%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ078+1 : TPTP v9.0.0. Released v3.5.0.
% 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 05:23:24 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : PUZ078+1 : TPTP v9.0.0. Released v3.5.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n004.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 02:46:23 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(truthday_type, type, (
% 0.19/0.41 truthday: $i > $o)).
% 0.19/0.41 tff(monday_type, type, (
% 0.19/0.41 monday: $i)).
% 0.19/0.41 tff(consecutive_type, type, (
% 0.19/0.41 consecutive: $i > $i)).
% 0.19/0.41 tff(tptp_fun_X_2_type, type, (
% 0.19/0.41 tptp_fun_X_2: $i)).
% 0.19/0.41 tff(friday_type, type, (
% 0.19/0.41 friday: $i)).
% 0.19/0.41 tff(tptp_fun_X_3_type, type, (
% 0.19/0.41 tptp_fun_X_3: $i)).
% 0.19/0.41 tff(day3_type, type, (
% 0.19/0.41 day3: $i > $o)).
% 0.19/0.41 tff(day2_type, type, (
% 0.19/0.41 day2: $i > $o)).
% 0.19/0.41 tff(tptp_fun_X_0_type, type, (
% 0.19/0.41 tptp_fun_X_0: $i)).
% 0.19/0.41 tff(wednesday_type, type, (
% 0.19/0.41 wednesday: $i)).
% 0.19/0.41 tff(sunday_type, type, (
% 0.19/0.41 sunday: $i)).
% 0.19/0.41 tff(saturday_type, type, (
% 0.19/0.41 saturday: $i)).
% 0.19/0.41 tff(thursday_type, type, (
% 0.19/0.41 thursday: $i)).
% 0.19/0.41 tff(tptp_fun_X_1_type, type, (
% 0.19/0.41 tptp_fun_X_1: $i)).
% 0.19/0.41 tff(day1_type, type, (
% 0.19/0.41 day1: $i > $o)).
% 0.19/0.41 tff(tuesday_type, type, (
% 0.19/0.41 tuesday: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 ((consecutive(X!2) = friday) <=> (friday = consecutive(X!2))),
% 0.19/0.41 inference(commutativity,[status(thm)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 ((friday = consecutive(X!2)) <=> (consecutive(X!2) = friday)),
% 0.19/0.41 inference(symmetry,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[X: $i] : refl((day2(X) <=> day3(consecutive(X))) <=> (day2(X) <=> day3(consecutive(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X: $i] : (day2(X) <=> day3(consecutive(X))) <=> ![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i] : (day2(X) <=> day3(consecutive(X))) <=> ![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(6,axiom,(![X: $i] : (day2(X) <=> day3(consecutive(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day3_follows_day2')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,(
% 0.19/0.41 ![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[7])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![X: $i] : (day2(X) <=> day3(consecutive(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(X!2) <=> day3(consecutive(X!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (day2(X!2) <=> day3(consecutive(X!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (?[X: $i] : day2(X) <=> ?[X: $i] : day2(X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,axiom,(?[X: $i] : day2(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day2_once')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (?[X: $i] : day2(X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,(
% 0.19/0.41 day2(X!2)),
% 0.19/0.41 inference(skolemize,[status(sab)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 ((~(day2(X!2) <=> day3(consecutive(X!2)))) | (~day2(X!2)) | day3(consecutive(X!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~(day2(X!2) <=> day3(consecutive(X!2)))) | day3(consecutive(X!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (day3(consecutive(X!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (?[X: $i] : day3(X) <=> ?[X: $i] : day3(X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(20,axiom,(?[X: $i] : day3(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day3_once')).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (?[X: $i] : day3(X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.41 tff(22,plain,(
% 0.19/0.41 day3(X!3)),
% 0.19/0.41 inference(skolemize,[status(sab)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(((X = Y) | (~day3(Y)) | (~day3(X))) <=> ((X = Y) | (~day3(Y)) | (~day3(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((day3(X) & day3(Y)) <=> (~((~day3(Y)) | (~day3(X))))), ((~(day3(X) & day3(Y))) <=> (~(~((~day3(Y)) | (~day3(X))))))), rewrite((~(~((~day3(Y)) | (~day3(X))))) <=> ((~day3(Y)) | (~day3(X)))), ((~(day3(X) & day3(Y))) <=> ((~day3(Y)) | (~day3(X))))), (((~(day3(X) & day3(Y))) | (X = Y)) <=> (((~day3(Y)) | (~day3(X))) | (X = Y)))), rewrite((((~day3(Y)) | (~day3(X))) | (X = Y)) <=> ((X = Y) | (~day3(Y)) | (~day3(X)))), (((~(day3(X) & day3(Y))) | (X = Y)) <=> ((X = Y) | (~day3(Y)) | (~day3(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite(((day3(X) & day3(Y)) => (X = Y)) <=> ((~(day3(X) & day3(Y))) | (X = Y)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((day3(X) & day3(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.41 tff(30,axiom,(![X: $i, Y: $i] : ((day3(X) & day3(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day3_unique')).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.41 tff(33,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~(day3(X) & day3(Y))) | (X = Y))),
% 0.19/0.41 inference(skolemize,[status(sab)],[32])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | ((~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | (~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (((X!3 = consecutive(X!2)) | (~day3(consecutive(X!2))) | (~day3(X!3))) <=> ((~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | ((X!3 = consecutive(X!2)) | (~day3(consecutive(X!2))) | (~day3(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | ((~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | ((X!3 = consecutive(X!2)) | (~day3(consecutive(X!2))) | (~day3(X!3)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | (~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | ((X!3 = consecutive(X!2)) | (~day3(consecutive(X!2))) | (~day3(X!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((X = Y) | (~day3(Y)) | (~day3(X)))) | (~day3(X!3)) | (~day3(consecutive(X!2))) | (X!3 = consecutive(X!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (X!3 = consecutive(X!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 35, 22, 18])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((consecutive(thursday) = friday) <=> (consecutive(thursday) = friday)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(44,axiom,(consecutive(thursday) = friday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','friday_follows_thursday')).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (consecutive(thursday) = friday),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((consecutive(friday) = saturday) <=> (consecutive(friday) = saturday)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(47,axiom,(consecutive(friday) = saturday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','saturday_follows_friday')).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (consecutive(friday) = saturday),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (day2(consecutive(friday)) <=> day2(saturday)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.41 tff(50,assumption,(~(consecutive(X!1) = consecutive(consecutive(consecutive(consecutive(X!2)))))), introduced(assumption)).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (^[X: $i] : refl((day1(X) <=> day2(consecutive(X))) <=> (day1(X) <=> day2(consecutive(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![X: $i] : (day1(X) <=> day2(consecutive(X))) <=> ![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![X: $i] : (day1(X) <=> day2(consecutive(X))) <=> ![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(54,axiom,(![X: $i] : (day1(X) <=> day2(consecutive(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day2_follows_day1')).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,(
% 0.19/0.41 ![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[55])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![X: $i] : (day1(X) <=> day2(consecutive(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(X!1) <=> day2(consecutive(X!1)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (day1(X!1) <=> day2(consecutive(X!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (?[X: $i] : day1(X) <=> ?[X: $i] : day1(X)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,axiom,(?[X: $i] : day1(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day1_once')).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (?[X: $i] : day1(X)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.41 tff(63,plain,(
% 0.19/0.41 day1(X!1)),
% 0.19/0.41 inference(skolemize,[status(sab)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~(day1(X!1) <=> day2(consecutive(X!1)))) | (~day1(X!1)) | day2(consecutive(X!1))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~(day1(X!1) <=> day2(consecutive(X!1)))) | day2(consecutive(X!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (day2(consecutive(X!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl(((X = Y) | (~day2(Y)) | (~day2(X))) <=> ((X = Y) | (~day2(Y)) | (~day2(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((day2(X) & day2(Y)) <=> (~((~day2(Y)) | (~day2(X))))), ((~(day2(X) & day2(Y))) <=> (~(~((~day2(Y)) | (~day2(X))))))), rewrite((~(~((~day2(Y)) | (~day2(X))))) <=> ((~day2(Y)) | (~day2(X)))), ((~(day2(X) & day2(Y))) <=> ((~day2(Y)) | (~day2(X))))), (((~(day2(X) & day2(Y))) | (X = Y)) <=> (((~day2(Y)) | (~day2(X))) | (X = Y)))), rewrite((((~day2(Y)) | (~day2(X))) | (X = Y)) <=> ((X = Y) | (~day2(Y)) | (~day2(X)))), (((~(day2(X) & day2(Y))) | (X = Y)) <=> ((X = Y) | (~day2(Y)) | (~day2(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~day2(Y)) | (~day2(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(day2(X) & day2(Y))) | (X = Y))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
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% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : rewrite(((truthday(X) & truthday(Y)) => (X = Y)) <=> ((~(truthday(X) & truthday(Y))) | (X = Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((truthday(X) & truthday(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.42 tff(153,axiom,(![X: $i, Y: $i] : ((truthday(X) & truthday(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','truth_unique')).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.19/0.43 tff(156,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : ((~(truthday(X) & truthday(Y))) | (X = Y))),
% 0.19/0.43 inference(skolemize,[status(sab)],[155])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(wednesday)) | (wednesday = monday))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(wednesday)) | (wednesday = monday))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((wednesday = monday) | (~truthday(wednesday)) | (~truthday(monday))) <=> ((~truthday(monday)) | (~truthday(wednesday)) | (wednesday = monday))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = monday) | (~truthday(wednesday)) | (~truthday(monday)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(wednesday)) | (wednesday = monday)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = monday) | (~truthday(wednesday)) | (~truthday(monday)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(wednesday)) | (wednesday = monday))),
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% 0.19/0.43 tff(163,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = monday) | (~truthday(wednesday)) | (~truthday(monday)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(wednesday)) | (wednesday = monday)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[164, 158, 145, 109, 144])).
