71,plain,
% 3.05/3.21 (^[A: $i] : refl((eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0)) <=> (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0)))),
% 3.05/3.21 inference(bind,[status(th)],[])).
% 3.05/3.21 tff(72,plain,
% 3.05/3.21 (![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0)) <=> ![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(quant_intro,[status(thm)],[71])).
% 3.05/3.21 tff(73,plain,
% 3.05/3.21 (![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0)) <=> ![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(74,plain,
% 3.05/3.21 (^[A: $i] : rewrite(((eq(f(A), a0) | eq(f(A), a1)) | eq(f(A), a2)) <=> (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0)))),
% 3.05/3.21 inference(bind,[status(th)],[])).
% 3.05/3.21 tff(75,plain,
% 3.05/3.21 (![A: $i] : ((eq(f(A), a0) | eq(f(A), a1)) | eq(f(A), a2)) <=> ![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(quant_intro,[status(thm)],[74])).
% 3.05/3.21 tff(76,axiom,(![A: $i] : ((eq(f(A), a0) | eq(f(A), a1)) | eq(f(A), a2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_04')).
% 3.05/3.21 tff(77,plain,
% 3.05/3.21 (![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.05/3.21 tff(78,plain,
% 3.05/3.21 (![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[77, 73])).
% 3.05/3.21 tff(79,plain,(
% 3.05/3.21 ![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(skolemize,[status(sab)],[78])).
% 3.05/3.21 tff(80,plain,
% 3.05/3.21 (![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))),
% 3.05/3.21 inference(modus_ponens,[status(thm)],[79, 72])).
% 3.05/3.21 tff(81,plain,
% 3.05/3.21 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(82,plain,
% 3.05/3.21 ((eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) <=> (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))),
% 3.05/3.21 inference(rewrite,[status(thm)],[])).
% 3.05/3.21 tff(83,plain,
% 3.05/3.21 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[82])).
% 3.05/3.22 tff(84,plain,
% 3.05/3.22 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))),
% 3.05/3.22 inference(transitivity,[status(thm)],[83, 81])).
% 3.05/3.22 tff(85,plain,
% 3.05/3.22 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(86,plain,
% 3.05/3.22 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[85, 84])).
% 3.05/3.22 tff(87,plain,
% 3.05/3.22 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[86, 80, 47])).
% 3.05/3.22 tff(88,plain,
% 3.05/3.22 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[87, 70])).
% 3.05/3.22 tff(89,plain,
% 3.05/3.22 ((~![A: $i] : le(A, A)) | le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(90,plain,
% 3.05/3.22 (le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[89, 7])).
% 3.05/3.22 tff(91,plain,
% 3.05/3.22 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(92,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(93,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[92, 91])).
% 3.05/3.22 tff(94,plain,
% 3.05/3.22 (le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[93, 16, 90])).
% 3.05/3.22 tff(95,plain,
% 3.05/3.22 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(96,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(97,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(s(s(elem!0)), max(s(elem!0), s(elem!0))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[96, 95])).
% 3.05/3.22 tff(98,plain,
% 3.05/3.22 (le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[97, 16, 94])).
% 3.05/3.22 tff(99,plain,
% 3.05/3.22 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(100,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(101,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.05/3.22 tff(102,plain,
% 3.05/3.22 (le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[101, 35, 98])).
% 3.05/3.22 tff(103,plain,
% 3.05/3.22 (^[A0: $i, A1: $i] : refl(((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2))))),
% 3.05/3.22 inference(bind,[status(th)],[])).
% 3.05/3.22 tff(104,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(quant_intro,[status(thm)],[103])).
% 3.05/3.22 tff(105,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(106,plain,
% 3.05/3.22 (^[A0: $i, A1: $i] : trans(monotonicity(rewrite(((~eq(f(A0), a2)) | (~eq(f(A1), a2))) <=> ((~eq(f(A1), a2)) | (~eq(f(A0), a2)))), ((((~eq(f(A0), a2)) | (~eq(f(A1), a2))) | (~le(s(A0), A1))) <=> (((~eq(f(A1), a2)) | (~eq(f(A0), a2))) | (~le(s(A0), A1))))), rewrite((((~eq(f(A1), a2)) | (~eq(f(A0), a2))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))), ((((~eq(f(A0), a2)) | (~eq(f(A1), a2))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))))),
% 3.05/3.22 inference(bind,[status(th)],[])).
