%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN663-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:39:47 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN663-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.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 12:40:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(p2_type, type, (
% 0.18/0.38 p2: ( $i * $i ) > $o)).
% 0.18/0.38 tff(f11_type, type, (
% 0.18/0.38 f11: ( $i * $i ) > $i)).
% 0.18/0.38 tff(c34_type, type, (
% 0.18/0.38 c34: $i)).
% 0.18/0.38 tff(f4_type, type, (
% 0.18/0.38 f4: $i > $i)).
% 0.18/0.38 tff(c36_type, type, (
% 0.18/0.38 c36: $i)).
% 0.18/0.38 tff(c32_type, type, (
% 0.18/0.38 c32: $i)).
% 0.18/0.38 tff(p3_type, type, (
% 0.18/0.38 p3: ( $i * $i ) > $o)).
% 0.18/0.38 tff(p10_type, type, (
% 0.18/0.38 p10: ( $i * $i ) > $o)).
% 0.18/0.38 tff(p25_type, type, (
% 0.18/0.38 p25: ( $i * $i ) > $o)).
% 0.18/0.38 tff(c33_type, type, (
% 0.18/0.38 c33: $i)).
% 0.18/0.38 tff(f16_type, type, (
% 0.18/0.38 f16: ( $i * $i ) > $i)).
% 0.18/0.38 tff(f9_type, type, (
% 0.18/0.38 f9: $i > $i)).
% 0.18/0.38 tff(f17_type, type, (
% 0.18/0.38 f17: $i > $i)).
% 0.18/0.38 tff(c31_type, type, (
% 0.18/0.38 c31: $i)).
% 0.18/0.38 tff(1,assumption,(~p3(f4(c36), f4(c36))), introduced(assumption)).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (^[X83: $i] : refl(p3(X83, X83) <=> p3(X83, X83))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.18/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(5,axiom,(![X83: $i] : p3(X83, X83)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_5')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![X83: $i] : p3(X83, X83)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,(
% 0.18/0.39 ![X83: $i] : p3(X83, X83)),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![X83: $i] : p3(X83, X83)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![X83: $i] : p3(X83, X83)) | p3(f4(c36), f4(c36))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.39 tff(11,plain,(p3(f4(c36), f4(c36))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(12,assumption,(~p10(c34, c34)), introduced(assumption)).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(16,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_2')).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (![X0: $i] : p10(X0, X0)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.39 tff(18,plain,(
% 0.18/0.39 ![X0: $i] : p10(X0, X0)),
% 0.18/0.39 inference(skolemize,[status(sab)],[17])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (![X0: $i] : p10(X0, X0)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 ((~![X0: $i] : p10(X0, X0)) | p10(c34, c34)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.18/0.39 tff(22,plain,(p10(c34, c34)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (^[X39: $i, X38: $i, X41: $i, X40: $i] : refl(((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) <=> ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (^[X39: $i, X38: $i, X41: $i, X40: $i] : trans(monotonicity(rewrite((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) <=> ((~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))), (((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40))) <=> (((~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) | (~p3(X38, X40))))), rewrite((((~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) | (~p3(X38, X40))) <=> ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))), (((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40))) <=> ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.39 tff(28,axiom,(![X39: $i, X38: $i, X41: $i, X40: $i] : ((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_47')).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.18/0.39 tff(31,plain,(
% 0.18/0.39 ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[30])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | (~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (((~p3(f4(c36), f4(c36))) | (~p10(c34, c34)) | p2(f11(f4(c36), c34), f11(f4(c36), c34))) <=> ((~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p3(f4(c36), f4(c36))) | (~p10(c34, c34)) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p3(f4(c36), f4(c36))) | (~p10(c34, c34)) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | (~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p3(f4(c36), f4(c36))) | (~p10(c34, c34)) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | (~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 ((~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (p2(f11(f4(c36), c34), f11(f4(c36), c34))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[39, 22, 11])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (^[X42: $i] : refl(((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34))) <=> ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34))) <=> ![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34))) <=> ![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (^[X42: $i] : trans(monotonicity(rewrite((p2(f11(f4(X42), c34), f11(f4(c32), c34)) | (~p25(X42, c33))) <=> ((~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))), (((p2(f11(f4(X42), c34), f11(f4(c32), c34)) | (~p25(X42, c33))) | (~p25(c32, X42))) <=> (((~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34))) | (~p25(c32, X42))))), rewrite((((~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34))) | (~p25(c32, X42))) <=> ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))), (((p2(f11(f4(X42), c34), f11(f4(c32), c34)) | (~p25(X42, c33))) | (~p25(c32, X42))) <=> ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![X42: $i] : ((p2(f11(f4(X42), c34), f11(f4(c32), c34)) | (~p25(X42, c33))) | (~p25(c32, X42))) <=> ![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.39 tff(46,axiom,(![X42: $i] : ((p2(f11(f4(X42), c34), f11(f4(c32), c34)) | (~p25(X42, c33))) | (~p25(c32, X42)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_49')).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.39 tff(49,plain,(
% 0.18/0.39 ![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[48])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (p25(c32, c36) <=> p25(c32, c36)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(52,axiom,(p25(c32, c36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_13')).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (p25(c32, c36)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (p25(c36, c33) <=> p25(c36, c33)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(55,axiom,(p25(c36, c33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_11')).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (p25(c36, c33)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))) | ((~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34)))) <=> ((~![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))) | (~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))) | ((~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((~![X42: $i] : ((~p25(c32, X42)) | (~p25(X42, c33)) | p2(f11(f4(X42), c34), f11(f4(c32), c34)))) | (~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (p2(f11(f4(c36), c34), f11(f4(c32), c34))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[59, 56, 53, 50])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (^[X37: $i, X35: $i, X36: $i] : refl(((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)) <=> ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)) <=> ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)) <=> ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (^[X37: $i, X35: $i, X36: $i] : trans(monotonicity(rewrite((p2(X36, X37) | (~p2(X35, X36))) <=> ((~p2(X35, X36)) | p2(X36, X37))), (((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37))) <=> (((~p2(X35, X36)) | p2(X36, X37)) | (~p2(X35, X37))))), rewrite((((~p2(X35, X36)) | p2(X36, X37)) | (~p2(X35, X37))) <=> ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))), (((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37))) <=> ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (![X37: $i, X35: $i, X36: $i] : ((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37))) <=> ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.40 tff(66,axiom,(![X37: $i, X35: $i, X36: $i] : ((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_30')).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.18/0.40 tff(69,plain,(
% 0.18/0.40 ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(skolemize,[status(sab)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (p2(f11(f4(c32), c34), f11(f4(c36), c34)) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (((~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34))) <=> (p2(f11(f4(c32), c34), f11(f4(c36), c34)) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (p2(f11(f4(c32), c34), f11(f4(c36), c34)) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (p2(f11(f4(c32), c34), f11(f4(c36), c34))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[76, 70, 60, 40])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (^[X96: $i] : refl((~p2(X96, f16(X96, f9(f17(c31))))) <=> (~p2(X96, f16(X96, f9(f17(c31))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(81,axiom,(![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_19')).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.40 tff(83,plain,(
% 0.18/0.40 ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[82])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 ((~![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))) | (~p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (~p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) <=> p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(88,axiom,(p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_40')).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) <=> ((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[91])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[92, 90])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f16(f11(f4(c36), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[95, 70, 89, 86, 77])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------