% 0.19/0.43 tff(166,plain,((~truthday(wednesday)) | (~truthday(monday))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (~truthday(wednesday)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[166, 109])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 ((~(truthday(wednesday) | truthday(friday))) | truthday(wednesday) | truthday(friday)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (truthday(friday)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[168, 167, 135])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(friday)) | (friday = monday))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(friday)) | (friday = monday))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (((friday = monday) | (~truthday(friday)) | (~truthday(monday))) <=> ((~truthday(monday)) | (~truthday(friday)) | (friday = monday))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((friday = monday) | (~truthday(friday)) | (~truthday(monday)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(friday)) | (friday = monday)))),
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% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((friday = monday) | (~truthday(friday)) | (~truthday(monday)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(friday)) | (friday = monday))),
% 0.19/0.43 inference(transitivity,[status(thm)],[172, 170])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((friday = monday) | (~truthday(friday)) | (~truthday(monday)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(friday)) | (friday = monday)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 158, 169, 109, 134])).
% 0.19/0.43 tff(177,plain,((~truthday(monday)) | (~(truthday(wednesday) | truthday(friday)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (~(truthday(wednesday) | truthday(friday))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[177, 109])).
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% 0.19/0.43 (^[X: $i] : refl(((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X)))) <=> ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X)))) <=> ![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (^[X: $i] : rewrite(((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday))))) <=> ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday))))) <=> ![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday))))) <=> ![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (^[X: $i] : rewrite((day3(X) => (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday))))) <=> ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday))))))),
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% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (![X: $i] : (day3(X) => (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday))))) <=> ![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.43 tff(186,axiom,(![X: $i] : (day3(X) => (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','statement3')).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.19/0.43 tff(189,plain,(
% 0.19/0.43 ![X: $i] : ((~day3(X)) | (truthday(X) <=> ((~truthday(wednesday)) & (~truthday(friday)))))),
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% 0.19/0.43 (![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 (![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[190, 180])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(consecutive(X!2))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(X!2)))))) <=> ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(consecutive(X!2))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(X!2)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(consecutive(X!2))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(X!2)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(consecutive(X!2))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(X!2))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(X!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[194, 191, 18])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(X!2))) | (truthday(wednesday) | truthday(friday)) | truthday(consecutive(X!2))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 ((truthday(wednesday) | truthday(friday)) | truthday(consecutive(X!2))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 (truthday(consecutive(X!2))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[197, 178])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(consecutive(X!2))) | (monday = consecutive(X!2)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(consecutive(X!2))) | (monday = consecutive(X!2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (((monday = consecutive(X!2)) | (~truthday(monday)) | (~truthday(consecutive(X!2)))) <=> ((~truthday(monday)) | (~truthday(consecutive(X!2))) | (monday = consecutive(X!2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((monday = consecutive(X!2)) | (~truthday(monday)) | (~truthday(consecutive(X!2))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(monday)) | (~truthday(consecutive(X!2))) | (monday = consecutive(X!2))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[200])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((monday = consecutive(X!2)) | (~truthday(monday)) | (~truthday(consecutive(X!2))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(consecutive(X!2))) | (monday = consecutive(X!2)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((monday = consecutive(X!2)) | (~truthday(monday)) | (~truthday(consecutive(X!2))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(monday)) | (~truthday(consecutive(X!2))) | (monday = consecutive(X!2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 (monday = consecutive(X!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[204, 158, 109, 198])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 ((consecutive(sunday) = monday) <=> (consecutive(sunday) = monday)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(207,axiom,(consecutive(sunday) = monday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','monday_follows_sunday')).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 (consecutive(sunday) = monday),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 (consecutive(sunday) = consecutive(X!2)),
% 0.19/0.43 inference(transitivity,[status(thm)],[208, 205])).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 (day3(consecutive(sunday)) <=> day3(consecutive(X!2))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (day3(consecutive(X!2)) <=> day3(consecutive(sunday))),
% 0.19/0.43 inference(symmetry,[status(thm)],[210])).
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% 0.19/0.43 (day3(consecutive(sunday))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[18, 211])).
% 0.19/0.43 tff(213,assumption,(~(X!2 = X!3)), introduced(assumption)).
% 0.19/0.43 tff(214,plain,
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% 0.19/0.43 tff(215,plain,
% 0.19/0.43 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(X!3)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X!3))))),
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% 0.19/0.43 tff(216,plain,
% 0.19/0.43 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(X!3)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X!3)))),
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% 0.19/0.43 tff(217,plain,
% 0.19/0.43 (~((truthday(wednesday) | truthday(friday)) <=> truthday(X!3))),
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% 0.19/0.43 tff(218,plain,
% 0.19/0.43 (((truthday(wednesday) | truthday(friday)) <=> truthday(X!3)) | (truthday(wednesday) | truthday(friday)) | truthday(X!3)),
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% 0.19/0.43 tff(219,plain,
% 0.19/0.43 ((truthday(wednesday) | truthday(friday)) | truthday(X!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.19/0.43 tff(220,plain,
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% 0.19/0.44 tff(234,axiom,(![X: $i] : (day2(X) => (truthday(X) <=> ((day2(thursday) | day2(saturday)) | day2(sunday))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','statement2')).
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% 0.19/0.44 inference(symmetry,[status(thm)],[294])).
% 0.19/0.44 tff(296,assumption,(~truthday(friday)), introduced(assumption)).
% 0.19/0.44 tff(297,assumption,(X!3 = X!0), introduced(assumption)).
% 0.19/0.44 tff(298,plain,
% 0.19/0.44 (consecutive(X!2) = X!1),
% 0.19/0.44 inference(transitivity,[status(thm)],[91, 297, 295])).
% 0.19/0.44 tff(299,plain,
% 0.19/0.44 (consecutive(consecutive(X!2)) = consecutive(X!1)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[298])).
% 0.19/0.44 tff(300,plain,
% 0.19/0.44 (consecutive(consecutive(consecutive(X!2))) = consecutive(consecutive(X!1))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.44 tff(301,plain,
% 0.19/0.44 (consecutive(consecutive(consecutive(X!2))) = consecutive(X!2)),
% 0.19/0.44 inference(transitivity,[status(thm)],[300, 88])).
% 0.19/0.44 tff(302,plain,
% 0.19/0.44 (consecutive(consecutive(consecutive(consecutive(X!2)))) = consecutive(consecutive(X!2))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[301])).
% 0.19/0.44 tff(303,plain,
% 0.19/0.44 (consecutive(consecutive(X!2)) = consecutive(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.44 inference(symmetry,[status(thm)],[302])).
% 0.19/0.44 tff(304,plain,
% 0.19/0.44 (consecutive(X!1) = consecutive(consecutive(X!2))),
% 0.19/0.44 inference(symmetry,[status(thm)],[299])).
% 0.19/0.44 tff(305,plain,
% 0.19/0.44 (consecutive(X!1) = consecutive(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[304, 303])).
% 0.19/0.44 tff(306,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[50, 305])).
% 0.19/0.44 tff(307,plain,((~(X!3 = X!0)) | (consecutive(X!1) = consecutive(consecutive(consecutive(consecutive(X!2))))) | (~(X!1 = X!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(308,plain,
% 0.19/0.44 (~(X!3 = X!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[307, 294, 50])).
% 0.19/0.44 tff(309,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(X!0)) | (~truthday(X!3)) | (X!3 = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!3)) | (X!3 = X!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(310,plain,
% 0.19/0.44 (((X!3 = X!0) | (~truthday(X!3)) | (~truthday(X!0))) <=> ((~truthday(X!0)) | (~truthday(X!3)) | (X!3 = X!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(311,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!3 = X!0) | (~truthday(X!3)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(X!0)) | (~truthday(X!3)) | (X!3 = X!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[310])).
% 0.19/0.44 tff(312,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!3 = X!0) | (~truthday(X!3)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!3)) | (X!3 = X!0))),
% 0.19/0.44 inference(transitivity,[status(thm)],[311, 309])).
% 0.19/0.44 tff(313,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!3 = X!0) | (~truthday(X!3)) | (~truthday(X!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(314,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!3)) | (X!3 = X!0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.44 tff(315,plain,
% 0.19/0.44 ((~truthday(X!3)) | (X!3 = X!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[314, 158, 285])).
% 0.19/0.44 tff(316,plain,
% 0.19/0.44 (~truthday(X!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[315, 308])).
% 0.19/0.44 tff(317,plain,
% 0.19/0.44 (truthday(wednesday) | truthday(friday)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[219, 316])).
% 0.19/0.44 tff(318,plain,
% 0.19/0.44 (truthday(wednesday)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[168, 317, 296])).
% 0.19/0.44 tff(319,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(wednesday)) | (~truthday(X!0)) | (wednesday = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(wednesday)) | (~truthday(X!0)) | (wednesday = X!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(320,plain,
% 0.19/0.44 (((wednesday = X!0) | (~truthday(wednesday)) | (~truthday(X!0))) <=> ((~truthday(wednesday)) | (~truthday(X!0)) | (wednesday = X!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(321,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = X!0) | (~truthday(wednesday)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(wednesday)) | (~truthday(X!0)) | (wednesday = X!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[320])).