% 3.05/3.22 tff(107,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : (((~eq(f(A0), a2)) | (~eq(f(A1), a2))) | (~le(s(A0), A1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(quant_intro,[status(thm)],[106])).
% 3.05/3.22 tff(108,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a2)) | (~eq(f(A1), a2))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_07')).
% 3.05/3.22 tff(109,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[108, 107])).
% 3.05/3.22 tff(110,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[109, 105])).
% 3.05/3.22 tff(111,plain,(
% 3.05/3.22 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(skolemize,[status(sab)],[110])).
% 3.05/3.22 tff(112,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[111, 104])).
% 3.05/3.22 tff(113,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(114,plain,
% 3.05/3.22 (((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(elem!0), a2))) <=> ((~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(115,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(elem!0), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[114])).
% 3.05/3.22 tff(116,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(elem!0), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[115, 113])).
% 3.05/3.22 tff(117,plain,
% 3.05/3.22 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(elem!0), a2)))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(118,plain,
% 3.05/3.22 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[117, 116])).
% 3.05/3.22 tff(119,plain,
% 3.05/3.22 ((~eq(f(elem!0), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[118, 112, 102])).
% 3.05/3.22 tff(120,plain,
% 3.05/3.22 (~eq(f(elem!0), a2)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[119, 88])).
% 3.05/3.22 tff(121,assumption,(eq(f(elem!0), a0)), introduced(assumption)).
% 3.05/3.22 tff(122,plain,
% 3.05/3.22 (^[A0: $i, A1: $i] : refl(((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))))),
% 3.05/3.22 inference(bind,[status(th)],[])).
% 3.05/3.22 tff(123,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(quant_intro,[status(thm)],[122])).
% 3.05/3.22 tff(124,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(125,plain,
% 3.05/3.22 (^[A0: $i, A1: $i] : trans(monotonicity(rewrite(((~eq(f(A0), a0)) | (~eq(f(A1), a0))) <=> ((~eq(f(A1), a0)) | (~eq(f(A0), a0)))), ((((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> (((~eq(f(A1), a0)) | (~eq(f(A0), a0))) | (~le(s(A0), A1))))), rewrite((((~eq(f(A1), a0)) | (~eq(f(A0), a0))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))), ((((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))))),
% 3.05/3.22 inference(bind,[status(th)],[])).
% 3.05/3.22 tff(126,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1))) <=> ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(quant_intro,[status(thm)],[125])).
% 3.05/3.22 tff(127,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos_05')).
% 3.05/3.22 tff(128,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[127, 126])).
% 3.05/3.22 tff(129,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[128, 124])).
% 3.05/3.22 tff(130,plain,(
% 3.05/3.22 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(skolemize,[status(sab)],[129])).
% 3.05/3.22 tff(131,plain,
% 3.05/3.22 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[130, 123])).
% 3.05/3.22 tff(132,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(133,plain,
% 3.05/3.22 (((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(134,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[133])).
% 3.05/3.22 tff(135,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.22 inference(transitivity,[status(thm)],[134, 132])).
% 3.05/3.22 tff(136,plain,
% 3.05/3.22 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(elem!0), a0)))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(137,plain,
% 3.05/3.22 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[136, 135])).
% 3.05/3.22 tff(138,plain,
% 3.05/3.22 ((~eq(f(elem!0), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0))),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[137, 131, 102])).
% 3.05/3.22 tff(139,plain,
% 3.05/3.22 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[138, 121])).
% 3.05/3.22 tff(140,assumption,(eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)), introduced(assumption)).
% 3.05/3.22 tff(141,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(142,plain,
% 3.05/3.22 (((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(143,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))))),
% 3.05/3.22 inference(monotonicity,[status(thm)],[142])).
% 3.05/3.22 tff(144,plain,
% 3.05/3.22 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))),
% 3.05/3.22 inference(transitivity,[status(thm)],[143, 141])).
