%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO614-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:41:58 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO614-1 : TPTP v9.0.0. Released v7.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:17:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(eq_type, type, (
% 0.19/0.46 eq: ( $i * $i ) > $o)).
% 0.19/0.46 tff(a1_type, type, (
% 0.19/0.46 a1: $i)).
% 0.19/0.46 tff(f_type, type, (
% 0.19/0.46 f: $i > $i)).
% 0.19/0.46 tff(s_type, type, (
% 0.19/0.46 s: $i > $i)).
% 0.19/0.46 tff(elem_0_type, type, (
% 0.19/0.46 elem_0: $i)).
% 0.19/0.46 tff(a0_type, type, (
% 0.19/0.46 a0: $i)).
% 0.19/0.46 tff(le_type, type, (
% 0.19/0.46 le: ( $i * $i ) > $o)).
% 0.19/0.46 tff(max_type, type, (
% 0.19/0.46 max: ( $i * $i ) > $i)).
% 0.19/0.46 tff(1,assumption,(eq(f(elem!0), a1)), introduced(assumption)).
% 0.19/0.46 tff(2,assumption,(~le(s(elem!0), s(elem!0))), introduced(assumption)).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (^[A: $i] : refl(le(A, A) <=> le(A, A))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 0.19/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (![A: $i] : le(A, A) <=> ![A: $i] : le(A, A)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(6,axiom,(![A: $i] : le(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_01')).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (![A: $i] : le(A, A)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.46 tff(8,plain,(
% 0.19/0.46 ![A: $i] : le(A, A)),
% 0.19/0.46 inference(skolemize,[status(sab)],[7])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (![A: $i] : le(A, A)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 ((~![A: $i] : le(A, A)) | le(s(elem!0), s(elem!0))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.19/0.46 tff(12,plain,(le(s(elem!0), s(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.46 tff(18,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a1)) | (~eq(f(A1), a1))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_06')).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.46 tff(21,plain,(
% 0.19/0.46 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[20])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~eq(f(elem!0), a1)) | (~eq(f(s(elem!0)), a1)) | (~le(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(s(elem!0)), a1)) | (~le(s(elem!0), s(elem!0))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~eq(f(s(elem!0)), a1)) | (~le(s(elem!0), s(elem!0))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (((~![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)) | (~eq(f(s(elem!0)), a1)) | (~le(s(elem!0), s(elem!0)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (((~![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)) | (~eq(f(s(elem!0)), a1)) | (~le(s(elem!0), s(elem!0))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(elem!0), a1)) | (~eq(f(s(elem!0)), a1)) | (~le(s(elem!0), s(elem!0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((~eq(f(elem!0), a1)) | (~eq(f(s(elem!0)), a1)) | (~le(s(elem!0), s(elem!0)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 ((~eq(f(elem!0), a1)) | (~eq(f(s(elem!0)), a1))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[29, 12])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (~eq(f(s(elem!0)), a1)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (^[A: $i] : refl((eq(f(A), a0) | eq(f(A), a1)) <=> (eq(f(A), a0) | eq(f(A), a1)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1)) <=> ![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1)) <=> ![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(35,axiom,(![A: $i] : (eq(f(A), a0) | eq(f(A), a1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_04')).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.46 tff(37,plain,(
% 0.19/0.46 ![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 0.19/0.46 inference(skolemize,[status(sab)],[36])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (![A: $i] : (eq(f(A), a0) | eq(f(A), a1))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))) <=> ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(s(elem!0)), a0) | eq(f(s(elem!0)), a1)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (eq(f(s(elem!0)), a0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 ((~![A: $i] : le(A, A)) | le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[43, 9])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (^[B: $i, A: $i, C: $i] : refl(((~le(max(A, B), C)) | le(A, C)) <=> ((~le(max(A, B), C)) | le(A, C)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(48,axiom,(![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_02')).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.47 tff(50,plain,(
% 0.19/0.47 ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 0.19/0.47 inference(skolemize,[status(sab)],[49])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(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), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[54, 51, 44])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(elem!0), max(max(s(elem!0), s(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), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | ((~le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(A, C))) | (~le(max(s(elem!0), s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[58, 51, 55])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 (((~![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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)) | (~eq(f(elem!0), a1))) <=> ((~eq(f(elem!0), a1)) | (~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)) | (~eq(f(elem!0), a1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 ((~![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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 ((~eq(f(elem!0), a1)) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[65, 22, 59])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[66, 1])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0) | eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))) <=> ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0) | eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0) | eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0) | eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[70, 38, 67])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (^[B: $i, A: $i, C: $i] : refl(((~le(max(A, B), C)) | le(B, C)) <=> ((~le(max(A, B), C)) | le(B, C)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(75,axiom,(![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_03')).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.47 tff(77,plain,(