% 0.19/0.44 tff(322,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = X!0) | (~truthday(wednesday)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(wednesday)) | (~truthday(X!0)) | (wednesday = X!0))),
% 0.19/0.44 inference(transitivity,[status(thm)],[321, 319])).
% 0.19/0.44 tff(323,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = X!0) | (~truthday(wednesday)) | (~truthday(X!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(324,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(wednesday)) | (~truthday(X!0)) | (wednesday = X!0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.19/0.44 tff(325,plain,
% 0.19/0.44 (wednesday = X!0),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[324, 158, 285, 318])).
% 0.19/0.44 tff(326,plain,
% 0.19/0.44 (wednesday = X!1),
% 0.19/0.44 inference(transitivity,[status(thm)],[325, 295])).
% 0.19/0.44 tff(327,plain,
% 0.19/0.44 (consecutive(wednesday) = consecutive(X!1)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[326])).
% 0.19/0.44 tff(328,plain,
% 0.19/0.44 ((consecutive(wednesday) = thursday) <=> (consecutive(wednesday) = thursday)),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(329,axiom,(consecutive(wednesday) = thursday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thursday_follows_wednesday')).
% 0.19/0.44 tff(330,plain,
% 0.19/0.44 (consecutive(wednesday) = thursday),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.19/0.44 tff(331,plain,
% 0.19/0.44 (thursday = consecutive(wednesday)),
% 0.19/0.44 inference(symmetry,[status(thm)],[330])).
% 0.19/0.44 tff(332,plain,
% 0.19/0.44 (thursday = consecutive(X!1)),
% 0.19/0.44 inference(transitivity,[status(thm)],[331, 327])).
% 0.19/0.44 tff(333,plain,
% 0.19/0.44 (day2(thursday) <=> day2(consecutive(X!1))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[332])).
% 0.19/0.44 tff(334,plain,
% 0.19/0.44 (day2(consecutive(X!1)) <=> day2(thursday)),
% 0.19/0.44 inference(symmetry,[status(thm)],[333])).
% 0.19/0.44 tff(335,plain,
% 0.19/0.44 (day2(thursday)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[66, 334])).
% 0.19/0.44 tff(336,plain,
% 0.19/0.44 ((day2(thursday) | day2(saturday) | day2(sunday)) | (~day2(thursday))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(337,plain,
% 0.19/0.44 (day2(thursday) | day2(saturday) | day2(sunday)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[336, 335])).
% 0.19/0.44 tff(338,plain,
% 0.19/0.44 ((X!0 = X!2) <=> (X!2 = X!0)),
% 0.19/0.44 inference(commutativity,[status(thm)],[])).
% 0.19/0.44 tff(339,plain,
% 0.19/0.44 (thursday = X!2),
% 0.19/0.44 inference(transitivity,[status(thm)],[331, 327, 87])).
% 0.19/0.44 tff(340,plain,
% 0.19/0.44 ((X!1 = thursday) <=> (X!0 = X!2)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[294, 339])).
% 0.19/0.44 tff(341,plain,
% 0.19/0.44 ((X!1 = thursday) <=> (X!2 = X!0)),
% 0.19/0.44 inference(transitivity,[status(thm)],[340, 338])).
% 0.19/0.44 tff(342,plain,
% 0.19/0.44 ((~(X!1 = thursday)) <=> (~(X!2 = X!0))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[341])).
% 0.19/0.44 tff(343,plain,
% 0.19/0.44 ((wednesday = thursday) <=> (X!1 = thursday)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[326])).
% 0.19/0.44 tff(344,plain,
% 0.19/0.44 ((~(wednesday = thursday)) <=> (~(X!1 = thursday))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[343])).
% 0.19/0.44 tff(345,plain,
% 0.19/0.44 ((~(wednesday = thursday)) <=> (~(wednesday = thursday))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(346,plain,
% 0.19/0.44 (~(wednesday = thursday)),
% 0.19/0.44 inference(and_elim,[status(thm)],[123])).
% 0.19/0.44 tff(347,plain,
% 0.19/0.44 (~(wednesday = thursday)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.19/0.44 tff(348,plain,
% 0.19/0.44 (~(X!1 = thursday)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[347, 344])).
% 0.19/0.44 tff(349,plain,
% 0.19/0.44 (~(X!2 = X!0)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[348, 342])).
% 0.19/0.44 tff(350,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(X!0)) | (~truthday(X!2)) | (X!2 = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!2)) | (X!2 = X!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(351,plain,
% 0.19/0.44 (((X!2 = X!0) | (~truthday(X!2)) | (~truthday(X!0))) <=> ((~truthday(X!0)) | (~truthday(X!2)) | (X!2 = X!0))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(352,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!2 = X!0) | (~truthday(X!2)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(X!0)) | (~truthday(X!2)) | (X!2 = X!0)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[351])).
% 0.19/0.44 tff(353,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!2 = X!0) | (~truthday(X!2)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!2)) | (X!2 = X!0))),
% 0.19/0.44 inference(transitivity,[status(thm)],[352, 350])).
% 0.19/0.45 tff(354,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((X!2 = X!0) | (~truthday(X!2)) | (~truthday(X!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(355,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(X!0)) | (~truthday(X!2)) | (X!2 = X!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.19/0.45 tff(356,plain,
% 0.19/0.45 ((~truthday(X!2)) | (X!2 = X!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[355, 158, 285])).
% 0.19/0.45 tff(357,plain,
% 0.19/0.45 (~truthday(X!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[356, 349])).
% 0.19/0.45 tff(358,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[244, 357, 337])).
% 0.19/0.45 tff(359,plain,((~(X!1 = X!0)) | truthday(friday) | (consecutive(X!1) = consecutive(consecutive(consecutive(consecutive(X!2)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(360,plain,
% 0.19/0.45 (truthday(friday)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[359, 293, 50])).
% 0.19/0.45 tff(361,assumption,(~(friday = X!0)), introduced(assumption)).
% 0.19/0.45 tff(362,assumption,(truthday(friday)), introduced(assumption)).
% 0.19/0.45 tff(363,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(friday)) | (~truthday(X!0)) | (friday = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(friday)) | (~truthday(X!0)) | (friday = X!0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(364,plain,
% 0.19/0.45 (((friday = X!0) | (~truthday(friday)) | (~truthday(X!0))) <=> ((~truthday(friday)) | (~truthday(X!0)) | (friday = X!0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(365,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((friday = X!0) | (~truthday(friday)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(friday)) | (~truthday(X!0)) | (friday = X!0)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[364])).
% 0.19/0.45 tff(366,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((friday = X!0) | (~truthday(friday)) | (~truthday(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(friday)) | (~truthday(X!0)) | (friday = X!0))),
% 0.19/0.45 inference(transitivity,[status(thm)],[365, 363])).
% 0.19/0.45 tff(367,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((friday = X!0) | (~truthday(friday)) | (~truthday(X!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(368,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(friday)) | (~truthday(X!0)) | (friday = X!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.19/0.45 tff(369,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[368, 158, 285, 362, 361])).
% 0.19/0.45 tff(370,plain,((~truthday(friday)) | (friday = X!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(371,plain,
% 0.19/0.45 (friday = X!0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[370, 360])).
% 0.19/0.45 tff(372,plain,
% 0.19/0.45 (day1(X!1) <=> day1(X!0)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[293])).
% 0.19/0.45 tff(373,plain,
% 0.19/0.45 (day1(X!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[63, 372])).
% 0.19/0.45 tff(374,assumption,(friday = X!0), introduced(assumption)).
% 0.19/0.45 tff(375,plain,
% 0.19/0.45 (day1(friday) <=> day1(X!0)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[374])).
% 0.19/0.45 tff(376,plain,
% 0.19/0.45 (day1(X!0) <=> day1(friday)),
% 0.19/0.45 inference(symmetry,[status(thm)],[375])).
% 0.19/0.45 tff(377,assumption,(day1(X!0)), introduced(assumption)).
% 0.19/0.45 tff(378,plain,
% 0.19/0.45 (day1(friday)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.19/0.45 tff(379,assumption,(~day1(friday)), introduced(assumption)).
% 0.19/0.45 tff(380,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[379, 378])).
% 0.19/0.45 tff(381,plain,((~(friday = X!0)) | day1(friday) | (~day1(X!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(382,plain,
% 0.19/0.45 (day1(friday)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[381, 373, 371])).
% 0.19/0.45 tff(383,plain,
% 0.19/0.45 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(friday) <=> day2(consecutive(friday)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(384,plain,
% 0.19/0.45 (day1(friday) <=> day2(consecutive(friday))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[383, 57])).
% 0.19/0.45 tff(385,plain,
% 0.19/0.45 ((~(day1(friday) <=> day2(consecutive(friday)))) | (~day1(friday)) | day2(consecutive(friday))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(386,plain,
% 0.19/0.45 ((~day1(friday)) | day2(consecutive(friday))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[385, 384])).
% 0.19/0.45 tff(387,plain,
% 0.19/0.45 (day2(consecutive(friday))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[386, 382])).
% 0.19/0.45 tff(388,plain,
% 0.19/0.45 (day2(saturday)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[387, 49])).
% 0.19/0.45 tff(389,plain,
% 0.19/0.45 ((day2(thursday) | day2(saturday) | day2(sunday)) | (~day2(saturday))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(390,plain,
% 0.19/0.45 (day2(thursday) | day2(saturday) | day2(sunday)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[389, 388])).