% 3.05/3.22 tff(145,plain,
% 3.05/3.22 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(elem!0), a0)))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(146,plain,
% 3.05/3.22 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))),
% 3.05/3.22 inference(modus_ponens,[status(thm)],[145, 144])).
% 3.05/3.22 tff(147,plain,
% 3.05/3.22 ($false),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[146, 131, 121, 140, 43])).
% 3.05/3.22 tff(148,plain,((~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(elem!0), a0))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.22 tff(149,plain,
% 3.05/3.22 (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)),
% 3.05/3.22 inference(unit_resolution,[status(thm)],[148, 121])).
% 3.05/3.22 tff(150,assumption,(eq(f(s(elem!0)), a1)), introduced(assumption)).
% 3.05/3.22 tff(151,plain,
% 3.05/3.22 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(rewrite,[status(thm)],[])).
% 3.05/3.22 tff(152,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.22 inference(quant_inst,[status(thm)],[])).
% 3.05/3.22 tff(153,plain,
% 3.05/3.22 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.05/3.23 tff(154,plain,
% 3.05/3.23 (le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[153, 35, 90])).
% 3.05/3.23 tff(155,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(156,plain,
% 3.05/3.23 (((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(s(elem!0)), a1))) <=> ((~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(157,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(s(elem!0)), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[156])).
% 3.05/3.23 tff(158,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(s(elem!0)), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[157, 155])).
% 3.05/3.23 tff(159,plain,
% 3.05/3.23 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(s(elem!0)), a1)))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(160,plain,
% 3.05/3.23 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[159, 158])).
% 3.05/3.23 tff(161,plain,
% 3.05/3.23 ((~eq(f(s(elem!0)), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[160, 62, 154])).
% 3.05/3.23 tff(162,plain,
% 3.05/3.23 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[161, 150])).
% 3.05/3.23 tff(163,plain,
% 3.05/3.23 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[87, 162])).
% 3.05/3.23 tff(164,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(165,plain,
% 3.05/3.23 (((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))) <=> ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(166,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[165])).
% 3.05/3.23 tff(167,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.23 inference(transitivity,[status(thm)],[166, 164])).
% 3.05/3.23 tff(168,plain,
% 3.05/3.23 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(169,plain,
% 3.05/3.23 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.05/3.23 tff(170,plain,
% 3.05/3.23 ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2))),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[169, 112, 52])).
% 3.05/3.23 tff(171,plain,
% 3.05/3.23 (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[170, 163])).
% 3.05/3.23 tff(172,plain,
% 3.05/3.23 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(173,plain,
% 3.05/3.23 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))),
% 3.05/3.23 inference(quant_inst,[status(thm)],[])).
% 3.05/3.23 tff(174,plain,
% 3.05/3.23 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)),
% 3.05/3.23 inference(modus_ponens,[status(thm)],[173, 172])).
% 3.05/3.23 tff(175,plain,
% 3.05/3.23 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[174, 80, 46])).
% 3.05/3.23 tff(176,plain,
% 3.05/3.23 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.23 inference(unit_resolution,[status(thm)],[175, 171])).
% 3.05/3.23 tff(177,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(178,plain,
% 3.05/3.23 (((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(s(elem!0)), a1))) <=> ((~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))),
% 3.05/3.23 inference(rewrite,[status(thm)],[])).
% 3.05/3.23 tff(179,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(s(elem!0)), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1))))),
% 3.05/3.23 inference(monotonicity,[status(thm)],[178])).
% 3.05/3.23 tff(180,plain,
% 3.05/3.23 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(s(elem!0)), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))),
% 3.05/3.23 inference(transitivity,[status(thm)],[179, 177])).
% 3.05/3.23 tff(181,plain,
% 3.05/3.23 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(s(elem!0)), a1)))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(182,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[181, 180])).
% 3.05/3.24 tff(183,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[182, 62, 150, 176, 28])).
% 3.05/3.24 tff(184,plain,((~eq(f(s(elem!0)), a1)) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(185,plain,
% 3.05/3.24 (~eq(f(s(elem!0)), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[184, 149, 139])).
% 3.05/3.24 tff(186,plain,
% 3.05/3.24 ((~![A: $i] : le(A, A)) | le(s(elem!0), s(elem!0))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(187,plain,
% 3.05/3.24 (le(s(elem!0), s(elem!0))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[186, 7])).