% 0.19/0.47 ![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 0.19/0.47 inference(skolemize,[status(sab)],[76])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(s(elem!0)), max(max(s(elem!0), s(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), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | ((~le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 ((~![B: $i, A: $i, C: $i] : ((~le(max(A, B), C)) | le(B, C))) | (~le(max(max(s(elem!0), s(elem!0)), s(s(elem!0))), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[81, 78, 44])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.47 tff(88,axiom,(![A0: $i, A1: $i] : (((~eq(f(A0), a0)) | (~eq(f(A1), a0))) | (~le(s(A0), A1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_05')).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.47 tff(91,plain,(
% 0.19/0.47 ![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[90])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (((~![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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[95, 93])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)) | (~eq(f(s(elem!0)), a0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(s(elem!0)), a0)) | (~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 ((~eq(f(s(elem!0)), a0)) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[98, 92, 82])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[99, 71, 42])).
% 0.19/0.47 tff(101,plain,(~eq(f(elem!0), a1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(elem!0), a0) | eq(f(elem!0), a1))) <=> ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(elem!0), a0) | eq(f(elem!0), a1))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | (eq(f(elem!0), a0) | eq(f(elem!0), a1))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~![A: $i] : (eq(f(A), a0) | eq(f(A), a1))) | eq(f(elem!0), a0) | eq(f(elem!0), a1)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (eq(f(elem!0), a0) | eq(f(elem!0), a1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[104, 38])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (eq(f(elem!0), a0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 101])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)) | (~le(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(s(elem!0)), a0)) | (~le(s(elem!0), s(elem!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (((~le(s(elem!0), s(elem!0))) | (~eq(f(s(elem!0)), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)) | (~le(s(elem!0), s(elem!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (((~![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)) | (~eq(f(s(elem!0)), a0)) | (~le(s(elem!0), s(elem!0)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (((~![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)) | (~eq(f(s(elem!0)), a0)) | (~le(s(elem!0), s(elem!0))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | (~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)) | (~le(s(elem!0), s(elem!0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ((~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0)) | (~le(s(elem!0), s(elem!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 92])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 ((~eq(f(elem!0), a0)) | (~eq(f(s(elem!0)), a0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 12])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (~eq(f(s(elem!0)), a0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[114, 106])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (eq(f(s(elem!0)), a1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[41, 38, 115])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 (((~![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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)) | (~eq(f(elem!0), a0))) <=> ((~eq(f(elem!0), a0)) | (~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[119, 117])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a0)) | (~eq(f(A0), a0)))) | ((~le(s(elem!0), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)) | (~eq(f(elem!0), a0)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 ((~![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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 ((~eq(f(elem!0), a0)) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[122, 92, 59])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[123, 106])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[70, 38, 124])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (((~![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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(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(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[128, 126])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | ((~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1)) | (~eq(f(s(elem!0)), a1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 ((~![A0: $i, A1: $i] : ((~le(s(A0), A1)) | (~eq(f(A1), a1)) | (~eq(f(A0), a1)))) | (~eq(f(s(elem!0)), a1)) | (~le(s(s(elem!0)), max(max(s(elem!0), s(elem!0)), s(s(elem!0))))) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 ((~eq(f(s(elem!0)), a1)) | (~eq(f(max(max(s(elem!0), s(elem!0)), s(s(elem!0)))), a1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[131, 22, 82])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[132, 125, 116])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------