% 0.19/0.45 tff(391,plain,
% 0.19/0.45 (X!0 = X!1),
% 0.19/0.45 inference(symmetry,[status(thm)],[293])).
% 0.19/0.45 tff(392,plain,
% 0.19/0.45 (friday = X!1),
% 0.19/0.45 inference(transitivity,[status(thm)],[371, 391])).
% 0.19/0.45 tff(393,plain,
% 0.19/0.45 (consecutive(friday) = consecutive(X!1)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[392])).
% 0.19/0.45 tff(394,plain,
% 0.19/0.45 (saturday = consecutive(friday)),
% 0.19/0.45 inference(symmetry,[status(thm)],[48])).
% 0.19/0.45 tff(395,plain,
% 0.19/0.45 (saturday = X!2),
% 0.19/0.45 inference(transitivity,[status(thm)],[394, 393, 87])).
% 0.19/0.45 tff(396,plain,
% 0.19/0.45 ((X!1 = saturday) <=> (X!0 = X!2)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[293, 395])).
% 0.19/0.45 tff(397,plain,
% 0.19/0.45 ((X!1 = saturday) <=> (X!2 = X!0)),
% 0.19/0.45 inference(transitivity,[status(thm)],[396, 338])).
% 0.19/0.45 tff(398,plain,
% 0.19/0.45 ((~(X!1 = saturday)) <=> (~(X!2 = X!0))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[397])).
% 0.19/0.45 tff(399,plain,
% 0.19/0.45 ((friday = saturday) <=> (X!1 = saturday)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[392])).
% 0.19/0.45 tff(400,plain,
% 0.19/0.45 ((~(friday = saturday)) <=> (~(X!1 = saturday))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[399])).
% 0.19/0.45 tff(401,plain,
% 0.19/0.45 ((~(friday = saturday)) <=> (~(friday = saturday))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(402,plain,
% 0.19/0.45 (~(friday = saturday)),
% 0.19/0.45 inference(and_elim,[status(thm)],[116])).
% 0.19/0.45 tff(403,plain,
% 0.19/0.45 (~(friday = saturday)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.19/0.45 tff(404,plain,
% 0.19/0.45 (~(X!1 = saturday)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[403, 400])).
% 0.19/0.45 tff(405,plain,
% 0.19/0.45 (~(X!2 = X!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[404, 398])).
% 0.19/0.45 tff(406,plain,
% 0.19/0.45 (~truthday(X!2)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[356, 405])).
% 0.19/0.45 tff(407,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[244, 406, 390])).
% 0.19/0.45 tff(408,plain,(consecutive(X!1) = consecutive(consecutive(consecutive(consecutive(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(409,plain,
% 0.19/0.45 (consecutive(consecutive(consecutive(consecutive(X!2)))) = consecutive(X!1)),
% 0.19/0.45 inference(symmetry,[status(thm)],[408])).
% 0.19/0.45 tff(410,assumption,(wednesday = consecutive(consecutive(consecutive(X!2)))), introduced(assumption)).
% 0.19/0.45 tff(411,plain,
% 0.19/0.45 (consecutive(wednesday) = consecutive(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[410])).
% 0.19/0.45 tff(412,plain,
% 0.19/0.45 (thursday = consecutive(X!1)),
% 0.19/0.45 inference(transitivity,[status(thm)],[331, 411, 409])).
% 0.19/0.45 tff(413,plain,
% 0.19/0.45 (consecutive(thursday) = consecutive(consecutive(X!1))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[412])).
% 0.19/0.45 tff(414,plain,
% 0.19/0.45 (consecutive(consecutive(X!1)) = consecutive(thursday)),
% 0.19/0.45 inference(symmetry,[status(thm)],[413])).
% 0.19/0.45 tff(415,plain,
% 0.19/0.45 (consecutive(X!2) = friday),
% 0.19/0.45 inference(transitivity,[status(thm)],[100, 414, 45])).
% 0.19/0.45 tff(416,plain,
% 0.19/0.45 (consecutive(consecutive(X!2)) = consecutive(friday)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[415])).
% 0.19/0.45 tff(417,plain,
% 0.19/0.45 (consecutive(friday) = consecutive(consecutive(X!2))),
% 0.19/0.45 inference(symmetry,[status(thm)],[416])).
% 0.19/0.45 tff(418,plain,
% 0.19/0.45 (saturday = consecutive(consecutive(X!2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[394, 417])).
% 0.19/0.45 tff(419,plain,
% 0.19/0.45 (consecutive(saturday) = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[418])).
% 0.19/0.45 tff(420,plain,
% 0.19/0.45 ((consecutive(saturday) = sunday) <=> (consecutive(saturday) = sunday)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(421,axiom,(consecutive(saturday) = sunday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sunday_follows_saturday')).
% 0.19/0.45 tff(422,plain,
% 0.19/0.45 (consecutive(saturday) = sunday),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.19/0.45 tff(423,plain,
% 0.19/0.45 (sunday = consecutive(saturday)),
% 0.19/0.45 inference(symmetry,[status(thm)],[422])).
% 0.19/0.45 tff(424,plain,
% 0.19/0.45 (sunday = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[423, 419])).
% 0.19/0.45 tff(425,plain,
% 0.19/0.45 ((consecutive(consecutive(consecutive(X!2))) = sunday) <=> (sunday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(commutativity,[status(thm)],[])).
% 0.19/0.45 tff(426,plain,
% 0.19/0.45 ((wednesday = sunday) <=> (consecutive(consecutive(consecutive(X!2))) = sunday)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[410])).
% 0.19/0.45 tff(427,plain,
% 0.19/0.45 ((wednesday = sunday) <=> (sunday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[426, 425])).
% 0.19/0.45 tff(428,plain,
% 0.19/0.45 ((~(wednesday = sunday)) <=> (~(sunday = consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[427])).
% 0.19/0.45 tff(429,plain,
% 0.19/0.45 ((~(wednesday = sunday)) <=> (~(wednesday = sunday))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(430,plain,
% 0.19/0.45 (~(wednesday = sunday)),
% 0.19/0.45 inference(and_elim,[status(thm)],[120])).
% 0.19/0.45 tff(431,plain,
% 0.19/0.45 (~(wednesday = sunday)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.19/0.45 tff(432,plain,
% 0.19/0.45 (~(sunday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[431, 428])).
% 0.19/0.45 tff(433,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[432, 424])).
% 0.19/0.45 tff(434,plain,(~(wednesday = consecutive(consecutive(consecutive(X!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(435,plain,
% 0.19/0.45 (day2(consecutive(consecutive(consecutive(consecutive(X!2))))) <=> day2(consecutive(X!1))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[409])).
% 0.19/0.45 tff(436,plain,
% 0.19/0.45 (day2(consecutive(X!1)) <=> day2(consecutive(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(symmetry,[status(thm)],[435])).
% 0.19/0.45 tff(437,plain,
% 0.19/0.45 (day2(consecutive(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[66, 436])).
% 0.19/0.45 tff(438,plain,
% 0.19/0.45 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(consecutive(consecutive(consecutive(X!2)))) <=> day2(consecutive(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(439,plain,
% 0.19/0.45 (day1(consecutive(consecutive(consecutive(X!2)))) <=> day2(consecutive(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[438, 57])).
% 0.19/0.45 tff(440,plain,
% 0.19/0.45 ((~(day1(consecutive(consecutive(consecutive(X!2)))) <=> day2(consecutive(consecutive(consecutive(consecutive(X!2))))))) | day1(consecutive(consecutive(consecutive(X!2)))) | (~day2(consecutive(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(441,plain,
% 0.19/0.45 (day1(consecutive(consecutive(consecutive(X!2)))) | (~day2(consecutive(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[440, 439])).
% 0.19/0.45 tff(442,plain,
% 0.19/0.45 (day1(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[441, 437])).
% 0.19/0.45 tff(443,plain,
% 0.19/0.45 (((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | ((~day1(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))))) <=> ((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | (~day1(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(444,plain,
% 0.19/0.45 ((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | ((~day1(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(445,plain,
% 0.19/0.45 ((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | (~day1(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.19/0.45 tff(446,plain,
% 0.19/0.45 ((~day1(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[445, 274])).
% 0.19/0.45 tff(447,plain,
% 0.19/0.45 (~((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[446, 442])).
% 0.19/0.45 tff(448,assumption,(truthday(monday) | truthday(tuesday)), introduced(assumption)).
% 0.19/0.45 tff(449,plain,
% 0.19/0.45 (truthday(monday)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[260, 448])).
% 0.19/0.45 tff(450,plain,
% 0.19/0.45 (X!2 = X!3),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[254, 449])).
% 0.19/0.45 tff(451,plain,
% 0.19/0.45 (X!3 = X!2),
% 0.19/0.45 inference(symmetry,[status(thm)],[450])).
% 0.19/0.45 tff(452,plain,
% 0.19/0.45 (consecutive(X!2) = consecutive(X!1)),
% 0.19/0.45 inference(transitivity,[status(thm)],[91, 451, 86])).
% 0.19/0.45 tff(453,plain,
% 0.19/0.45 (consecutive(consecutive(X!2)) = consecutive(consecutive(X!1))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[452])).
% 0.19/0.45 tff(454,plain,
% 0.19/0.45 (consecutive(consecutive(X!2)) = consecutive(X!2)),
% 0.19/0.45 inference(transitivity,[status(thm)],[453, 88])).