% 3.05/3.24 tff(188,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(189,plain,
% 3.05/3.24 (((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(190,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[189])).
% 3.05/3.24 tff(191,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)))),
% 3.05/3.24 inference(transitivity,[status(thm)],[190, 188])).
% 3.05/3.24 tff(192,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0)))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(193,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[192, 191])).
% 3.05/3.24 tff(194,plain,
% 3.05/3.24 ((~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[193, 131, 187])).
% 3.05/3.24 tff(195,plain,
% 3.05/3.24 (~eq(f(s(elem!0)), a0)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[194, 121])).
% 3.05/3.24 tff(196,plain,
% 3.05/3.24 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(197,plain,
% 3.05/3.24 ((eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a1) | eq(f(s(elem!0)), a0)) <=> (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(198,plain,
% 3.05/3.24 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a1) | eq(f(s(elem!0)), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1)))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[197])).
% 3.05/3.24 tff(199,plain,
% 3.05/3.24 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a1) | eq(f(s(elem!0)), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))),
% 3.05/3.24 inference(transitivity,[status(thm)],[198, 196])).
% 3.05/3.24 tff(200,plain,
% 3.05/3.24 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a1) | eq(f(s(elem!0)), a0))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(201,plain,
% 3.05/3.24 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1)),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[200, 199])).
% 3.05/3.24 tff(202,plain,
% 3.05/3.24 (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[201, 80, 195])).
% 3.05/3.24 tff(203,plain,
% 3.05/3.24 (eq(f(s(elem!0)), a2)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[202, 185])).
% 3.05/3.24 tff(204,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(205,plain,
% 3.05/3.24 (((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(s(elem!0)), a2))) <=> ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(206,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(s(elem!0)), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[205])).
% 3.05/3.24 tff(207,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(s(elem!0)), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[206, 204])).
% 3.05/3.24 tff(208,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~eq(f(s(elem!0)), a2)))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(209,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[208, 207])).
% 3.05/3.24 tff(210,plain,
% 3.05/3.24 ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2))),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[209, 112, 154])).
% 3.05/3.24 tff(211,plain,
% 3.05/3.24 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[210, 203])).
% 3.05/3.24 tff(212,plain,
% 3.05/3.24 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[86, 80, 139])).
% 3.05/3.24 tff(213,plain,
% 3.05/3.24 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[212, 211])).
% 3.05/3.24 tff(214,assumption,(eq(f(s(elem!0)), a2)), introduced(assumption)).
% 3.05/3.24 tff(215,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(216,plain,
% 3.05/3.24 (((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(s(elem!0)), a2))) <=> ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(217,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(s(elem!0)), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[216])).
% 3.05/3.24 tff(218,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(s(elem!0)), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.24 inference(transitivity,[status(thm)],[217, 215])).
% 3.05/3.24 tff(219,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(s(elem!0)), a2)))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(220,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.05/3.24 tff(221,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[220, 112, 214, 44, 28])).
% 3.05/3.24 tff(222,plain,((~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(s(elem!0)), a2))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(223,plain,
% 3.05/3.24 (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[222, 203])).
% 3.05/3.24 tff(224,plain,
% 3.05/3.24 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[174, 80, 149])).
% 3.05/3.24 tff(225,plain,
% 3.05/3.24 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[224, 223])).
% 3.05/3.24 tff(226,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[69, 225, 213])).
% 3.05/3.24 tff(227,plain,(~eq(f(elem!0), a0)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(228,plain,
% 3.05/3.24 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(elem!0), a1) | eq(f(elem!0), a0) | eq(f(elem!0), a2))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(elem!0), a1) | eq(f(elem!0), a0) | eq(f(elem!0), a2))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(229,plain,
% 3.05/3.24 ((eq(f(elem!0), a2) | eq(f(elem!0), a1) | eq(f(elem!0), a0)) <=> (eq(f(elem!0), a1) | eq(f(elem!0), a0) | eq(f(elem!0), a2))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(230,plain,
% 3.05/3.24 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(elem!0), a2) | eq(f(elem!0), a1) | eq(f(elem!0), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(elem!0), a1) | eq(f(elem!0), a0) | eq(f(elem!0), a2)))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[229])).