% 0.19/0.45 tff(455,plain,
% 0.19/0.45 (day2(consecutive(consecutive(X!2))) <=> day2(consecutive(X!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[454])).
% 0.19/0.45 tff(456,plain,
% 0.19/0.45 (day2(consecutive(X!2)) <=> day2(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(symmetry,[status(thm)],[455])).
% 0.19/0.45 tff(457,plain,
% 0.19/0.45 (consecutive(X!1) = consecutive(X!2)),
% 0.19/0.45 inference(transitivity,[status(thm)],[87, 450, 42])).
% 0.19/0.45 tff(458,plain,
% 0.19/0.45 (day2(consecutive(X!1)) <=> day2(consecutive(X!2))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[457])).
% 0.19/0.45 tff(459,plain,
% 0.19/0.45 (day2(consecutive(X!2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[66, 458])).
% 0.19/0.45 tff(460,plain,
% 0.19/0.45 (day2(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[459, 456])).
% 0.19/0.45 tff(461,plain,
% 0.19/0.45 (~(truthday(wednesday) | truthday(friday))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[177, 449])).
% 0.19/0.45 tff(462,plain,
% 0.19/0.45 (((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))) | (~(truthday(monday) | truthday(tuesday))) | (~truthday(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(463,plain,
% 0.19/0.45 (~truthday(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[462, 448, 447])).
% 0.19/0.45 tff(464,plain,
% 0.19/0.45 (((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))) | (truthday(wednesday) | truthday(friday)) | truthday(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(465,plain,
% 0.19/0.45 ((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[464, 463, 461])).
% 0.19/0.45 tff(466,plain,
% 0.19/0.45 (((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))))) <=> ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(467,plain,
% 0.19/0.45 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(468,plain,
% 0.19/0.45 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.19/0.45 tff(469,plain,
% 0.19/0.45 ((~day3(consecutive(consecutive(consecutive(X!2))))) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[468, 191])).
% 0.19/0.45 tff(470,plain,
% 0.19/0.45 (~day3(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[469, 465])).
% 0.19/0.45 tff(471,plain,
% 0.19/0.45 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(consecutive(consecutive(X!2))) <=> day3(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(472,plain,
% 0.19/0.45 (day2(consecutive(consecutive(X!2))) <=> day3(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[471, 9])).
% 0.19/0.45 tff(473,plain,
% 0.19/0.45 ((~(day2(consecutive(consecutive(X!2))) <=> day3(consecutive(consecutive(consecutive(X!2)))))) | (~day2(consecutive(consecutive(X!2)))) | day3(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(474,plain,
% 0.19/0.45 ((~day2(consecutive(consecutive(X!2)))) | day3(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[473, 472])).
% 0.19/0.45 tff(475,plain,
% 0.19/0.45 (~day2(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[474, 470])).
% 0.19/0.45 tff(476,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[475, 460])).
% 0.19/0.45 tff(477,plain,(~(truthday(monday) | truthday(tuesday))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(478,plain,
% 0.19/0.45 (((truthday(monday) | truthday(tuesday)) <=> truthday(consecutive(consecutive(consecutive(X!2))))) | (truthday(monday) | truthday(tuesday)) | truthday(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(479,plain,
% 0.19/0.45 (truthday(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[478, 477, 447])).
% 0.19/0.45 tff(480,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))) | (wednesday = consecutive(consecutive(consecutive(X!2)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))) | (wednesday = consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(481,plain,
% 0.19/0.45 (((wednesday = consecutive(consecutive(consecutive(X!2)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2)))))) <=> ((~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))) | (wednesday = consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(482,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = consecutive(consecutive(consecutive(X!2)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))) | (wednesday = consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[481])).
% 0.19/0.45 tff(483,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = consecutive(consecutive(consecutive(X!2)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))) | (wednesday = consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[482, 480])).
% 0.19/0.45 tff(484,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | ((wednesday = consecutive(consecutive(consecutive(X!2)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(485,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~truthday(X)) | (~truthday(Y)))) | (~truthday(wednesday)) | (~truthday(consecutive(consecutive(consecutive(X!2))))) | (wednesday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.19/0.45 tff(486,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[485, 158, 145, 479, 434])).
% 0.19/0.45 tff(487,plain,(~truthday(wednesday)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(488,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : refl(((X = Y) | (~day1(Y)) | (~day1(X))) <=> ((X = Y) | (~day1(Y)) | (~day1(X))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(489,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[488])).
% 0.19/0.45 tff(490,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((day1(X) & day1(Y)) <=> (~((~day1(Y)) | (~day1(X))))), ((~(day1(X) & day1(Y))) <=> (~(~((~day1(Y)) | (~day1(X))))))), rewrite((~(~((~day1(Y)) | (~day1(X))))) <=> ((~day1(Y)) | (~day1(X)))), ((~(day1(X) & day1(Y))) <=> ((~day1(Y)) | (~day1(X))))), (((~(day1(X) & day1(Y))) | (X = Y)) <=> (((~day1(Y)) | (~day1(X))) | (X = Y)))), rewrite((((~day1(Y)) | (~day1(X))) | (X = Y)) <=> ((X = Y) | (~day1(Y)) | (~day1(X)))), (((~(day1(X) & day1(Y))) | (X = Y)) <=> ((X = Y) | (~day1(Y)) | (~day1(X)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(491,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[490])).
% 0.19/0.45 tff(492,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(493,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : rewrite(((day1(X) & day1(Y)) => (X = Y)) <=> ((~(day1(X) & day1(Y))) | (X = Y)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(494,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((day1(X) & day1(Y)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[493])).
% 0.19/0.45 tff(495,axiom,(![X: $i, Y: $i] : ((day1(X) & day1(Y)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','day1_unique')).
% 0.19/0.45 tff(496,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.19/0.45 tff(497,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[496, 492])).
% 0.19/0.45 tff(498,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : ((~(day1(X) & day1(Y))) | (X = Y))),
% 0.19/0.45 inference(skolemize,[status(sab)],[497])).
% 0.19/0.45 tff(499,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[498, 491])).
% 0.19/0.45 tff(500,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[499, 489])).
% 0.19/0.45 tff(501,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(X!1)) | (X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(502,plain,
% 0.19/0.45 (((X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))) | (~day1(X!1))) <=> ((~day1(X!1)) | (X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(503,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))) | (~day1(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(X!1)) | (X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2)))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[502])).
% 0.19/0.45 tff(504,plain,
% 0.19/0.45 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))) | (~day1(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[503, 501])).
% 0.19/0.45 tff(505,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2))))) | (~day1(X!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(506,plain,
% 0.19/0.45 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.19/0.45 tff(507,plain,
% 0.19/0.45 ((X!1 = consecutive(consecutive(consecutive(X!2)))) | (~day1(consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[506, 500, 63])).
% 0.19/0.45 tff(508,plain,
% 0.19/0.45 (X!1 = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[507, 442])).
% 0.19/0.45 tff(509,plain,
% 0.19/0.45 (truthday(X!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[280, 477])).
% 0.19/0.45 tff(510,plain,
% 0.19/0.45 (X!1 = X!0),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[292, 509])).
% 0.19/0.45 tff(511,plain,
% 0.19/0.45 (X!0 = X!1),
% 0.19/0.45 inference(symmetry,[status(thm)],[510])).
% 0.19/0.45 tff(512,plain,
% 0.19/0.45 (X!0 = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[511, 508])).
% 0.19/0.45 tff(513,plain,
% 0.19/0.45 (day1(X!0) <=> day1(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[512])).
% 0.19/0.45 tff(514,plain,
% 0.19/0.45 (day1(consecutive(consecutive(consecutive(X!2)))) <=> day1(X!0)),
% 0.19/0.45 inference(symmetry,[status(thm)],[513])).
% 0.19/0.45 tff(515,plain,
% 0.19/0.45 (day1(X!0)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[442, 514])).
% 0.19/0.45 tff(516,assumption,(X!1 = friday), introduced(assumption)).
% 0.19/0.45 tff(517,plain,
% 0.19/0.45 (friday = X!1),
% 0.19/0.45 inference(symmetry,[status(thm)],[516])).
% 0.19/0.45 tff(518,plain,
% 0.19/0.45 (friday = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[517, 508])).
% 0.19/0.45 tff(519,plain,
% 0.19/0.45 (consecutive(friday) = consecutive(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[518])).
% 0.19/0.45 tff(520,plain,
% 0.19/0.45 (saturday = consecutive(X!1)),
% 0.19/0.45 inference(transitivity,[status(thm)],[394, 519, 409])).
% 0.19/0.45 tff(521,plain,
% 0.19/0.45 (consecutive(saturday) = consecutive(consecutive(X!1))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[520])).
% 0.19/0.45 tff(522,plain,
% 0.19/0.45 (consecutive(consecutive(X!1)) = consecutive(saturday)),
% 0.19/0.45 inference(symmetry,[status(thm)],[521])).
% 0.19/0.45 tff(523,plain,
% 0.19/0.45 (consecutive(X!2) = sunday),
% 0.19/0.45 inference(transitivity,[status(thm)],[100, 522, 422])).
% 0.19/0.45 tff(524,plain,
% 0.19/0.45 (consecutive(consecutive(X!2)) = consecutive(sunday)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[523])).
% 0.19/0.45 tff(525,plain,
% 0.19/0.45 (consecutive(sunday) = consecutive(consecutive(X!2))),
% 0.19/0.45 inference(symmetry,[status(thm)],[524])).