% 3.05/3.24 tff(231,plain,
% 3.05/3.24 (((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(elem!0), a2) | eq(f(elem!0), a1) | eq(f(elem!0), a0))) <=> ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(elem!0), a1) | eq(f(elem!0), a0) | eq(f(elem!0), a2))),
% 3.05/3.24 inference(transitivity,[status(thm)],[230, 228])).
% 3.05/3.24 tff(232,plain,
% 3.05/3.24 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | (eq(f(elem!0), a2) | eq(f(elem!0), a1) | eq(f(elem!0), a0))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(233,plain,
% 3.05/3.24 ((~![A: $i] : (eq(f(A), a2) | eq(f(A), a1) | eq(f(A), a0))) | eq(f(elem!0), a1) | eq(f(elem!0), a0) | eq(f(elem!0), a2)),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[232, 231])).
% 3.05/3.24 tff(234,plain,
% 3.05/3.24 (eq(f(elem!0), a1) | eq(f(elem!0), a2)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[233, 80, 227])).
% 3.05/3.24 tff(235,plain,
% 3.05/3.24 (eq(f(elem!0), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[234, 120])).
% 3.05/3.24 tff(236,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(237,plain,
% 3.05/3.24 (((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))),
% 3.05/3.24 inference(rewrite,[status(thm)],[])).
% 3.05/3.24 tff(238,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1))))),
% 3.05/3.24 inference(monotonicity,[status(thm)],[237])).
% 3.05/3.24 tff(239,plain,
% 3.05/3.24 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)))),
% 3.05/3.24 inference(transitivity,[status(thm)],[238, 236])).
% 3.05/3.24 tff(240,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | (~eq(f(elem!0), a1)))),
% 3.05/3.24 inference(quant_inst,[status(thm)],[])).
% 3.05/3.24 tff(241,plain,
% 3.05/3.24 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1))),
% 3.05/3.24 inference(modus_ponens,[status(thm)],[240, 239])).
% 3.05/3.24 tff(242,plain,
% 3.05/3.24 ($false),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[241, 62, 235, 48, 43])).
% 3.05/3.24 tff(243,plain,((~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.24 tff(244,plain,
% 3.05/3.24 (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[243, 47])).
% 3.05/3.24 tff(245,plain,
% 3.05/3.24 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)),
% 3.05/3.24 inference(unit_resolution,[status(thm)],[175, 244])).
% 3.05/3.24 tff(246,plain,
% 3.05/3.24 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[170, 245])).
% 3.05/3.25 tff(247,plain,
% 3.05/3.25 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[87, 246])).
% 3.05/3.25 tff(248,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(249,plain,
% 3.05/3.25 (((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(250,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[249])).
% 3.05/3.25 tff(251,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[250, 248])).
% 3.05/3.25 tff(252,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~eq(f(elem!0), a1)))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(253,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)) | (~le(s(elem!0), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[252, 251])).
% 3.05/3.25 tff(254,plain,
% 3.05/3.25 ((~eq(f(elem!0), a1)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[253, 62, 102])).
% 3.05/3.25 tff(255,plain,
% 3.05/3.25 (~eq(f(elem!0), a1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[254, 247])).
% 3.05/3.25 tff(256,plain,
% 3.05/3.25 (eq(f(elem!0), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[234, 255])).
% 3.05/3.25 tff(257,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(elem!0), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(258,plain,
% 3.05/3.25 (((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(elem!0), a2))) <=> ((~eq(f(elem!0), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(259,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(elem!0), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(elem!0), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[258])).
% 3.05/3.25 tff(260,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(elem!0), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[259, 257])).
% 3.05/3.25 tff(261,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~eq(f(elem!0), a2)))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(262,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)) | (~le(s(elem!0), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[261, 260])).
% 3.05/3.25 tff(263,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[262, 112, 256, 245, 43])).
% 3.05/3.25 tff(264,plain,(eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(265,plain,
% 3.05/3.25 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[264, 46])).
% 3.05/3.25 tff(266,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(267,plain,
% 3.05/3.25 (((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(s(elem!0)), a0))) <=> ((~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(268,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(s(elem!0)), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[267])).
% 3.05/3.25 tff(269,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(s(elem!0)), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[268, 266])).
% 3.05/3.25 tff(270,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0)))))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(s(elem!0)), a0)))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(271,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~le(s(s(elem!0)), max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[270, 269])).
% 3.05/3.25 tff(272,plain,
% 3.05/3.25 ((~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[271, 131, 154])).
% 3.05/3.25 tff(273,plain,
% 3.05/3.25 (~eq(f(s(elem!0)), a0)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[272, 265])).
% 3.05/3.25 tff(274,plain,
% 3.05/3.25 (eq(f(s(elem!0)), a2) | eq(f(s(elem!0)), a0)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[201, 80, 45])).
% 3.05/3.25 tff(275,plain,
% 3.05/3.25 (eq(f(s(elem!0)), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[274, 273])).
% 3.05/3.25 tff(276,plain,
% 3.05/3.25 (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[222, 275])).
% 3.05/3.25 tff(277,plain,
% 3.05/3.25 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[175, 276])).
% 3.05/3.25 tff(278,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2)) | (~le(s(elem!0), s(elem!0))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2)) | (~le(s(elem!0), s(elem!0))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(279,plain,
% 3.05/3.25 (((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(elem!0), a2))) <=> ((~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2)) | (~le(s(elem!0), s(elem!0))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(280,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(elem!0), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2)) | (~le(s(elem!0), s(elem!0)))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[279])).
% 3.05/3.25 tff(281,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(elem!0), a2)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2)) | (~le(s(elem!0), s(elem!0))))),
% 3.05/3.25 inference(transitivity,[status(thm)],[280, 278])).
% 3.05/3.25 tff(282,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a2)) | (~eq(f(elem!0), a2)))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(283,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a2)) | (~eq(f(A0), a2)))) | (~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2)) | (~le(s(elem!0), s(elem!0)))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[282, 281])).
% 3.05/3.25 tff(284,plain,
% 3.05/3.25 ((~eq(f(elem!0), a2)) | (~eq(f(s(elem!0)), a2))),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[283, 112, 187])).
% 3.05/3.25 tff(285,plain,
% 3.05/3.25 (~eq(f(elem!0), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[284, 275])).
% 3.05/3.25 tff(286,plain,
% 3.05/3.25 (eq(f(elem!0), a1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[234, 285])).
% 3.05/3.25 tff(287,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[241, 62, 286, 277, 43])).
% 3.05/3.25 tff(288,plain,(eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0) | eq(f(s(elem!0)), a1)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(289,plain,
% 3.05/3.25 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[288, 45])).
% 3.05/3.25 tff(290,assumption,(eq(f(s(elem!0)), a0)), introduced(assumption)).
% 3.05/3.25 tff(291,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(292,plain,
% 3.05/3.25 (((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(s(elem!0)), a0))) <=> ((~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(293,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(s(elem!0)), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[292])).
% 3.05/3.25 tff(294,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(s(elem!0)), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)))),
% 3.05/3.25 inference(transitivity,[status(thm)],[293, 291])).
% 3.05/3.25 tff(295,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(s(elem!0)), a0)))),
% 3.05/3.25 inference(quant_inst,[status(thm)],[])).
% 3.05/3.25 tff(296,plain,
% 3.05/3.25 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))),
% 3.05/3.25 inference(modus_ponens,[status(thm)],[295, 294])).
% 3.05/3.25 tff(297,plain,
% 3.05/3.25 ($false),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[296, 131, 290, 140, 28])).
% 3.05/3.25 tff(298,plain,((~eq(f(s(elem!0)), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))), inference(lemma,lemma(discharge,[]))).
% 3.05/3.25 tff(299,plain,
% 3.05/3.25 (~eq(f(s(elem!0)), a0)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[298, 289])).
% 3.05/3.25 tff(300,plain,
% 3.05/3.25 (eq(f(s(elem!0)), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[274, 299])).
% 3.05/3.25 tff(301,plain,
% 3.05/3.25 (~eq(f(elem!0), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[284, 300])).
% 3.05/3.25 tff(302,plain,
% 3.05/3.25 (eq(f(elem!0), a1)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[234, 301])).