% 0.19/0.45 tff(526,plain,
% 0.19/0.45 (monday = consecutive(sunday)),
% 0.19/0.45 inference(symmetry,[status(thm)],[208])).
% 0.19/0.45 tff(527,plain,
% 0.19/0.45 (monday = consecutive(consecutive(X!2))),
% 0.19/0.45 inference(transitivity,[status(thm)],[526, 525])).
% 0.19/0.45 tff(528,plain,
% 0.19/0.45 (consecutive(monday) = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[527])).
% 0.19/0.45 tff(529,plain,
% 0.19/0.45 ((consecutive(monday) = tuesday) <=> (consecutive(monday) = tuesday)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(530,axiom,(consecutive(monday) = tuesday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','tuesday_follows_monday')).
% 0.19/0.45 tff(531,plain,
% 0.19/0.45 (consecutive(monday) = tuesday),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.19/0.46 tff(532,plain,
% 0.19/0.46 (tuesday = consecutive(monday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[531])).
% 0.19/0.46 tff(533,plain,
% 0.19/0.46 (tuesday = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[532, 528])).
% 0.19/0.46 tff(534,plain,
% 0.19/0.46 ((tuesday = friday) <=> (tuesday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[518])).
% 0.19/0.46 tff(535,plain,
% 0.19/0.46 ((~(tuesday = friday)) <=> (~(tuesday = consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[534])).
% 0.19/0.46 tff(536,plain,
% 0.19/0.46 ((~(tuesday = friday)) <=> (~(tuesday = friday))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(537,plain,
% 0.19/0.46 (~(tuesday = friday)),
% 0.19/0.46 inference(and_elim,[status(thm)],[126])).
% 0.19/0.46 tff(538,plain,
% 0.19/0.46 (~(tuesday = friday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.19/0.46 tff(539,plain,
% 0.19/0.46 (~(tuesday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[538, 535])).
% 0.19/0.46 tff(540,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[539, 533])).
% 0.19/0.46 tff(541,plain,(~(X!1 = friday)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(542,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(X!1)) | (~day1(friday)) | (X!1 = friday))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (~day1(friday)) | (X!1 = friday))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(543,plain,
% 0.19/0.46 (((X!1 = friday) | (~day1(friday)) | (~day1(X!1))) <=> ((~day1(X!1)) | (~day1(friday)) | (X!1 = friday))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(544,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = friday) | (~day1(friday)) | (~day1(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(X!1)) | (~day1(friday)) | (X!1 = friday)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[543])).
% 0.19/0.46 tff(545,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = friday) | (~day1(friday)) | (~day1(X!1)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (~day1(friday)) | (X!1 = friday))),
% 0.19/0.46 inference(transitivity,[status(thm)],[544, 542])).
% 0.19/0.46 tff(546,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((X!1 = friday) | (~day1(friday)) | (~day1(X!1)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(547,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(X!1)) | (~day1(friday)) | (X!1 = friday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.19/0.46 tff(548,plain,
% 0.19/0.46 ((~day1(friday)) | (X!1 = friday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[547, 500, 63])).
% 0.19/0.46 tff(549,plain,
% 0.19/0.46 (~day1(friday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[548, 541])).
% 0.19/0.46 tff(550,plain,
% 0.19/0.46 (~(friday = X!0)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[381, 549, 515])).
% 0.19/0.46 tff(551,plain,
% 0.19/0.46 (~truthday(friday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[370, 550])).
% 0.19/0.46 tff(552,plain,
% 0.19/0.46 (~(truthday(wednesday) | truthday(friday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[168, 551, 487])).
% 0.19/0.46 tff(553,plain,
% 0.19/0.46 (truthday(X!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[219, 552])).
% 0.19/0.46 tff(554,plain,
% 0.19/0.46 (X!3 = X!0),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[315, 553])).
% 0.19/0.46 tff(555,plain,
% 0.19/0.46 (X!0 = X!3),
% 0.19/0.46 inference(symmetry,[status(thm)],[554])).
% 0.19/0.46 tff(556,plain,
% 0.19/0.46 (consecutive(consecutive(consecutive(X!2))) = X!1),
% 0.19/0.46 inference(symmetry,[status(thm)],[508])).
% 0.19/0.46 tff(557,plain,
% 0.19/0.46 (consecutive(consecutive(consecutive(X!2))) = consecutive(X!2)),
% 0.19/0.46 inference(transitivity,[status(thm)],[556, 510, 555, 42])).
% 0.19/0.46 tff(558,plain,
% 0.19/0.46 ((friday = consecutive(consecutive(consecutive(X!2)))) <=> (friday = consecutive(X!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[557])).
% 0.19/0.46 tff(559,plain,
% 0.19/0.46 ((friday = consecutive(consecutive(consecutive(X!2)))) <=> (consecutive(X!2) = friday)),
% 0.19/0.46 inference(transitivity,[status(thm)],[558, 2])).
% 0.19/0.46 tff(560,plain,
% 0.19/0.46 ((~(friday = consecutive(consecutive(consecutive(X!2))))) <=> (~(consecutive(X!2) = friday))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[559])).
% 0.19/0.46 tff(561,plain,
% 0.19/0.46 ((consecutive(consecutive(consecutive(X!2))) = friday) <=> (friday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(commutativity,[status(thm)],[])).
% 0.19/0.46 tff(562,plain,
% 0.19/0.46 ((X!1 = friday) <=> (consecutive(consecutive(consecutive(X!2))) = friday)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[508])).
% 0.19/0.46 tff(563,plain,
% 0.19/0.46 ((X!1 = friday) <=> (friday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[562, 561])).
% 0.19/0.46 tff(564,plain,
% 0.19/0.46 ((~(X!1 = friday)) <=> (~(friday = consecutive(consecutive(consecutive(X!2)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[563])).
% 0.19/0.46 tff(565,plain,
% 0.19/0.46 (~(friday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[541, 564])).
% 0.19/0.46 tff(566,plain,
% 0.19/0.46 (~(consecutive(X!2) = friday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[565, 560])).
% 0.19/0.46 tff(567,plain,
% 0.19/0.46 (X!3 = consecutive(consecutive(consecutive(X!2)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[554, 511, 508])).
% 0.19/0.46 tff(568,plain,
% 0.19/0.46 (day1(X!3) <=> day1(consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[567])).
% 0.19/0.46 tff(569,plain,
% 0.19/0.46 (day1(consecutive(consecutive(consecutive(X!2)))) <=> day1(X!3)),
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% 0.19/0.46 tff(570,plain,
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% 0.19/0.46 inference(modus_ponens,[status(thm)],[442, 569])).
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% 0.19/0.46 inference(monotonicity,[status(thm)],[526])).
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% 0.19/0.46 inference(monotonicity,[status(thm)],[571])).
% 0.19/0.46 tff(573,plain,
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% 0.19/0.46 tff(574,plain,
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% 0.19/0.46 tff(575,plain,
% 0.19/0.46 ((~day3(tuesday)) <=> (~day3(consecutive(monday)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[574])).
% 0.19/0.46 tff(576,plain,
% 0.19/0.46 (((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday)) | (truthday(wednesday) | truthday(friday)) | truthday(tuesday)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(577,plain,
% 0.19/0.46 (((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday)) | (truthday(wednesday) | truthday(friday))),
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% 0.19/0.46 tff(578,plain,
% 0.19/0.46 ((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[577, 552])).
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% 0.19/0.46 (((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(tuesday)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday))))) <=> ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(tuesday)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday))))),
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% 0.19/0.46 tff(580,plain,
% 0.19/0.46 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | ((~day3(tuesday)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(581,plain,
% 0.19/0.46 ((~![X: $i] : ((~day3(X)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(X))))) | (~day3(tuesday)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.19/0.46 tff(582,plain,
% 0.19/0.46 ((~day3(tuesday)) | (~((truthday(wednesday) | truthday(friday)) <=> truthday(tuesday)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[581, 191])).
% 0.19/0.46 tff(583,plain,
% 0.19/0.46 (~day3(tuesday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[582, 578])).
% 0.19/0.46 tff(584,plain,
% 0.19/0.46 (~day3(consecutive(monday))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[583, 575])).
% 0.19/0.46 tff(585,plain,
% 0.19/0.46 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(monday) <=> day3(consecutive(monday)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(586,plain,
% 0.19/0.46 (day2(monday) <=> day3(consecutive(monday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[585, 9])).
% 0.19/0.46 tff(587,plain,
% 0.19/0.46 ((~(day2(monday) <=> day3(consecutive(monday)))) | (~day2(monday)) | day3(consecutive(monday))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(588,plain,
% 0.19/0.46 ((~day2(monday)) | day3(consecutive(monday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[587, 586])).
% 0.19/0.46 tff(589,plain,
% 0.19/0.46 (~day2(monday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[588, 584])).
% 0.19/0.46 tff(590,plain,
% 0.19/0.46 (~day2(consecutive(sunday))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[589, 572])).
% 0.19/0.46 tff(591,plain,
% 0.19/0.46 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(sunday) <=> day2(consecutive(sunday)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(592,plain,
% 0.19/0.46 (day1(sunday) <=> day2(consecutive(sunday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[591, 57])).
% 0.19/0.46 tff(593,plain,
% 0.19/0.46 ((~(day1(sunday) <=> day2(consecutive(sunday)))) | (~day1(sunday)) | day2(consecutive(sunday))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(594,plain,
% 0.19/0.46 ((~day1(sunday)) | day2(consecutive(sunday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[593, 592])).