% 3.05/3.25 tff(303,plain,
% 3.05/3.25 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.25 inference(unit_resolution,[status(thm)],[210, 300])).
% 3.05/3.25 tff(304,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(305,plain,
% 3.05/3.25 (((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0))) <=> ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.25 inference(rewrite,[status(thm)],[])).
% 3.05/3.25 tff(306,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))))),
% 3.05/3.25 inference(monotonicity,[status(thm)],[305])).
% 3.05/3.25 tff(307,plain,
% 3.05/3.25 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))))),
% 3.05/3.26 inference(transitivity,[status(thm)],[306, 304])).
% 3.05/3.26 tff(308,plain,
% 3.05/3.26 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0))))))) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(309,plain,
% 3.05/3.26 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)) | (~le(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[308, 307])).
% 3.05/3.26 tff(310,plain,
% 3.05/3.26 ((~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)) | (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[309, 131, 52])).
% 3.05/3.26 tff(311,plain,
% 3.05/3.26 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[310, 289])).
% 3.05/3.26 tff(312,plain,
% 3.05/3.26 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1) | eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[86, 80, 311])).
% 3.05/3.26 tff(313,plain,
% 3.05/3.26 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[312, 303])).
% 3.05/3.26 tff(314,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[254, 313, 302])).
% 3.05/3.26 tff(315,plain,(eq(f(s(elem!0)), a1)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(316,plain,
% 3.05/3.26 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(317,plain,
% 3.05/3.26 (((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)))),
% 3.05/3.26 inference(rewrite,[status(thm)],[])).
% 3.05/3.26 tff(318,plain,
% 3.05/3.26 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1))))),
% 3.05/3.26 inference(monotonicity,[status(thm)],[317])).
% 3.05/3.26 tff(319,plain,
% 3.05/3.26 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(elem!0), a1)))) <=> ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)))),
% 3.05/3.26 inference(transitivity,[status(thm)],[318, 316])).
% 3.05/3.26 tff(320,plain,
% 3.05/3.26 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(elem!0), a1)))),
% 3.05/3.26 inference(quant_inst,[status(thm)],[])).
% 3.05/3.26 tff(321,plain,
% 3.05/3.26 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1))),
% 3.05/3.26 inference(modus_ponens,[status(thm)],[320, 319])).
% 3.05/3.26 tff(322,plain,
% 3.05/3.26 ((~eq(f(elem!0), a1)) | (~eq(f(s(elem!0)), a1))),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[321, 62, 187])).
% 3.05/3.26 tff(323,plain,
% 3.05/3.26 (~eq(f(elem!0), a1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[322, 315])).
% 3.05/3.26 tff(324,plain,
% 3.05/3.26 (eq(f(elem!0), a2)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[234, 323])).
% 3.05/3.26 tff(325,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[262, 112, 324, 44, 43])).
% 3.05/3.26 tff(326,plain,(~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2)), inference(lemma,lemma(discharge,[]))).
% 3.05/3.26 tff(327,plain,
% 3.05/3.26 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a2)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[119, 324])).
% 3.05/3.26 tff(328,plain,
% 3.05/3.26 (~eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[161, 315])).
% 3.05/3.26 tff(329,plain,
% 3.05/3.26 (eq(f(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), a0)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[86, 80, 328, 327])).
% 3.05/3.26 tff(330,plain,
% 3.05/3.26 (~eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a0)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[310, 329])).
% 3.05/3.26 tff(331,plain,
% 3.05/3.26 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a2) | eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[174, 80, 330])).
% 3.05/3.26 tff(332,plain,
% 3.05/3.26 (eq(f(max(s(max(s(s(elem!0)), max(s(s(elem!0)), max(s(elem!0), s(elem!0))))), max(max(s(elem!0), elem!0), max(elem!0, s(s(elem!0)))))), a1)),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[331, 326])).
% 3.05/3.26 tff(333,plain,
% 3.05/3.26 ($false),
% 3.05/3.26 inference(unit_resolution,[status(thm)],[182, 62, 315, 332, 28])).
% 3.05/3.26 % SZS output end Proof
% 3.05/3.26 % E exiting
%------------------------------------------------------------------------------