% 0.19/0.46 tff(595,plain,
% 0.19/0.46 (~day1(sunday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[594, 590])).
% 0.19/0.46 tff(596,assumption,(consecutive(X!2) = sunday), introduced(assumption)).
% 0.19/0.46 tff(597,plain,
% 0.19/0.46 (sunday = consecutive(X!2)),
% 0.19/0.46 inference(symmetry,[status(thm)],[596])).
% 0.19/0.46 tff(598,plain,
% 0.19/0.46 (sunday = X!3),
% 0.19/0.46 inference(transitivity,[status(thm)],[597, 91])).
% 0.19/0.46 tff(599,plain,
% 0.19/0.46 (day1(sunday) <=> day1(X!3)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[598])).
% 0.19/0.46 tff(600,plain,
% 0.19/0.46 (day1(X!3) <=> day1(sunday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[599])).
% 0.19/0.46 tff(601,assumption,(day1(X!3)), introduced(assumption)).
% 0.19/0.46 tff(602,plain,
% 0.19/0.46 (day1(sunday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.19/0.46 tff(603,assumption,(~day1(sunday)), introduced(assumption)).
% 0.19/0.46 tff(604,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[603, 602])).
% 0.19/0.46 tff(605,plain,((~(consecutive(X!2) = sunday)) | day1(sunday) | (~day1(X!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(606,plain,
% 0.19/0.46 (~(consecutive(X!2) = sunday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[605, 595, 570])).
% 0.19/0.46 tff(607,plain,
% 0.19/0.46 ((consecutive(consecutive(consecutive(X!2))) = wednesday) <=> (wednesday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(commutativity,[status(thm)],[])).
% 0.19/0.46 tff(608,plain,
% 0.19/0.46 ((X!1 = wednesday) <=> (consecutive(consecutive(consecutive(X!2))) = wednesday)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[508])).
% 0.19/0.46 tff(609,plain,
% 0.19/0.46 ((X!1 = wednesday) <=> (wednesday = consecutive(consecutive(consecutive(X!2))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[608, 607])).
% 0.19/0.46 tff(610,plain,
% 0.19/0.46 ((wednesday = consecutive(consecutive(consecutive(X!2)))) <=> (X!1 = wednesday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[609])).
% 0.19/0.46 tff(611,plain,
% 0.19/0.46 ((~(wednesday = consecutive(consecutive(consecutive(X!2))))) <=> (~(X!1 = wednesday))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[610])).
% 0.19/0.46 tff(612,plain,
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% 0.19/0.46 inference(modus_ponens,[status(thm)],[434, 611])).
% 0.19/0.46 tff(613,plain,
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% 0.19/0.46 tff(614,plain,
% 0.19/0.46 (consecutive(consecutive(consecutive(X!2))) = consecutive(X!2)),
% 0.19/0.46 inference(transitivity,[status(thm)],[556, 294, 613, 42])).
% 0.19/0.46 tff(615,plain,
% 0.19/0.46 ((wednesday = consecutive(consecutive(consecutive(X!2)))) <=> (wednesday = consecutive(X!2))),
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% 0.19/0.46 tff(616,plain,
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% 0.19/0.46 tff(617,plain,
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% 0.19/0.46 inference(commutativity,[status(thm)],[])).
% 0.19/0.46 tff(618,plain,
% 0.19/0.46 ((consecutive(X!2) = wednesday) <=> (X!1 = wednesday)),
% 0.19/0.46 inference(transitivity,[status(thm)],[617, 616, 610])).
% 0.19/0.46 tff(619,assumption,(consecutive(X!2) = wednesday), introduced(assumption)).
% 0.19/0.46 tff(620,plain,
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% 0.19/0.46 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.19/0.46 tff(621,assumption,(~(X!1 = wednesday)), introduced(assumption)).
% 0.19/0.46 tff(622,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[621, 620])).
% 0.19/0.46 tff(623,plain,((~(consecutive(X!2) = wednesday)) | (X!1 = wednesday) | (~(X!1 = X!0)) | (~(X!3 = X!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(624,plain,
% 0.19/0.46 (~(consecutive(X!2) = wednesday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[623, 554, 612, 510])).
% 0.19/0.46 tff(625,plain,
% 0.19/0.46 (truthday(consecutive(X!2))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[197, 552])).
% 0.19/0.46 tff(626,assumption,(consecutive(X!2) = tuesday), introduced(assumption)).
% 0.19/0.46 tff(627,plain,
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% 0.19/0.46 inference(symmetry,[status(thm)],[626])).
% 0.19/0.46 tff(628,plain,
% 0.19/0.46 (truthday(tuesday) <=> truthday(consecutive(X!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[627])).
% 0.19/0.46 tff(629,plain,
% 0.19/0.46 (truthday(consecutive(X!2)) <=> truthday(tuesday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[628])).
% 0.19/0.46 tff(630,assumption,(truthday(consecutive(X!2))), introduced(assumption)).
% 0.19/0.46 tff(631,plain,
% 0.19/0.46 (truthday(tuesday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.19/0.46 tff(632,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[258, 631])).
% 0.19/0.46 tff(633,plain,((~(consecutive(X!2) = tuesday)) | (~truthday(consecutive(X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(634,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[633, 625])).
% 0.19/0.46 tff(635,plain,
% 0.19/0.46 ((consecutive(tuesday) = wednesday) <=> (consecutive(tuesday) = wednesday)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(636,axiom,(consecutive(tuesday) = wednesday), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wednesday_follows_tuesday')).
% 0.19/0.46 tff(637,plain,
% 0.19/0.46 (consecutive(tuesday) = wednesday),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.19/0.46 tff(638,plain,
% 0.19/0.46 (wednesday = consecutive(tuesday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[637])).
% 0.19/0.46 tff(639,plain,
% 0.19/0.46 (day2(wednesday) <=> day2(consecutive(tuesday))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[638])).
% 0.19/0.46 tff(640,plain,
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% 0.19/0.46 inference(symmetry,[status(thm)],[639])).
% 0.19/0.46 tff(641,plain,
% 0.19/0.46 ((~day2(consecutive(tuesday))) <=> (~day2(wednesday))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[640])).
% 0.19/0.46 tff(642,plain,
% 0.19/0.46 (((truthday(monday) | truthday(tuesday)) <=> truthday(tuesday)) | (truthday(monday) | truthday(tuesday)) | truthday(tuesday)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(643,plain,
% 0.19/0.46 (((truthday(monday) | truthday(tuesday)) <=> truthday(tuesday)) | (truthday(monday) | truthday(tuesday))),
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% 0.19/0.46 tff(644,plain,
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% 0.19/0.46 tff(645,plain,
% 0.19/0.46 (((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | ((~day1(tuesday)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(tuesday))))) <=> ((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | (~day1(tuesday)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(tuesday))))),
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% 0.19/0.46 tff(646,plain,
% 0.19/0.46 ((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | ((~day1(tuesday)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(tuesday))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(647,plain,
% 0.19/0.46 ((~![X: $i] : ((~day1(X)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(X))))) | (~day1(tuesday)) | (~((truthday(monday) | truthday(tuesday)) <=> truthday(tuesday)))),
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% 0.19/0.46 tff(648,plain,
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% 0.19/0.46 tff(649,plain,
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% 0.19/0.46 tff(650,plain,
% 0.19/0.46 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(tuesday) <=> day2(consecutive(tuesday)))),
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% 0.19/0.46 tff(651,plain,
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% 0.19/0.46 tff(652,plain,
% 0.19/0.46 ((~(day1(tuesday) <=> day2(consecutive(tuesday)))) | day1(tuesday) | (~day2(consecutive(tuesday)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(653,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[652, 651])).
% 0.19/0.46 tff(654,plain,
% 0.19/0.46 (~day2(consecutive(tuesday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[653, 649])).
% 0.19/0.46 tff(655,plain,
% 0.19/0.46 (~day2(wednesday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[654, 641])).
% 0.19/0.46 tff(656,plain,
% 0.19/0.46 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(wednesday) <=> day3(consecutive(wednesday)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(657,plain,
% 0.19/0.46 (day2(wednesday) <=> day3(consecutive(wednesday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[656, 9])).
% 0.19/0.46 tff(658,plain,
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% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(659,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[658, 657])).
% 0.19/0.46 tff(660,plain,
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% 0.19/0.46 inference(unit_resolution,[status(thm)],[659, 655])).
% 0.19/0.46 tff(661,assumption,(consecutive(X!2) = thursday), introduced(assumption)).
% 0.19/0.46 tff(662,plain,
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% 0.19/0.46 tff(663,plain,
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% 0.19/0.46 inference(transitivity,[status(thm)],[330, 662])).
% 0.19/0.46 tff(664,plain,
% 0.19/0.46 (day3(consecutive(wednesday)) <=> day3(consecutive(X!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[663])).
% 0.19/0.46 tff(665,plain,
% 0.19/0.46 (day3(consecutive(X!2)) <=> day3(consecutive(wednesday))),
% 0.19/0.46 inference(symmetry,[status(thm)],[664])).
% 0.19/0.46 tff(666,plain,
% 0.19/0.46 (day3(consecutive(wednesday))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 665])).
% 0.19/0.46 tff(667,assumption,(~day3(consecutive(wednesday))), introduced(assumption)).
% 0.19/0.46 tff(668,plain,
% 0.19/0.46 ($false),
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% 0.19/0.46 tff(669,plain,((~(consecutive(X!2) = thursday)) | day3(consecutive(wednesday))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(670,plain,
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% 0.19/0.46 tff(671,assumption,(consecutive(X!2) = saturday), introduced(assumption)).
% 0.19/0.46 tff(672,plain,
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% 0.19/0.46 tff(673,plain,
% 0.19/0.46 (consecutive(friday) = consecutive(X!2)),
% 0.19/0.46 inference(transitivity,[status(thm)],[48, 672])).
% 0.19/0.46 tff(674,plain,
% 0.19/0.46 (day3(consecutive(friday)) <=> day3(consecutive(X!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[673])).
% 0.19/0.46 tff(675,plain,
% 0.19/0.46 (day3(consecutive(X!2)) <=> day3(consecutive(friday))),
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% 0.19/0.46 tff(676,plain,
% 0.19/0.46 (day3(consecutive(friday))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 675])).
% 0.19/0.46 tff(677,plain,
% 0.19/0.46 (friday = consecutive(thursday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[45])).
% 0.19/0.46 tff(678,plain,
% 0.19/0.46 (day2(friday) <=> day2(consecutive(thursday))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[677])).
% 0.19/0.46 tff(679,plain,
% 0.19/0.46 (day2(consecutive(thursday)) <=> day2(friday)),
% 0.19/0.46 inference(symmetry,[status(thm)],[678])).
% 0.19/0.46 tff(680,plain,
% 0.19/0.46 ((~day2(consecutive(thursday))) <=> (~day2(friday))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[679])).
% 0.19/0.46 tff(681,plain,
% 0.19/0.46 (day1(consecutive(X!2)) <=> day1(X!3)),
% 0.19/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.19/0.46 tff(682,plain,
% 0.19/0.46 (day1(X!3) <=> day1(consecutive(X!2))),
% 0.19/0.46 inference(symmetry,[status(thm)],[681])).
% 0.19/0.46 tff(683,plain,
% 0.19/0.46 (day1(consecutive(consecutive(consecutive(X!2)))) <=> day1(consecutive(X!2))),
% 0.19/0.46 inference(transitivity,[status(thm)],[569, 682])).
% 0.19/0.46 tff(684,plain,
% 0.19/0.46 (day1(consecutive(X!2))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[442, 683])).
% 0.19/0.46 tff(685,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(686,plain,
% 0.19/0.46 (((consecutive(X!2) = thursday) | (~day1(thursday)) | (~day1(consecutive(X!2)))) <=> ((~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(687,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((consecutive(X!2) = thursday) | (~day1(thursday)) | (~day1(consecutive(X!2))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[686])).
% 0.19/0.46 tff(688,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((consecutive(X!2) = thursday) | (~day1(thursday)) | (~day1(consecutive(X!2))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[687, 685])).
% 0.19/0.46 tff(689,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | ((consecutive(X!2) = thursday) | (~day1(thursday)) | (~day1(consecutive(X!2))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(690,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((X = Y) | (~day1(Y)) | (~day1(X)))) | (~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.19/0.46 tff(691,plain,
% 0.19/0.46 ((~day1(thursday)) | (consecutive(X!2) = thursday) | (~day1(consecutive(X!2)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[690, 500])).
% 0.19/0.46 tff(692,plain,
% 0.19/0.46 (~day1(thursday)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[691, 684, 670])).
% 0.19/0.46 tff(693,plain,
% 0.19/0.46 ((~![X: $i] : (day1(X) <=> day2(consecutive(X)))) | (day1(thursday) <=> day2(consecutive(thursday)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(694,plain,
% 0.19/0.46 (day1(thursday) <=> day2(consecutive(thursday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[693, 57])).
% 0.19/0.46 tff(695,plain,
% 0.19/0.46 ((~(day1(thursday) <=> day2(consecutive(thursday)))) | day1(thursday) | (~day2(consecutive(thursday)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(696,plain,
% 0.19/0.46 (day1(thursday) | (~day2(consecutive(thursday)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[695, 694])).
% 0.19/0.46 tff(697,plain,
% 0.19/0.46 (~day2(consecutive(thursday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[696, 692])).
% 0.19/0.46 tff(698,plain,
% 0.19/0.46 (~day2(friday)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[697, 680])).
% 0.19/0.46 tff(699,plain,
% 0.19/0.46 ((~![X: $i] : (day2(X) <=> day3(consecutive(X)))) | (day2(friday) <=> day3(consecutive(friday)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(700,plain,
% 0.19/0.46 (day2(friday) <=> day3(consecutive(friday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[699, 9])).
% 0.19/0.46 tff(701,plain,
% 0.19/0.46 ((~(day2(friday) <=> day3(consecutive(friday)))) | day2(friday) | (~day3(consecutive(friday)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(702,plain,
% 0.19/0.46 (day2(friday) | (~day3(consecutive(friday)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[701, 700])).
% 0.19/0.46 tff(703,plain,
% 0.19/0.46 (~day3(consecutive(friday))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[702, 698])).
% 0.19/0.46 tff(704,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[703, 676])).
% 0.19/0.46 tff(705,plain,(~(consecutive(X!2) = saturday)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(706,plain,
% 0.19/0.46 (![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) <=> ![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(707,plain,
% 0.19/0.46 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((X = monday) | (X = tuesday)) | (X = wednesday)) <=> ((X = wednesday) | (X = tuesday) | (X = monday))), (((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) <=> (((X = wednesday) | (X = tuesday) | (X = monday)) | (X = thursday)))), rewrite((((X = wednesday) | (X = tuesday) | (X = monday)) | (X = thursday)) <=> ((X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))), (((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) <=> ((X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)))), ((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) <=> (((X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) | (X = friday)))), rewrite((((X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) | (X = friday)) <=> ((X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))), ((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) <=> ((X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)))), (((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) | (X = saturday)) <=> (((X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) | (X = saturday)))), rewrite((((X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) | (X = saturday)) <=> ((X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))), (((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) | (X = saturday)) <=> ((X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)))), ((((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) | (X = saturday)) | (X = sunday)) <=> (((X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) | (X = sunday)))), rewrite((((X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday)) | (X = sunday)) <=> ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))), ((((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) | (X = saturday)) | (X = sunday)) <=> ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(708,plain,
% 0.19/0.46 (![X: $i] : (((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) | (X = saturday)) | (X = sunday)) <=> ![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[707])).
% 0.19/0.46 tff(709,axiom,(![X: $i] : (((((((X = monday) | (X = tuesday)) | (X = wednesday)) | (X = thursday)) | (X = friday)) | (X = saturday)) | (X = sunday))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','days_of_week')).
% 0.19/0.46 tff(710,plain,
% 0.19/0.46 (![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.19/0.46 tff(711,plain,
% 0.19/0.46 (![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[710, 706])).
% 0.19/0.46 tff(712,plain,(
% 0.19/0.46 ![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))),
% 0.19/0.46 inference(skolemize,[status(sab)],[711])).
% 0.19/0.46 tff(713,plain,
% 0.19/0.46 (((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | ((consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday))) <=> ((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(714,plain,
% 0.19/0.47 (((consecutive(X!2) = sunday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = friday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday)) <=> ((consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(715,plain,
% 0.19/0.47 (((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | ((consecutive(X!2) = sunday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = friday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday))) <=> ((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | ((consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[714])).
% 0.19/0.47 tff(716,plain,
% 0.19/0.47 (((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | ((consecutive(X!2) = sunday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = friday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday))) <=> ((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday))),
% 0.19/0.47 inference(transitivity,[status(thm)],[715, 713])).
% 0.19/0.47 tff(717,plain,
% 0.19/0.47 ((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | ((consecutive(X!2) = sunday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = friday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(718,plain,
% 0.19/0.47 ((~![X: $i] : ((X = sunday) | (X = saturday) | (X = friday) | (X = thursday) | (X = wednesday) | (X = tuesday) | (X = monday))) | (consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.19/0.47 tff(719,plain,
% 0.19/0.47 ((consecutive(X!2) = tuesday) | (consecutive(X!2) = monday) | (consecutive(X!2) = wednesday) | (consecutive(X!2) = thursday) | (consecutive(X!2) = friday) | (consecutive(X!2) = saturday) | (consecutive(X!2) = sunday)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[718, 712])).
% 0.19/0.47 tff(720,plain,
% 0.19/0.47 (consecutive(X!2) = monday),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[719, 705, 670, 634, 624, 606, 566])).
% 0.19/0.47 tff(721,plain,
% 0.19/0.47 (monday = consecutive(X!2)),
% 0.19/0.47 inference(symmetry,[status(thm)],[720])).
% 0.19/0.47 tff(722,plain,
% 0.19/0.47 (truthday(monday) <=> truthday(consecutive(X!2))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[721])).
% 0.19/0.47 tff(723,plain,
% 0.19/0.47 (truthday(consecutive(X!2)) <=> truthday(monday)),
% 0.19/0.47 inference(symmetry,[status(thm)],[722])).
% 0.19/0.47 tff(724,plain,
% 0.19/0.47 (truthday(monday)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[625, 723])).
% 0.19/0.47 tff(725,plain,
% 0.19/0.47 ((truthday(monday) | truthday(tuesday)) | (~truthday(monday))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(726,plain,
% 0.19/0.47 (~truthday(monday)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[725, 477])).
% 0.19/0.47 tff(727,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[726, 724])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------